(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 11.1' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 363695, 10663] NotebookOptionsPosition[ 345219, 10194] NotebookOutlinePosition[ 345591, 10211] CellTagsIndexPosition[ 345548, 10208] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Orthic Triangle", "Title",ExpressionUUID->"c12f3fc0-466a-4170-b0d9-48cb6898bf5f"], Cell[CellGroupData[{ Cell["Author", "Subsection",ExpressionUUID->"6590cf23-08b2-4d4a-a77e-2205a6c3c6f9"], Cell["\<\ Eric W. Weisstein April 2, 2006\ \>", "Text",ExpressionUUID->"b2f404bb-e7b7-43fa-97d3-8fe2f5985ef8"], Cell[TextData[{ "This notebook downloaded from ", ButtonBox["http://mathworld.wolfram.com/notebooks/PlaneGeometry/\ OrthicTriangle.nb", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://mathworld.wolfram.com/notebooks/PlaneGeometry/OrthicTriangle.\ nb"], None}], "." }], "Text",ExpressionUUID->"dcee03b9-a778-4cd5-8015-183f9360eab2"], Cell[TextData[{ "For more information, see Eric's ", StyleBox["MathWorld", FontSlant->"Italic"], " entry ", ButtonBox["http://mathworld.wolfram.com/OrthicTriangle.html", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://mathworld.wolfram.com/OrthicTriangle.html"], None}], "." }], "Text",ExpressionUUID->"8aa6672a-75c7-4db7-97a7-1ec663559008"], Cell["\<\ \[Copyright]2006 Wolfram Research, Inc. except for portions noted otherwise\ \>", "Text",ExpressionUUID->"1beec0f9-8b9a-48c4-9ff8-f7edc8daecea"] }, Open ]], Cell[CellGroupData[{ Cell["Figure", "Section",ExpressionUUID->"dadb3a0a-3ea8-4a63-94e8-8f04c22d038a"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.", ",", "0."}], "}"}], ",", RowBox[{"{", RowBox[{"3.", ",", "0."}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "2.2"}], "}"}]}], "}"}], "]"}]}], ";"}], "\n", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"t", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"ht", "=", RowBox[{"OrthicTriangle", "[", "t", "]"}]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", "\[IndentingNewLine]", RowBox[{"Altitudes", "[", "t", "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"PerpSquare", "[", RowBox[{"#", ",", ".1", ",", "3"}], "]"}], "&"}], "/@", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Altitudes", "[", "t", "]"}], ",", RowBox[{"Sides", "[", "t", "]"}]}], "}"}], "]"}]}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{ RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Point", "/@", RowBox[{"Vertices", "[", "t", "]"}]}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Append", "[", RowBox[{"#", ",", "Red"}], "]"}], "&"}], "/@", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Point", "/@", RowBox[{"Vertices", "[", "ht", "]"}]}], ",", RowBox[{"{", RowBox[{ "\"\<\!\(\*SubscriptBox[\(H\), \(A\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(H\), \(B\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(H\), \(C\)]\)\>\""}], "}"}]}], "}"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"Orthocenter", "[", "t", "]"}], ",", "\"\\"", ",", "Red"}], "}"}], "}"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"PointSize", "[", ".025", "]"}], ",", RowBox[{"LabelOffset", "\[Rule]", ".08"}]}], "}"}]}], "\[IndentingNewLine]", "]"}]}], "\n", "}"}], "]"}], ",", RowBox[{"AspectRatio", "->", "Automatic"}]}], "]"}]}], "Input",ExpressionUU\ ID->"a7db8556-d7f6-4745-9e55-207bdb5c9e32"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .74026 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.309215 0.0176252 0.309215 [ [ 0 0 0 0 ] [ 1 .74026 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .74026 L 0 .74026 L closepath clip newpath 0 g .5 Mabswid [ ] 0 setdash .02381 .01763 m .95145 .01763 L .42579 .6979 L .02381 .01763 L s 1 0 0 r .60464 .46645 m .26389 .42391 L .42579 .01763 L .60464 .46645 L s 0 0 1 r .60464 .46645 m .02381 .01763 L s .26389 .42391 m .95145 .01763 L s .42579 .01763 m .42579 .6979 L s .58017 .44754 m .56126 .47201 L .58573 .49091 L s .29051 .40818 m .27478 .38156 L .24816 .39729 L s .42579 .04855 m .45671 .04855 L .45671 .01763 L s 1 g .04855 .04236 -5.8125 -7 Mabsadd m .04855 .04236 5.8125 -7 Mabsadd L .04855 .04236 5.8125 7 Mabsadd L .04855 .04236 -5.8125 7 Mabsadd L fill 0 g gsave .04855 .04236 -66.8125 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.312 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (A) show 70.625 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .025 w .02381 .01763 Mdot 1 g .97619 .04236 -5.71875 -7 Mabsadd m .97619 .04236 5.71875 -7 Mabsadd L .97619 .04236 5.71875 7 Mabsadd L .97619 .04236 -5.71875 7 Mabsadd L fill 0 g gsave .97619 .04236 -66.7188 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (B) show 70.438 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .95145 .01763 Mdot 1 g .45053 .72263 -6.0625 -7 Mabsadd m .45053 .72263 6.0625 -7 Mabsadd L .45053 .72263 6.0625 7 Mabsadd L .45053 .72263 -6.0625 7 Mabsadd L fill 0 g gsave .45053 .72263 -67.0625 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (C) show 71.125 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .42579 .6979 Mdot 1 g .62937 .49118 -9.75 -7 Mabsadd m .62937 .49118 9.75 -7 Mabsadd L .62937 .49118 9.75 7 Mabsadd L .62937 .49118 -9.75 7 Mabsadd L fill 1 0 0 r gsave .62937 .49118 -70.75 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 72.000 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (A) show 78.500 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .60464 .46645 Mdot 1 g .28863 .44865 -9.6875 -7 Mabsadd m .28863 .44865 9.6875 -7 Mabsadd L .28863 .44865 9.6875 7 Mabsadd L .28863 .44865 -9.6875 7 Mabsadd L fill 1 0 0 r gsave .28863 .44865 -70.6875 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 71.875 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (B) show 78.375 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .26389 .42391 Mdot 1 g .45053 .04236 -9.96875 -7 Mabsadd m .45053 .04236 9.96875 -7 Mabsadd L .45053 .04236 9.96875 7 Mabsadd L .45053 .04236 -9.96875 7 Mabsadd L fill 1 0 0 r gsave .45053 .04236 -70.9688 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 71.750 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (C) show 78.938 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .42579 .01763 Mdot 1 g .45053 .35298 -6.84375 -7 Mabsadd m .45053 .35298 6.84375 -7 Mabsadd L .45053 .35298 6.84375 7 Mabsadd L .45053 .35298 -6.84375 7 Mabsadd L fill 1 0 0 r gsave .45053 .35298 -67.8438 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 72.688 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .42579 .32825 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 213.188}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},ImageCache->GraphicsData["CompressedBitmap", "\<\ eJytnOl6FccRhgedowUkQGDMLiSxb8YGbMALBgwG4wBxHIQxYIxYhMAmrDFJ 7GAc4pDVieMsJHHibH+4Ba6Bv/nJLXALJ9NdPVVzRu/MnOGI5xEadVXX93VN r9Xdc3D0xvi5S6M3LpwZHdp3bfTK+IUz14f2Xr4WJ9WmRNGUoSiK/jcUuedG /Bj+8/+G3X/hj/Dc6X7VnM5VeYofv9K0GaJUd786XcJleYofv9S06aJUc7+6 XcIleYoff6tpfSmlGy6hW9AduZrnlFD9IqteZpPYeaVgWLScnpGlYne7pw73 9Lk8xZk73FM95Yo7/ldd3Risf6Y5aoqsClG/KE1LlKKOoLRp0yYt93hIixMb iUM6lJwTPHighbmTKV/IOgHZ+ybqSgP5H/f348ePu1LE4pz37t3zEvdXmuID QTaKIyONWLlJD9NSTG6phzqBpxDpbOzZs6dx8+ZNnzgSW4zRgyzqTak8SFwR Xu3FBNARcETSJCakTXh7Hyu3LuDWHYCdd0bEkAJnuD169KjJzcPDw8YtljX6 +5u5pdLq+q5/CC+XnNaTQu0XK94z8XNCrC+Ydj69e/duUoYaIJxLODlLof5p 1XM8g94n6qxu4DQtADo+iRdi0AyduOp5jbGxMUetriZPJSRSJgtrWCrN3uLU XGKd/g06LzgKziPx38G5oW+QZuCyxr6MrEKYp94rIllSA38E9nqAblKjAkWf +PDhQ1/pAt0ZIVtcyXxpGtqOms0fz6Vblz5FXrb76RAXhpcuPYHX/Eh9O00R smRrvvIl3VlH6NrvydtJODjb84HkMSBpnWqv5jDpPDG2QJXIxG2AKjDWD6Ie MHEEoKhN1UDvuhKerjlMOj+fiNVqAxhpg8hVJTJDc5h0gRCZlUfEZzwMZusA Xwe9y6BHHlmYT6QXTHynDUqXtGDk/0BkdotE3mqDyAdKhIq9SIg81SKRQwDQ CXqdoDeuRKjYi/OJ9GnGduDPgx55ZECIzAHRdDDxJkBRz9kFeme1YFTsJflE rJEZwP42iJxWIk/nEyHRDM3YDvwo6FGxB/OJ9IOJ1wGqG/S6Qe+kFmwuoA0J ERIRkT1tEDmhROYBWlh5kYiIvAYANCYRkeOgV5HSLC1Lq0R6QO+oWlkAGEsF fj6IrNsxgB1tEDmiRBYC2rJ8ItbaDWA7ANAoPRX0DoMe+Wa5UCLRU1qWdoi8 rVYW58OTs6y1G8CLADAN9IjIW0pkANBW5BOxvsUAtrVIZBroHQI98s1KobSo RUpb26B0QH2zBNBW5ROZqxm3gFmaLvSC3n61MggYqwWeXGQ9igFsboPIG6BX QIkqElHaCFB9LVLaq74ZBrQ1+UTma8ZW4ftAb7daWQoYawWeKo31KAawoQ0i u5TIMkBbl0/EmrQBrAcAmslNB70doFdAabBFSuvaoLRdfbMC0NbnE1mkGdeC WZpSEvzLamUlYDwj8EMgsiZtAKtaJDID9F4EPfKI1MOIGhRRSkr1JJS2qm9W VyMyoBlXgNmZAD8T9J5XK2sA41mBp5ZtLckAEr0nIbIZ9Mgjz+VTGgQTSa1K Q9EslyhtVN+s1RwZaYQtm4gkaWVE+kFvgxJZpzlMKvHyMFMCIk3j5pPAPwN6 FYkMg4lkupCGmgV6s0BvrRbMyGXrErZsIpL0tk9CZLUS2aA5Mq2LiSzVjAvA LC07CH4V6JFHXhAi1P0uAxPJIrWM0mzQW64Fey6fyCoQEZFkHvskRMzDGzWH SbfkE7EKbADJ8isNQEsy0hsCPfKNTNCx1zOntkNkiVrZBBjb8uGt3hgA9Zi0 JCMii5XI8/lEaEAiIjSqEpE5oGfR+xcATaYLEfX+KzUjTXho+UXwtBNBHnkp n8hqMEErOKJEretpLdgWzZGZyUXY+xMRWma3SsSiC1s1h0lfySdi9cYAKDg1 F/Ra7W8KKK0H0RotS6tEqAeeqVZsHmvS7fnw5iUDoB0ZWpoSkelK5CVAe1WI 0DBERGiznojMAz1atpNvdgglGqLXaVnaIWJbUq9Ug2+aW0k6rowJtFtBt4Pl nQL6bBloSKOuKElLg9LWCZV5Vz58dnEd/8IyE3xNy/wqWJYQMQ6utHzOhMiz yJlzGgF3Zz4uzTNo3dyhegZJI1Z2ZugctQswdufDr8mYCOWaAEVTCBscCVQ2 KCKaSSRDwYR6k9m3Mqh5KpU3rG1hB5h/PR+ZggMUmqelz9zAs/mdeyiksVdk m0FEAQGKh9PieI66gnZmqaUHIjRxoNAAxXwpWjFbidCg9TKg7csnshxM2B4t wdMKjIjQECRh2ojmdMvABMHT0GIDMAVit2kOS9ufT4SCJVQt6XXZAEyzzwIi NKcbBhO260bwvSqlRQDNjd6sBk9dBG1+EjmKYJD/vyWUiO0gmKBpK+1V96hv aOFDTeOAEKG3tgRM0GyRBuUuJUJTOOq1CogMgAnbPyg6TjGxh222Qr34QSFC M7nFYIKi5TTE2tyBQi40eh6qRsQ2wJpA9VxbZHuc6Ww0R/q2IFPnRuEq299p SHpkhyfTbAiepqVyeAg7efKdh/enowdBSiuBAgCa9i0pBKA1j5zDwqkpzaWL AWiZ+XY1AAvX+wPi1OtRwOO7gkLDPq1VLbDiK7sX0kBTAEXzaopdUGWn2SZF 2A7nQ1GvuVBLpQGF0kPqORWJIqByiBHneBRXtH5PtyFLTgZTi6WY8JFqRGjl opRKzgFT8J0C94HSThDRQGvb/TozKDl2TkRoT+UdIUIrkdxIZNPBwbJz5fSS aN/taD4RikRaGEsbUUltIY8MAdq7QuQ1ENGskMJYSqmlewvlg/kgcDlWjWa/ +ksAis6I19NnxDVfbvfOxHaDiKb3NvmnIDT1kHTo4ng1UFqZ0J5PcQdtaScE fg+IKFZr6wwKD9FqJbf7zqDJHQY9bpkWWaQgao4F2HqRZny2ZJkEDjZVlGiJ mYrwQAoRokUM7eHRab+TArU3OCQlSthgFMfCkAMgpRATdeJ0DPP9NKG6ikKz TJ+dTiQWnRwEXNtmIJfQad1TgrcPjNWT/9OJ6ctUlkpcaBylrryA1RsgqjEr u2xkZxhMTu2Mukk66jxaxqWriUvgo3Ro25PCssWDi6WdFgCJPEyswy6BFolE wyaABE4n8s+Ug1sbpx6VzvnQvhrd1DgrCD7okVn/0eYUtVWCsmjhBChfzs5Q rLQdwrNtYEKhyzhyN09qll8k0UbOEKTREWjrPy1tLAXQ457WgjE6u0ERQbpg db6VElCDpLsHBQD2IrwffeunwcFPcXODq3SBUC6/pipVtwJ4L091TxQ0XQFp FFqma4AXBPRIkindjCKpkP51UXCbpkmES3de5dJqiNHlLvfq6eWetjPqtXus xesAZUd3KrI6kKiXTORtCT6YAvD2pO9LTgbxngNdb/0gw6Bk3k5DUCPCQbCu brJIRQ38UtO8lvZhhlXJks+bqOcR6VMi2ZCrcx69YVudWNolyXAwUS9Z/NGg 44dY36p6g4cyb0nmh51KLvmJrUdXMvglVYXa6IA6gpZf4asDjYlQJXWCoNLb REn97HP/yyXJ8GZbv667DDByu4PuFBBdTybCna1ktENTPVlnjai6VRnq/Ym0 7xm8r7qs/PUgVN+cqwa0Srn2JwWEKUswekQNmFEaHGXwb663UaqXbCWI5tPG quFmB+8o6Xtb7TTTDdyK/Q7A06Sj8JRJSeugoSDMsY4C/GBh6Sf2mmVdI11C PVMNnkK7arakGwzD/btggs5701FBnS+VvOeLkwhV8k4D1DEwQVNvClgLVOsd 4Hg1SIpKS4+WukJpIlqbUDz5YzFxAkQUvZ8EExRC/kRMvAei3JlxRu/H1UzQ 5YBbYuIkiGiRW2DifRDRsp2Cx59WMzEEerfFxCkQUSBjEPQ+q2aCgqc/EROj IKIN6gITp0FEm+0UTb1TzQTdEPypmDgDIoqXUVD180kzcRZEFEakaObPqpmg C713xcQ5ENHuAQUufy4mxkBEa9NJMEHRyl+IifMgyj/51az3y2omKDb4KzEx DqLcg18ZvV+LiQsgoq2BSTBBX5X4jZi4CCK6gUjBwC+qmaCQnnxTLSyBm0UU ki8w8SGI6LwXxfZ+V80Exey+FBOXQFR8Ns/0fj9pJr4HIorm0KdxvhITl0FE hy4p8PeHaiYo8vZHMXEFRMVnxkzvT5Nm4iqIaB+CInx/rmaC4nUyt46ugYhi 7RRi+ouYuA4i2nKaBBMUavurmLgBohqYoM/T/a2aiTrofS0mvg+i3JgMm/go 0EyJRB4x+b+XZyO0f4jwZqCTzhbxtyG/KcxBobV/iuwH7pfPECVxVa8T/Ssl 98z/k4LwH878d6sJE2z4TxN6Ov8NDN2/8PkYmZ93+Y/RuW/WOULuxz3HaV+n tbqTb/8ln65r3L9/33/bMf47qTq3oPSJR5JsDauspP5Ns8h9K88Bgch9qM6J U6JPA9XwJUr/AT73z31w0anGvxPs26HsrkTJtw+TD0bGgEErmvJ/hlsfhQ== \ \>"],ImageRangeCache->{{{0., 287.}, {212.188, 0.}} -> {-0.0790516, \ -0.0570118, 0.0112826, \ 0.0112826}},ExpressionUUID->"e746970f-1fa0-4382-b175-90b51459bb21"], Cell[BoxData[ TagBox[ RowBox[{"\[SkeletonIndicator]", "Graphics", "\[SkeletonIndicator]"}], False, Editable->False]], "Output",ExpressionUUID->"212edaee-d5cb-48a9-9e81-\ 1908c6e9ae03"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Vertices", "Section",ExpressionUUID->"8e6ce092-5333-4037-961b-e8800b057a38"], Cell[BoxData[ RowBox[{"<<", "Utilities`Typesetting`"}]], "Input",ExpressionUUID->"c8a946cb-e041-4e2f-adcd-2e30421a1aa7"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"CevianTriangle", "[", "Orthocenter", "]"}], "//", "MatrixForm"}], "//", "TraditionalForm"}]], "Input",ExpressionUUID->"bdd4f038-0851-4676-\ 8222-bee189063644"], Cell[BoxData[ FormBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", RowBox[{"sec", "B"}], RowBox[{"sec", "C"}]}, { RowBox[{"sec", "A"}], "0", RowBox[{"sec", "C"}]}, { RowBox[{"sec", "A"}], RowBox[{"sec", "B"}], "0"} }], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",ExpressionUUID->\ "1029c11c-b437-4cfb-9ebc-cb34e1d70a02"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Side Lengths", "Section",ExpressionUUID->"62909f42-a1dd-4e89-996d-f076f78f0c8a"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"DistanceTrilinears", "[", RowBox[{"SideLengths", "[", RowBox[{"CevianTriangle", "[", "Orthocenter", "]"}], "]"}], "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]], "Input",ExpressionUUID->\ "6af1546f-8463-429c-b221-ce20b7a223ad"], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox[ RowBox[{"a", " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Sign", "[", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}], RowBox[{"2", " ", "b", " ", "c", " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["a", "4"], "-", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}], "2"]}], "]"}]}]], ",", FractionBox[ RowBox[{"b", " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Sign", "[", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}], RowBox[{"2", " ", "a", " ", "c", " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["b", "4"], "-", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"a", "-", "c"}], ")"}], "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"a", "+", "c"}], ")"}], "2"]}]}], "]"}]}]], ",", RowBox[{"-", FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}], " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Sign", "[", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}], RowBox[{"2", " ", "a", " ", "b", " ", RowBox[{"Sign", "[", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], ")"}], "2"], "-", SuperscriptBox["c", "4"]}], "]"}]}]]}]}], "}"}]], "Output",ExpressionU\ UID->"888a7cd5-a746-4d8f-bc87-8d6622ed0bdb"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"Abs", "[", "%", "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]], "Input",ExpressionUUID->\ "bbc04a1f-6e8f-40cc-b2ab-d51e5a11322c"], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox[ RowBox[{"a", " ", RowBox[{"Abs", "[", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}], RowBox[{"2", " ", "b", " ", "c"}]], ",", FractionBox[ RowBox[{"b", " ", RowBox[{"Abs", "[", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}], RowBox[{"2", " ", "a", " ", "c"}]], ",", FractionBox[ RowBox[{"c", " ", RowBox[{"Abs", "[", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], "]"}]}], RowBox[{"2", " ", "a", " ", "b"}]]}], "}"}]], "Output",ExpressionUUID->\ "9b0249c9-8222-497c-a735-bffcf7933205"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"abc", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"LawOfCosines", "[", "%", "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]}]], "Input",ExpressionUUID->\ "416509cd-3fee-497f-af2f-6a6692a0e801"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"a", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "A", "]"}], "]"}]}], ",", RowBox[{"b", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "B", "]"}], "]"}]}], ",", RowBox[{"c", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "C", "]"}], "]"}]}]}], "}"}]], "Output",ExpressionUUI\ D->"3866edde-c60a-416b-a490-e1b7e617549f"] }, Open ]], Cell[CellGroupData[{ Cell["Acute", "Subsection",ExpressionUUID->"5decba0b-dbf9-497a-a983-9e25650118e5"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{"abc", ",", RowBox[{"AcuteQ", "[", "]"}]}], "]"}]], "Input",ExpressionUUID->"55800865-\ 3f7b-4114-adf8-9cfda5d9fdf5"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"a", " ", RowBox[{"Cos", "[", "A", "]"}]}], ",", RowBox[{"b", " ", RowBox[{"Cos", "[", "B", "]"}]}], ",", RowBox[{"c", " ", RowBox[{"Cos", "[", "C", "]"}]}]}], "}"}]], "Output",ExpressionUUID->\ "0bd40363-6858-40ca-8664-34a1e04b3765"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Semiperimeter", "Section",ExpressionUUID->"db0e2772-8d34-4931-b14c-cd87f2f356c3"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"Plus", "@@", RowBox[{"DistanceTrilinears", "[", "abc", "]"}]}], "/", "2"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], "]"}]], "Input",ExpressionUUID->\ "4229ea00-49ca-41f1-bd49-8f229da8489a"], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"Abs", "[", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], "]"}]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", RowBox[{"Abs", "[", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", RowBox[{"Abs", "[", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}]}], RowBox[{"4", " ", "a", " ", "b", " ", "c"}]]], "Output",ExpressionUUID->\ "cce216c4-2104-4db7-b9a0-6aa72eb1c231"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"sh", "=", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"LawOfCosines", "[", "%", "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]}]], "Input",ExpressionUUID->\ "3719391d-8161-4e07-9a92-2fa0286fae7f"], Cell[BoxData[ RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "A", "]"}], "]"}]}], "+", RowBox[{"b", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "B", "]"}], "]"}]}], "+", RowBox[{"c", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "C", "]"}], "]"}]}]}], ")"}]}]], "Output",Expression\ UUID->"5906de36-3de5-4f4d-9478-a0753e90953a"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LawOfCosines", "[", RowBox[{"Factor", "[", RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{"Refine", "[", RowBox[{"sh", ",", RowBox[{ RowBox[{ RowBox[{"Pi", "/", "2"}], "<=", "A", "<", "Pi"}], "&&", RowBox[{"0", "<", "B", "<", RowBox[{"Pi", "/", "2"}]}], "&&", RowBox[{"0", "<", "C", "<", RowBox[{"Pi", "/", "2"}]}]}]}], "]"}], "]"}]}], "]"}], "]"}]], "Input",ExpressionUUID->"8066e823-0ab2-42e4-98a8-e28dc2a281d6"], Cell[BoxData[ RowBox[{"a", " ", RowBox[{"Cos", "[", "B", "]"}], " ", RowBox[{"Cos", "[", "C", "]"}]}]], "Output",ExpressionUUID->"09bb5cbb-ec63-\ 44f9-a8e6-0aab27eb2d87"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LawOfCosines", "[", RowBox[{"Factor", "[", RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{"Refine", "[", RowBox[{"sh", ",", RowBox[{ RowBox[{ RowBox[{"Pi", "/", "2"}], "<=", "B", "<", "Pi"}], "&&", RowBox[{"0", "<", "A", "<", RowBox[{"Pi", "/", "2"}]}], "&&", RowBox[{"0", "<", "C", "<", RowBox[{"Pi", "/", "2"}]}]}]}], "]"}], "]"}]}], "]"}], "]"}]], "Input",ExpressionUUID->"2a671ee2-e594-4155-ab11-e8ccf6f2d306"], Cell[BoxData[ RowBox[{"b", " ", RowBox[{"Cos", "[", "A", "]"}], " ", RowBox[{"Cos", "[", "C", "]"}]}]], "Output",ExpressionUUID->"ceb5861e-7028-\ 4483-9316-13b2040a0303"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LawOfCosines", "[", RowBox[{"Factor", "[", RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{"Refine", "[", RowBox[{"sh", ",", RowBox[{ RowBox[{ RowBox[{"Pi", "/", "2"}], "<=", "C", "<", "Pi"}], "&&", RowBox[{"0", "<", "A", "<", RowBox[{"Pi", "/", "2"}]}], "&&", RowBox[{"0", "<", "B", "<", RowBox[{"Pi", "/", "2"}]}]}]}], "]"}], "]"}]}], "]"}], "]"}]], "Input",ExpressionUUID->"944f1535-3d58-4e86-b3a6-611fce50030f"], Cell[BoxData[ RowBox[{"c", " ", RowBox[{"Cos", "[", "A", "]"}], " ", RowBox[{"Cos", "[", "B", "]"}]}]], "Output",ExpressionUUID->"64b6f29c-e185-\ 45d0-9919-81925d7e7459"] }, Open ]], Cell[CellGroupData[{ Cell["Acute", "Subsection",ExpressionUUID->"916e9202-56a1-4252-913b-bcecd094d0e3"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"DistanceTrilinears", "[", "%", "]"}], RowBox[{"\[CapitalDelta]", "/", RowBox[{"Area", "[", "]"}]}], " ", RowBox[{ RowBox[{"Circumradius", "[", "]"}], "/", "R"}]}], ",", RowBox[{"AcuteQ", "[", "]"}]}], "]"}]], "Input",ExpressionUUID->"659aed88-\ fe96-408a-b35b-5eb8f93c9dbf"], Cell[BoxData[ FractionBox["\[CapitalDelta]", "R"]], "Output",ExpressionUUID->"65abedcc-71cc-42cd-84d6-9472ef9a7ee5"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Circumradius", "Section",ExpressionUUID->"43d00bc1-fe07-44ef-8408-5660b09cf3a6"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"LawOfCosines", "[", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"Circumradius", "[", "abc", "]"}], RowBox[{"R", "/", RowBox[{"Circumradius", "[", "]"}]}]}], ",", RowBox[{ RowBox[{"TriangleQ", "[", "]"}], "&&", RowBox[{ RowBox[{"Pi", "/", "2"}], "<", "A", "<", "Pi"}], "&&", RowBox[{"B", "<", RowBox[{"Pi", "/", "2"}]}], "&&", RowBox[{"C", "<", RowBox[{"Pi", "/", "2"}]}]}]}], "]"}], "]"}]}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], "]"}], ",", RowBox[{ RowBox[{"TriangleQ", "[", "]"}], "&&", RowBox[{ RowBox[{"Pi", "/", "2"}], "<", "A", "<", "Pi"}], "&&", RowBox[{"B", "<", RowBox[{"Pi", "/", "2"}]}], "&&", RowBox[{"C", "<", RowBox[{"Pi", "/", "2"}]}]}]}], "]"}]], "Input",ExpressionUUID->\ "d6d2d2bd-d9c3-442b-a811-5e99ee3909bf"], Cell[BoxData[ FractionBox["R", "2"]], "Output",ExpressionUUID->"be9f99ea-d490-4db4-a25d-c22d22ac0a8a"] }, Open ]], Cell[CellGroupData[{ Cell["Acute", "Subsection",ExpressionUUID->"1032a1e1-d300-4a02-a6a4-ddc21949f69b"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"LawOfCosines", "[", RowBox[{ RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Circumradius", "[", "abc", "]"}], ",", RowBox[{"AcuteQ", "[", "]"}]}], "]"}], "]"}]}], RowBox[{"R", "/", RowBox[{"Circumradius", "[", "]"}]}]}], "]"}], ",", RowBox[{ RowBox[{"TriangleQ", "[", "]"}], "&&", RowBox[{"AcuteQ", "[", "]"}]}]}], "]"}]], "Input",ExpressionUUID->\ "1e92700f-3515-493f-9866-4978a5ad9c3f"], Cell[BoxData[ FractionBox["R", "2"]], "Output",ExpressionUUID->"2cc55769-6716-4caa-ad71-ec4091966955"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Inradius", "Section",ExpressionUUID->"3a266e72-ea14-4b61-965e-8e5932f7314f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"rh", "=", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"LawOfCosines", "[", RowBox[{ RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Inradius", "[", "abc", "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], "]"}]}], RowBox[{"R", "/", RowBox[{"Circumradius", "[", "]"}]}]}], "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]}]], "Input",ExpressionUUID->\ "f518e683-ad90-4ad4-80a0-497fec804edc"], Cell[BoxData[ RowBox[{"2", " ", "R", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "A", "]"}], "]"}], " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "B", "]"}], "]"}], " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "C", "]"}], "]"}]}]], "Output",ExpressionUUID->\ "e14f9aee-c996-42c2-acee-12de2b09037b"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Area", "Section",ExpressionUUID->"546c42ef-2324-469d-ae4a-5f98606b7413"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{"area", "=", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"DistanceTrilinears", "[", RowBox[{"CevianTriangleArea", "[", "Orthocenter", "]"}], "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]}], "]"}]], "Input",ExpressionUUI\ D->"53aae19c-3c6d-414a-b218-aef5ebf6b68e"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"8.308594`", " ", "Second"}], ",", RowBox[{ FractionBox["1", RowBox[{"16", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"]}]], RowBox[{"(", RowBox[{ SqrtBox[ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"a", "-", "b", "-", "c"}], ")"}]}], " ", RowBox[{"(", RowBox[{"a", "+", "b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "-", "b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b", "+", "c"}], ")"}]}]], " ", RowBox[{"Abs", "[", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Abs", "[", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}], " ", RowBox[{"Abs", "[", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], "]"}]}], ")"}]}]}], "}"}]], "Output",Expre\ ssionUUID->"3c7603d7-ab31-4ffb-aed1-d99157ab2134"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"LawOfCosines", "[", "area", "]"}], " ", RowBox[{ RowBox[{"Circumradius", "[", "]"}], "/", "R"}]}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]], "Input",ExpressionUUID->\ "74fb2ae5-f94c-4d81-8510-d4b2b6c66442"], Cell[BoxData[ FractionBox[ RowBox[{"a", " ", "b", " ", "c", " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "A", "]"}], "]"}], " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "B", "]"}], "]"}], " ", RowBox[{"Abs", "[", RowBox[{"Cos", "[", "C", "]"}], "]"}]}], RowBox[{"2", " ", "R"}]]], "Output",ExpressionUUID->"9a2fb4ec-4e05-4064-\ a10d-60e58fa24da3"] }, Open ]], Cell[CellGroupData[{ Cell["Acute", "Subsection",ExpressionUUID->"cfd11433-f4eb-4864-81d1-054e69b2676e"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{"%", ",", RowBox[{"AcuteQ", "[", "]"}]}], "]"}]], "Input",ExpressionUUID->"b5b5f2aa-\ faca-4304-b1ee-e5f802ff063c"], Cell[BoxData[ FractionBox[ RowBox[{"a", " ", "b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}], " ", RowBox[{"Cos", "[", "B", "]"}], " ", RowBox[{"Cos", "[", "C", "]"}]}], RowBox[{"2", " ", "R"}]]], "Output",ExpressionUUID->"7b7ebb9a-33d6-42ff-\ 9c1e-696c02f3e893"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Points", "Section",ExpressionUUID->"09e989de-a244-419c-8e42-990ba6e6ed5c"], Cell[BoxData["\<\"Rehashing triangle centers...\"\>"], "Print",ExpressionUUID->"e4d91556-6716-4a1b-acb6-c2b3c1a18d9a"], Cell[CellGroupData[{ Cell["Centroid", "Subsection",ExpressionUUID->"31681a80-ba49-4aac-837c-f56002bed697"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Centroid", "[", "OrthicTriangle", "]"}]], "Input",ExpressionUUID->"a033d69c-0452-46bd-8b39-6fd52afe60ae"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "a", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}]}], "+", RowBox[{"b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}]}], ")"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}]}], "-", RowBox[{"2", " ", "b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"]}], "-", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "a", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}]}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}]}], "-", RowBox[{"2", " ", "b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"]}], "-", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}]}], ")"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "b"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"c", " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", "a", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}]}], "+", RowBox[{"b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"2", " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"c", " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}]}]}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"a", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "b"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"c", " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "a", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", RowBox[{"Sec", "[", "A", "]"}], " ", RowBox[{"Sec", "[", "B", "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"2", " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"c", " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}]}]}]}], "}"}]], "Output",ExpressionUUID->"2570b415-1c91-43a4-86a4-76498e2da926"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"g", "=", RowBox[{"Symmetrize", "[", RowBox[{"-", RowBox[{"ToAngles", "[", RowBox[{"Symmetrize", "[", RowBox[{"Factor", "[", RowBox[{"ToSidelengths", "[", RowBox[{"Centroid", "[", "OrthicTriangle", "]"}], "]"}], "]"}], "]"}], "]"}]}], "]"}]}]], "Input",ExpressionUUID->"33144581-c433-4577-bb23-\ 67329c2e5d18"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox["a", "2"], " ", RowBox[{"Cos", "[", RowBox[{"B", "-", "C"}], "]"}]}], ",", RowBox[{ SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"A", "-", "C"}], "]"}]}], ",", RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"Cos", "[", RowBox[{"A", "-", "B"}], "]"}]}]}], "}"}]], "Output",ExpressionUUID->\ "b782cf12-9ef7-42e4-a535-ab39e0bc9615"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"IncidentCenters", "[", RowBox[{"KimberlingCenters", ",", "g"}], "]"}], "//", "Timing"}]], "Input",\ ExpressionUUID->"dedc52f6-2ce8-4d8c-b450-92dc646951fe"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"35.640000000000015`", " ", "Second"}], ",", RowBox[{"{", RowBox[{"X", "[", "51", "]"}], "}"}]}], "}"}]], "Output",ExpressionUUID->\ "16ac69b5-efc6-4fa1-a2a8-a46b222cc8e0"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Circumcenter", "Subsection",ExpressionUUID->"4b651366-10b3-4f6d-aed4-fbf7cdfaec33"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Circumcenter", "[", "OrthicTriangle", "]"}]], "Input",ExpressionUUID->"3fba3f26-5748-4577-a49b-ea3f4a8521c7"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"a", " ", RowBox[{"(", RowBox[{ RowBox[{"1024", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "-", RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], "2"]}]}], ")"}]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "-", RowBox[{"512", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"b", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "512"}], " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "+", RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}]}], ")"}]}]}], ",", RowBox[{ RowBox[{"a", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "512"}], " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "+", RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "512"}], " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "+", RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"b", " ", RowBox[{"(", RowBox[{ RowBox[{"1024", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "-", RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], "2"]}]}], ")"}]}]}], ",", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"1024", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "-", RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], "2"]}]}], ")"}]}], "+", RowBox[{"a", " ", RowBox[{"(", RowBox[{ RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "-", RowBox[{"512", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}]}], ")"}]}], "+", RowBox[{"b", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "512"}], " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}], "+", RowBox[{"256", " ", SuperscriptBox["Area", "10"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", RowBox[{"Sec", "[", "C", "]"}]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "3"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"2", " ", "a", " ", SuperscriptBox["b", "2"], " ", "c", " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", "c", " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "+", RowBox[{"b", " ", SuperscriptBox["c", "3"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "2"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "A", "]"}], "2"], " ", RowBox[{"Sec", "[", "B", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"Sec", "[", "A", "]"}], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}], "-", RowBox[{"a", " ", "b", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "B", "]"}], "3"], " ", SuperscriptBox[ RowBox[{"Sec", "[", "C", "]"}], "3"]}]}], ")"}]}]}], ")"}]}]}]}], "}"}]], "Output",ExpressionUUID->"a64a6893-2f84-4ec0-be4f-18d317f6c3f3"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"o", "=", RowBox[{"Symmetrize", "[", RowBox[{"-", RowBox[{"ToAngles", "[", RowBox[{"Symmetrize", "[", RowBox[{"ToSidelengths", "[", RowBox[{"Circumcenter", "[", "OrthicTriangle", "]"}], "]"}], "]"}], "]"}]}], "]"}]}]], "Input",ExpressionUUID->"790953ab-7e59-4f09-9cf1-\ 25780cb3536d"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{"B", "-", "C"}], "]"}], ",", RowBox[{"Cos", "[", RowBox[{"A", "-", "C"}], "]"}], ",", RowBox[{"Cos", "[", RowBox[{"A", "-", "B"}], "]"}]}], "}"}]], "Output",ExpressionUUID->\ "db5935dd-926f-4635-8520-8b550c051ac3"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"IncidentCenters", "[", RowBox[{"KimberlingCenters", ",", "o"}], "]"}], "//", "Timing"}]], "Input",\ ExpressionUUID->"a501b8aa-b505-4f92-98ee-2aa7145cbfbe"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"35.43000000000001`", " ", "Second"}], ",", RowBox[{"{", RowBox[{"X", "[", "5", "]"}], "}"}]}], "}"}]], "Output",ExpressionUUID->\ "b1d7f841-c160-4c41-80f3-1efb159483a1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Name", "[", RowBox[{"X", "[", "5", "]"}], "]"}]], "Input",ExpressionUUID->"55cbdf54-\ 6483-4143-bb9f-7fdf3aeff994"], Cell[BoxData["\<\"nine-point center\"\>"], "Output",ExpressionUUID->"8068163a-e98f-4b7b-a539-0cd2b1dcc6c9"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Incenter", "Subsection",ExpressionUUID->"75b79556-59fd-4fcb-a2d8-1faad31d819c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Incenter", "[", "OrthicTriangle", "]"}]], "Input",ExpressionUUID->"f2719b48-017b-4f56-825f-b876e8037d28"], Cell[BoxData[ RowBox[{"Incenter", "[", "OrthicTriangle", "]"}]], "Output",ExpressionUUID->"c50057e2-19f1-40ed-8d82-f5aef678cdf2"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{".3", ",", ".5"}], "}"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Incenter", "[", RowBox[{"OrthicTriangle", "[", "t", "]"}], "]"}]}], "Input",ExpressionUUID->\ "506cdab6-cac5-42e1-ad7a-c8777bb329fb"], Cell[BoxData[ RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0.30000000000000004`", ",", "0.41999999999999993`"}], "}"}], "]"}]], "Output",ExpressionUUID->"3d9f4e63-eb6b-4284-b933-ed6e70dd9f58"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Orthocenter", "[", "t", "]"}]], "Input",ExpressionUUID->"b083376f-172a-49d7-b7df-f131078bb9c1"], Cell[BoxData[ RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0.29999999999999993`", ",", "0.42`"}], "}"}], "]"}]], "Output",Exp\ ressionUUID->"4593346d-24a9-4ce7-b727-56c376e5dde8"] }, Open ]], Cell["orthocenter", "Text",ExpressionUUID->"cb5532bf-e19a-4058-9d18-1c285cf39e2c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CenterFunction", "[", "Orthocenter", "]"}]], "Input",ExpressionUUID->"fd5b75ca-fa32-4276-9e4c-e73e55585dee"], Cell[BoxData[ RowBox[{"Sec", "[", "A", "]"}]], "Output",ExpressionUUID->"92d91bd6-b471-4dc9-bf96-c42fce85f94e"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Orthocenter", "Subsection",ExpressionUUID->"44120aaf-5774-4c46-9fa5-007d56b162d5"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"h", "=", RowBox[{"Symmetrize", "[", RowBox[{"ToAngles", "[", RowBox[{"Symmetrize", "[", RowBox[{"ToSidelengths", "[", RowBox[{"Orthocenter", "[", "OrthicTriangle", "]"}], "]"}], "]"}], "]"}], "]"}]}]], "Input",ExpressionUUID->"41b6adb0-8a8d-4529-8648-\ 556cd001ac33"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "A"}], "]"}], " ", RowBox[{"Cos", "[", RowBox[{"B", "-", "C"}], "]"}]}], ",", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "B"}], "]"}], " ", RowBox[{"Cos", "[", RowBox[{"A", "-", "C"}], "]"}]}], ",", RowBox[{ RowBox[{"Cos", "[", RowBox[{"A", "-", "B"}], "]"}], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "C"}], "]"}]}]}], "}"}]], "Output",ExpressionUUID->\ "d61da313-8fa0-40c4-935f-b507a40a114e"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"IncidentCenters", "[", RowBox[{"KimberlingCenters", ",", "h"}], "]"}], "//", "Timing"}]], "Input",\ ExpressionUUID->"897c24f9-ccbc-4092-84ef-577e675c3e5a"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"38.77000000000001`", " ", "Second"}], ",", RowBox[{"{", RowBox[{"X", "[", "52", "]"}], "}"}]}], "}"}]], "Output",ExpressionUUID->\ "b381d548-03b1-45ac-855e-4a885d254554"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Symmedian Point", "Subsection",ExpressionUUID->"d1287cbb-b4c4-401c-94a2-cbdbc3d7b444"], Cell["...a work in progress...", "Text",ExpressionUUID->"6cc78935-b428-4452-b8ec-a4950c17b1a0"], Cell[BoxData[ RowBox[{"t", "=", "OrthicTriangle"}]], "Input",ExpressionUUID->"0f993b02-12e4-49ff-9f05-2594c1be4a8e"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"t", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"OrthicTriangle", "[", "t", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Medians", "[", RowBox[{"OrthicTriangle", "[", "t", "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cartesian", "[", RowBox[{"k", "[", "t", "]"}], "]"}], ",", "\"\\"", ",", "Red"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Cartesian", "[", RowBox[{"g", "[", "t", "]"}], "]"}], ",", "\"\\"", ",", "Blue"}], "}"}]}], "\[IndentingNewLine]", "}"}], "\[IndentingNewLine]", "]"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}]], "Input",ExpressionUUID->"753e6e09-371a-498e-8c46-\ c0c330b8adeb"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 0.840863 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 g .5 Mabswid [ ] 0 setdash .02381 .01472 m .97619 .01472 L .30952 .60332 L .02381 .01472 L s 0 0 1 r .5 .43515 m .17159 .31917 L .30952 .01472 L .5 .43515 L s 0 g .24056 .16694 m .5 .43515 L s .40476 .22493 m .17159 .31917 L s .3358 .37716 m .30952 .01472 L s 1 g .37466 .35725 -6.34375 -7 Mabsadd m .37466 .35725 6.34375 -7 Mabsadd L .37466 .35725 6.34375 7 Mabsadd L .37466 .35725 -6.34375 7 Mabsadd L fill 1 0 0 r gsave .37466 .35725 -67.3438 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (K) show 71.688 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02 w .32704 .25634 Mdot 1 g .37466 .35725 -6.34375 -7 Mabsadd m .37466 .35725 6.34375 -7 Mabsadd L .37466 .35725 6.34375 7 Mabsadd L .37466 .35725 -6.34375 7 Mabsadd L fill 0 0 1 r gsave .37466 .35725 -67.3438 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor (G) show 71.688 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .32704 .25634 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},ImageCache->GraphicsData["CompressedBitmap", "\<\ eJy1m4tvFEUcx5deW/qilLaUWig9BJUWC2J5FFoohdpCAfHBy6BigwgYeYhF 0YjgCxVDFCOCL0BIQMWoYIKKJj4S/bfW7vzmZveun992z0tJ2N7t7zvf78zc 7Pwec7dxaHjv7v1Dw/t2DaUHDg8d2rtv1wvp/oOHR26lJnjehLTneTfSXvDa H3lpL+bfrOBi34zxeqK0GGlaG1zKIne9lO8YR949CPduwz1LUQamDe6eUQz+ IkV5fhS/Aq5CKMrBNGiuJZmJcLaA6mfAV/4/qluArxJjBZjWRQZmqbyinHvB u5vQdpJOu9ZcJ0YpRvXUUBYFt2rkViUQDSQgugHtYij7YXgy5OIoLrD/AM2n iK0KTA8kZ/4emtfqzH3AnDLXkizmzJR8Bxx1YpwEpjV50l8HjnqdfjXQFwOO Ft41wE0VqWow9RYgdRVwDbrUKqAoAVwKcFeCq1n7d4yPwGXAWanJYOpJKFUM uEuAa9KlVgJFaUKpi4CbLlI1YFpRgNQFwM3QpbqBghwJSX0BuGaRmgKmrgKk PgfcTF1qOVCQQyoB3Pngapa49fm10HBZAQLnABcj1QkU5LpKAXcWcHeKVB2Y lhYg9THgZhcuNRFwHwFujkjVg2kxUJB/JakzgLurcKkywH0AuLtFaiqYOoCC PDBJnQ6uZom3Fi5QDrj3AWelGsC0ECjIH5PUKcC1jY/Ue4CbJ1LTwLQAKMix kNQ7gLt3fKROAq5dpBrBND+hVAXg3lL5UKodKMiHkdSb6izZcILmdmypSsCd CK7mabpfF5gHDclzkcBxwFmpJjC1JZSqAtwxwHXoUq1AQT6MpF4F3CKRmg6m uQmlJgHuFcAt1qXuAQryYST1MuCWJJEK7yWVOgo4cas24CO3JRT2Pvqw6ggu c+9IcDVLfHkyAUGxkySBYcBZqWYwibcvjlL4eagdBlyXrjYbKIoARw8ZyT8P OInDbUxLAVs2RQpwtF9NhrYHAbdCl58FFJRikRMg+QOAk9zKawFTGigoF6JE tAbaPge4Hl2+BSgoaaEYguSfDa7mSZLiQmR8YcOZ0JCyCwrHpkDbvYCLkW8G Copi6R7J7wGcVG4iiys0zQAKGimlC7XQdjfg+vKTj48Q4+WfBpwU3CJPdmhq Agp6tGgRkvwuwPXnJ08bC5W866DtEOCkNhrZVkNTI1CQl6cdgOR3BlfzuA3m J0pOOKnoE4Cz8nPA1AAUlJDRplvnxkei6/MTpXyJapBmPZhb4ocyJN4OAMsJ RCQ4CE2huw77QHkAObtqN3AqFz0GLTbm1xEK4snpV7rJoPrBNmghJ0M2tx97 NckTSfVse0xgZoFyoK2gsEkXp91DNsPcUwDZfExrCkw3A/lD0pLiXXIZuWFY MNhSN1hyrI8466O6FDVsyYzFL3Kjoql4GPis1FwwUehj/Lo5/kqwADcB6WZd jwLNFqc3Dax0QrlFBFrBRJ90NF4M7mdG5tOWugFIt+p6lDOa5Whg7rNKsrGt B/pt+Smbp7Ao+zEPlyYNd10OLni3XRq0gYke4EY3XAk2Rj2H9LEOuJ7uyE+t wTWUCeAthyTD88NQwYrPAxNVoeqdOAXytPHSM9MHuMf1jlBt1Dz6qexdJt4V UUdWA048dKTURNFUSFHjZoRiEfLL5D16Afek3hGq7Fe7GckrKslh6QHcTulI O5jo4KTKzQhFCRSd0T6+EnBP6R2h8KLCzQgVxSg0Jh/X7YYjMXqktEoLLmxY 5hpStYISA5JfDriYjtDBc6mbhxZoQQkSOeBlgJOkyVZs+Sw/DAcoj6HkkMSX Am732OIpN3IKrikxpnhgCeCeEYn7ckyBaJEbMQUASUUXAW6PJho4Wo9dCKXk FIR0AE4KEpHDGC/TBPdpSr9JaiHg9o2WCudz5EoBALkgCn/MCjETJFUlW5XP dtO+jVMo5KbEnoRoY8qShD3LMFC6S36NQh7yD/tFlD5Ttxn4abAmPeugj/+A LlruRGkrpMoBidIakCopPi0u5fNp+ydvTeEWPcOHdFGX8Prk/KjyTaK0CKUc HTm7zlmfhoFcf1LROZmu2zI/Srm4y6dPzSWcPm3sJEpOwcrTtlvvBOiZFJde EhUQg8eehiJcqjUe0Ts0zXWIdj8Kj8hDkw+mzrUA7kW9c02uczR66Vxx7mwV a3gKw+kk4iXpELlskxiap4PCH5ot2gWpI3TSdVTvyEw3MxQYU3gdX10NcXR8 KKeNka8Ihaa06wglTy548inAJNdOXWrMsNjDXOzIbCelPtNedhmRFjzNHH0T wnaEYsrw0NAVK4L/NK+0YKg6ekxXo/NqqimSFG2sr4kURe1tbiJpRiiBIR91 XBcw4Yf5CONLxKEAufsTItAFpvluBDR0WqL01LyuCyx0AuRdSIBiwDdEoBtM HU6AekZbc5jNvq3TLnG08WWRkJY2WCuwAkydTkAv+nBucVIn7coMza+MISXf JN97why92/WUi2G487+r8/U4vtEVPU7i5ftfWMnodWS5235ARq7glE7W58ii 5aYMX5gFnhaKVUDR7yhEPMoQvLbfNsS26zICovKhIKmQNOi6EgOiOqiFU5Vs AO6d0eH9cE++Hxr5cUBoWuN6fFYHkY6FU4GR5vATHd4D987pcFq65wVOZVfa RD7V4bRXfiZwmtlON31f6iAKiyycPlxKBi7ocMqNLgp8LZgoPb6kw6mC8JXA aR0vgHuXdTjV1a4IfBBMJhc2s31VB1FpxsLp2IOyzms6nA7RvhY4HefQ4eo3 OpxqZ98KfCOYKKW7rsPTbvrkR0t44EV5RgycqgzyYys8r6PY8kcdTuUE+ZGY PT/NNlEh4KYOp+DwJ4HT2WZ4InNLB1EgGQOn4Et+QyjntzkmCqV+0eGUucuP He1BbbaJ0ozbOpySot8ETgfeFIf9rsPDmv4fAtoCIDriiIFT2PGnwOmrAXS2 9ZcOp7Tyb4HL2eqo08p/otZohOR5/8qL7cBpW5k3efxS15vwH2axXe0=\ \>"],ImageRangeCache->{{{0., 287.}, {176.938, 0.}} -> {0., 0., 0., \ 0.}},ExpressionUUID->"d80e64c9-5376-491e-bbac-f81b5d59f6ef"], Cell[BoxData[ TagBox[ RowBox[{"\[SkeletonIndicator]", "Graphics", "\[SkeletonIndicator]"}], False, Editable->False]], "Output",ExpressionUUID->"2fec26ae-8417-40f0-a653-\ 55d6255b204f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"k", "=", RowBox[{"Intersections", "@@", RowBox[{"Take", "[", RowBox[{ RowBox[{"(", RowBox[{"klines", "=", RowBox[{"Line", "@@@", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Vertices", "[", RowBox[{"Triangle", "[", "OrthicTriangle", "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{"Reflection", "[", RowBox[{"g", ",", "#"}], "]"}], "&"}], "/@", RowBox[{"AngleBisectors", "[", "OrthicTriangle", "]"}]}]}], "}"}], "]"}]}]}], ")"}], ",", "2"}], "]"}]}]}], ";"}]], "Input",Exp\ ressionUUID->"ed86bfad-f025-421c-bd99-03a1e3c32edc"], Cell[BoxData[ RowBox[{ RowBox[{"Transpose", "::", "\<\"nmtx\"\>"}], ":", " ", "\<\"The first two levels of the one-dimensional list \ \\!\\({\\(\\({\\(\\({0, \\(\\(Sec[B]\\)\\), \\(\\(Sec[C]\\)\\)}\\)\\), \ \\(\\({\\(\\(Sec[A]\\)\\), 0, \\(\\(Sec[C]\\)\\)}\\)\\), \ \\(\\({\\(\\(Sec[A]\\)\\), \\(\\(Sec[B]\\)\\), 0}\\)\\)}\\)\\), \\(\\(\\(\\({\ \\(\\(Line[\\(\\(\\(\\({1, 0, 0}\\)\\), \\(\\({0, 1, 1}\\)\\)\\)\\)]\\)\\), \ \\(\\(Line[\\(\\(\\(\\({0, 1, 0}\\)\\), \\(\\({1, 0, 1}\\)\\)\\)\\)]\\)\\), \ \\(\\(Line[\\(\\(\\(\\({0, 0, 1}\\)\\), \\(\\({1, 1, \ 0}\\)\\)\\)\\)]\\)\\)}\\)\\)[\\(\\(Reflection[\\(\\(\\(\\({\\(\[LeftSkeleton] \ 1 \[RightSkeleton]\\)}\\)\\), OrthicTriangle\\)\\)]\\)\\)]\\)\\)}\\) cannot \ be transposed. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"Transpose::nmtx\\\"]\\)\"\>"}]], "Message",ExpressionUUID->\ "913feb94-ff6e-4e9e-a369-300806422ddb"], Cell[BoxData[ RowBox[{ RowBox[{"Take", "::", "\<\"take\"\>"}], ":", " ", "\<\"Cannot take positions \\!\\(1\\) through \\!\\(2\\) in \ \\!\\(Transpose[\\(\\(Line[\\(\\(\\(\\({\\(\\({0, \\(\\(Sec[B]\\)\\), \ \\(\\(Sec[C]\\)\\)}\\)\\), \\(\\({\\(\\(Sec[A]\\)\\), 0, \ \\(\\(Sec[C]\\)\\)}\\)\\), \\(\\({\\(\\(Sec[A]\\)\\), \\(\\(Sec[B]\\)\\), \ 0}\\)\\)}\\)\\), \\(\\(\\(\\({\\(\\(Line[\\(\\(\\(\\({1, 0, 0}\\)\\), \ \\(\\({0, 1, 1}\\)\\)\\)\\)]\\)\\), \\(\\(Line[\\(\\(\\(\\({0, 1, 0}\\)\\), \ \\(\\({1, 0, 1}\\)\\)\\)\\)]\\)\\), \\(\\(Line[\\(\\(\\(\\({0, 0, 1}\\)\\), \ \\(\\({1, 1, 0}\\)\\)\\)\\)]\\)\\)}\\)\\)[\\(\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)\\)]\\)\\)\\)\\)]\\)\\)]\\). \\!\\(\\*ButtonBox[\\\"More\ \[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"Take::take\\\"]\\)\"\>"}]], "Message",ExpressionUUID->\ "a801aec8-a18b-4c5e-897e-72594656c335"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"t", "=", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{".3", ",", ".7"}], "}"}]}], "}"}], "]"}]}], ";"}]], "Input",Exp\ ressionUUID->"8adb164e-7191-432e-a96a-c196384f1639"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SymmedianPoint", "[", RowBox[{"OrthicTriangle", "[", "t", "]"}], "]"}]], "Input",ExpressionUUID->\ "179d9c4a-5423-4591-a89a-f14562237a88"], Cell[BoxData[ RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0.2800237812128418`", ",", "0.312128418549346`"}], "}"}], "]"}]], "Output",ExpressionUUID->"54c4f805-47aa-4ba8-bc93-a0b8f7564313"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Cartesian", "[", RowBox[{"k", "[", "t", "]"}], "]"}]], "Input",ExpressionUUID->"5c92f545-\ 8e23-4096-8fe5-c5370fb37907"], Cell[BoxData[ RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0.3183908045977012`", ",", "0.2873563218390804`"}], "}"}], "]"}]], "Output",ExpressionUUID->"85cb5545-1a2f-4685-91f3-6846c0e9af62"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Cartesian", "[", RowBox[{ RowBox[{"CyclicTrilinears", "[", RowBox[{ RowBox[{"Tan", "[", "A", "]"}], RowBox[{"Cos", "[", RowBox[{"B", "-", "C"}], "]"}]}], "]"}], "[", "t", "]"}], "]"}]], "Input",ExpressionUUID->"dfeac559-e2f2-45cd-8392-f5ffa68ba4e8"], Cell[BoxData[ RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0.28002378121284177`", ",", "0.312128418549346`"}], "}"}], "]"}]], "Output",ExpressionUUID->"59b2fb80-2787-4457-83e7-6be1e6527a6e"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"IncidentCenters", "[", RowBox[{"KimberlingCenters", ",", RowBox[{"CyclicTrilinears", "[", RowBox[{ RowBox[{"Tan", "[", "A", "]"}], RowBox[{"Cos", "[", RowBox[{"B", "-", "C"}], "]"}]}], "]"}]}], "]"}], "//", "Timing"}]], "Input",ExpressionUUID->"291dcf51-5693-4085-8351-ccef6b9ced49"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"37.69999999999999`", " ", "Second"}], ",", RowBox[{"{", RowBox[{"X", "[", "53", "]"}], "}"}]}], "}"}]], "Output",ExpressionUUID->\ "b7819e0c-b3ed-48cf-b342-b8b38cd219c8"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Symmedian Figure", "Section",ExpressionUUID->"20b41ab3-72f9-40d2-aede-aebee7a1c1d0"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"tri", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.", ",", "0."}], "}"}], ",", RowBox[{"{", RowBox[{"1.3", ",", "2.2"}], "}"}], ",", RowBox[{"{", RowBox[{"3.", ",", "0."}], "}"}]}], "}"}]}], ";"}], "\n", RowBox[{ RowBox[{"o", "=", RowBox[{ RowBox[{"OrthicTriangle", "[", "tri", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"alt", "=", RowBox[{"AltitudeFeet", "[", "tri", "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"ktri", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{"tri", "[", RowBox[{"[", "i", "]"}], "]"}], "}"}], ",", RowBox[{"o", "[", RowBox[{"[", RowBox[{"{", RowBox[{ RowBox[{"addn", "[", RowBox[{"i", ",", "1", ",", "3"}], "]"}], ",", RowBox[{"addn", "[", RowBox[{"i", ",", "2", ",", "3"}], "]"}]}], "}"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "3"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"k", "=", RowBox[{"SymmedianPoint", "/@", "ktri"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"m", "=", RowBox[{"Midpoints", "[", "tri", "]"}]}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{"pts", "=", RowBox[{"{", "\n", "\t", RowBox[{ RowBox[{"tri", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(A\), \(1\)]\)\>\"", ",", RowBox[{"tri", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(A\), \(2\)]\)\>\"", ",", RowBox[{"tri", "[", RowBox[{"[", "3", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(A\), \(3\)]\)\>\"", ",", "\n", RowBox[{"alt", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(H\), \(1\)]\)\>\"", ",", RowBox[{"alt", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(H\), \(2\)]\)\>\"", ",", RowBox[{"alt", "[", RowBox[{"[", "3", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(H\), \(3\)]\)\>\"", ",", "\n", "\t\t\t\t", "Orthocenter", ",", "\"\\"", ",", "Centroid", ",", "\"\\"", ",", "\n", "\t\t", RowBox[{"k", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(K\), \(1\)]\)\>\"", ",", RowBox[{"k", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(K\), \(2\)]\)\>\"", ",", RowBox[{"k", "[", RowBox[{"[", "3", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(K\), \(3\)]\)\>\"", ",", "\n", "\t\t\t", RowBox[{"m", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(M\), \(3\)]\)\>\"", ",", RowBox[{"m", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(M\), \(1\)]\)\>\"", ",", RowBox[{"m", "[", RowBox[{"[", "3", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(M\), \(2\)]\)\>\""}], "\n", "}"}]}], ";"}], "\n", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", "\n", "\t", RowBox[{ RowBox[{"Triangle", "[", "tri", "]"}], ",", "\n", "\t", RowBox[{"{", RowBox[{ RowBox[{"Dashing", "[", RowBox[{"{", RowBox[{".02", ",", ".02"}], "}"}], "]"}], ",", RowBox[{"Altitudes", "[", "tri", "]"}]}], "}"}], ",", "\n", "\t\t\t", RowBox[{"Table", "[", RowBox[{ RowBox[{"Line", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"tri", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"m", "[", RowBox[{"[", RowBox[{"addn", "[", RowBox[{"i", ",", "1", ",", "3"}], "]"}], "]"}], "]"}]}], "}"}], " ", "/.", " ", RowBox[{"Point", "->", "Identity"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "3"}], "}"}]}], "]"}], ",", "\n", "\t", RowBox[{"PointLabels", "[", RowBox[{"tri", ",", "pts"}], "]"}], ",", "\n", "\t", RowBox[{"{", RowBox[{ RowBox[{"Thickness", "[", ".01", "]"}], ",", RowBox[{"OrthicTriangle", "[", "tri", "]"}]}], "}"}]}], "\n", "}"}], "]"}], ",", RowBox[{"AspectRatio", "->", "Automatic"}]}], "]"}]}], "Input",ExpressionUU\ ID->"6c0679b9-2360-4683-8e90-d3781318f2c6"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .76066 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.312256 0.0181109 0.312256 [ [ 0 0 0 0 ] [ 1 .76066 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .76066 L 0 .76066 L closepath clip newpath 0 g .5 Mabswid [ ] 0 setdash .02381 .01811 m .42974 .70507 L .96058 .01811 L .02381 .01811 L s [ .02 .02 ] 0 setdash .61035 .47135 m .02381 .01811 L s .42974 .01811 m .42974 .70507 L s .26625 .4284 m .96058 .01811 L s [ ] 0 setdash .02381 .01811 m .69516 .36159 L s .42974 .70507 m .49219 .01811 L s .96058 .01811 m .22678 .36159 L s .02 w .02381 .01811 Mdot .42974 .70507 Mdot .96058 .01811 Mdot .61035 .47135 Mdot .42974 .01811 Mdot .26625 .4284 Mdot .42974 .33179 Mdot .47138 .2471 Mdot .24894 .13329 Mdot .44387 .54972 Mdot .63879 .16873 Mdot .22678 .36159 Mdot .69516 .36159 Mdot .49219 .01811 Mdot gsave .03942 .05558 -69.5938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.312500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (A) show 70.625000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 76.187500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .44536 .74254 -69.5938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.312500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (A) show 70.625000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2) show 76.187500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .97619 .05558 -69.5938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.312500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (A) show 70.625000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (3) show 76.187500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .62596 .50882 -70.1562 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.125000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 71.750000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 77.312500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .44536 .05558 -70.1562 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.125000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 71.750000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2) show 77.312500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .28186 .46587 -70.1562 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.125000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 71.750000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (3) show 77.312500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .44536 .36926 -67.8438 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.125000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 72.687500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .48699 .28457 -67.3438 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (G) show 71.687500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .26455 .17076 -69.7812 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (K) show 71.000000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 76.562500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .45948 .5872 -69.7812 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (K) show 71.000000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2) show 76.562500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .6544 .20621 -69.7812 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (K) show 71.000000 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (3) show 76.562500 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .24239 .39906 -70.8125 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.125000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (M) show 73.062500 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (3) show 78.625000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .71077 .39906 -70.8125 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.125000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (M) show 73.062500 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (1) show 78.625000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore gsave .50781 .05558 -70.8125 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 18.000000 moveto 558.000000 18.000000 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 18.000000 lineto closepath clip newpath 63.000000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.125000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (M) show 73.062500 16.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 8.500000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (2) show 78.625000 14.000000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Times-Italic %%DocumentSuppliedResources: %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedFonts: %%DocumentFonts: font Times-Italic grestore .01 w .61035 .47135 m .42974 .01811 L .26625 .4284 L .61035 .47135 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{282.75, 215.062}, ImageMargins->{{42, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},ImageCache->GraphicsData["CompressedBitmap", "\<\ eJytnImfFcURx2f37cFyyBFugV3kEg+CUTyAgAdBUEBMBDQqsBwCKmIQY9Co Mfd9R/3k/q/y52x8XUP9Zvp9a2YeyufDbr+p7qpfV1dXVVfP26OzNy5fvDp7 48r52Zmnr8++ffnK+XdmDl67/sWj3khRjKwtiuJ/M0W/PfdFs/yR/t3Z/1F+ aGmP93/1+mOveWuxtz7x1nzrPtb/Nd5/cNVbi7z1sbemKt37jeKO/OlE/8Gb wOQjp07lEEf7rdF+641+a8wY36J+6NTRHPZk+pX6z1X+pS5XnFWad9Gr9ipu er8eUBcY+3lA6jmaS40C3nMBY0BdaAKmgDTmAi64xu6Afu+6gIk2Aawgaf1c XcOjrpY0cDICOeYrlkbYkFvdbHmzYROZUsp1nMjx3fqcYTpTx15ZvvoMiyKW Ptj1svOn5ZgPz0Zs5HgdYhMcWc2rrrl8ENhZD/QajnjNZcwHEBFUnBlpaq5q GMU4LVnFdl+uixmN1kRUI+eKw0HnNUi66X8KN2yAN1dGOfHJyB41KBNCzzS1 F11M6Tkr3WTOkRGPVaU39CYMZyS5riky6yZNJSgj/eaItebc/46BkaZpL3QF nPTWKLSkqFz98LvS+2ydQzYb2szjjndg5SmUBEq9w+V+x7mkfpPafM1zkAFT cCDkge8yg7dfoSaWOPV50LlauU24sSfqrLeWggwhKKM7TYKUOekDxeK5TD3s iObXe6XWaW99raNiJ2O4pEuBVOtIvyVbygLUVB1mz71jBp1iPO3SEjDlHHH3 +rPDLpS8q5aclHLaJyHohGWFwVwyDMzE7JAL0AITkFecSvkPaXNlDGmlMzvo rQUOhHSoJSQqiV9l4mn3rHJmB7y1sFHAS05dG4taBiSxlXqf8Jku9BYp9ZSP uBOoq2OhpA7ti/3ekmcl8SfqGgm3+RoDQqRwkyVme332Yc4bgvt2fWzqtxz6 rY3B0TZa4Mx2e4uyHPkW2tLHfSztpAaYRCKYsqpHG2EqZSaYx5y6EajlyXYF kKZ94C7XQyg+PJQdcS53AXVdLH6jD3ywUdETTiXxz9THptZq6LfegKwE0lIf uNhbO33Ow0M6BJDI3zRACndhYrbDWxQUdFykUHywcewaeLbBYK7qCFM6vM9b y71FycwBB7ygI6Rpg0TrTJCUylVOEuX/LS58ubeytPwpH74dmM/EWMgPJGNL p4XNzlZxNJP8hBPuAVa23VFB21zKJp9VKGW/E+SQNtyGvAl3AmJGiWBKTPeB 0GkYYU4F948mpBqd0rCZRiBTPmKv91sE/UgPmwwSRfNwkyQB611oM6THvEWR lyBtjiGFhqmUJJy9gvwj3vpGLH5dR/ErnNlqn2mz+F3eehD6bYnFk7EudaGy FtlSmOz0fPZZrNgEI7YapPVAuh+e6TippSEgSmx2eosycwrF2wwSmc9ddY2E wUPJnHS4zlt3g14pbyd9NYAjow5PYB2eKXhrCdeV07vVrwwOcmuUn9M87rbR 00PNo1MdVidnHTeaYCfv/ygw2h5DpB2UZzhFUa3h0sEoN/oiWURRxtoJ3+2j bjSZSAt2ZWRtR6jNo10sbdEW1LZVUtKrT4dC/b2Gi9JswpVXHMvVEUgl1l0P /OmTIhtZ5ZDAyVNkupR+aTc3lc03eIvSMkJ6nyElVDOurcEsLsXd8duBuM5b j8PI+1vgZLOk9QiEp04Kf/KnFB52GAxyOOGZr9esDTDVbNkVibJ88d7hEJLy 1jjCol5h71qgE+AsYHaIYmR3XzcQmzviX+1CFRIpRRUQHTJtTdrumSjh32kg twBpjw9UeKNkNCs/VgouA36K6jVb4dkDLaiykzCVAlSHkQPOj8W+75VrZFws M0WMKgMpgyKXpMCmbFxrvXM4oVt84DJnpsBHW1PiVQ5TlTOIJ+QwLEsus6r2 JZQt6Kg81O1Qr74VhJkTtcC+HzLUtLaEepFLXubyMlcV1kek0LBiJGMbjDcE cVeMntZBlq7jENU/Ety06HSWeSgGQm5O56iVPruwwJUeHQfqw7GAh3wglbVk 2qFbyuLBc9D5EetAFqRKIjk/rTfl3XPVkNGrh5ZHgJvl1hgNt/tAKVJZQuXO /tb/unKyE9ZjwwmnZ0rhUr6gt5J6HgqyESTUnpU5WrtQqVtCdUp4BkbsjgXQ M2XDk/UYcxg67zHeYXqlClQWiTWNSX+m48U3gd9eE7UjmkYv2s29yGVml/1Z a/9tYFDKogmF0UiukOrd++CZqaVMq8BUaK8r9Wy+68xu4Tug2RejucenRsyU tWWBhZzmFHXuf3oKOu+3DpRSyHuQKegaILxpz56lqJJ83ZMxkAeAtM11Q7mg MqmwXBECeQKoj7cAUdIWhhF+k6m2V0YdAxmK4cIa51ZnscTVkhf4i2BVml90 yqxlD3R+MsalCwwrKnO9gRLp4KUl6UoQqY5kVo0FWV1tKN/NUyyf+Jj7nyyL fDgWSmmPipiyTFJ8fgApimraq9nTxA60iM8qYbQx4tdN+DUqJYY9N/vwNPIt G7kLSLpuzd7G6ZDj017rRfqVG1SLou7BGOuMT1enC8onDdd4rjf1JK8dZtqU UJYgyRSnnZlMloJ6rrw+LCV3slVKp5+2AZR+6jJJZiLvSA6bVlEnJ+1UOmsd agFCjoxScPKOzbia71ks00P/pIuJsDITumSi6hAvb0HVtwZIKsyFlfYwy9La Sjd0XWJ5NebvqpKmgfQKKnksXYwLA11mPGuMdkcssrx6g6MhA9ChOLstzPod iYVKT9qg0x2FqoJB9aqjJpQitcxVkSTNdDLalitcI6o0UW2qQaj2ro4oKmxn R5kOO1KZ+Fpv0RXFMYO0F0jZa4iqtZPRN70YT9B6boJyXVk/Kxzg8UwhdH6d GZ1/0G0w3DXOVy6Rov3xGBoVQqkmHXxhQgimvUUxvkSwD7jMDbhdkk92vMqx z/hYUuHzFeFjblmK8aM+/Q5CtWVS/pUW5oWKfsfr/pqSCOVWo9DSFc3GWIDe PyFvQeYZfBuheTO2IQj9FRV4cl8QbTj5xAHxWkKJp1IniWoONBu9dcIG0IFR 9+C6p+8azkbdTjPqSRtOJ2WlajIoaYfuyZWjUaQ+FYuSY9JxP0+nfMEUY8Kk oBRFhYj0SbEqfAc7+wKI/LvCLF21q8pYRuoD0Kk5GaP9Q6lAeNrKTu3k6+k8 UOYzer85M64wVZOW6DKAYJK708pT/joUoDIntIgTfFunXjeYq2ai2alxuuOk aN10Z7OmHJcFnzStxm924dTyUFYU+tIXbk//JNOnA5i2FVlcHoarUjuYeA37 vFz/+e8xDxDhCa95BuF9cOfvjh2pAm4e1LylaSUJ/HT/ZxhYxzvgqGYbmfPM vlUXbmKqSMrpKVGj133zVarLLcHtj8RXwHGWRgVBxTdFETpP0AFIUqspYnYH MPh1zPFo+4QZfPZMzoVeoVHCLhBlfn/YxdMNFImnXZDdumXUsybqkIuiuygS pSyGErDZCtt5wyhQlcY2tkv6FKpRNLOlHOBcRd8990RL5cnbBejApqoeBb7z JuoIkOa5UFooEko5ifwQhf0LJv4okBa7eDoNU+KV//GFzqJWuSjap5S5Nn8D 8aKJOhbhTqJ0z0KnxtdiFunTJucz7bOmKHXJ+NDVPjliev9KxqcDIMWUyyZK 347U9Q8dtUJRFHiW+g4cc9fE4uk6uinpik/8kEwt9RWnet7r9oEu2+lURlLI f1C/FY6mqNeBU7c3hwUyhB7SHl+cS5nw9c66d2WbbtYmO4HnNJZeiSNBenH+ qg19NhQ0kBNT2KNTx9XKFLQTepGOur7F9JaxfaFjd3p2zVicABLdRDSwOAkk WgNiqwvIizGz0O12ENrg/08BabqjKDPmhr9Vo2DNYfbLC2/v1/VZCelFIIXB NXtGl0ThGT3Yt6UFvATD+NsEg88oknT/0spXg4Ecd4rHyTNeMQHf7TgwZNYB yKXhRNEuo3yERJU5ystAmh5GVLZ/yhm8At3JMEnUD4ZjQc9uGotXgdRUTaFJ trKqh+Ow7vO+9TgNpJSZJVMjg/2gy0C6MPqhDTwDpFVdBp4FEr0iE95YfdjG h1eBqo4fGXEWSHSoohLUxzEL6k7PfmQszkUa7c7ifKgTSIJ095NRP4mZWR1j IAkK/s4PnWN/bLQLQFrmqJpzI6pr/qSF7WCRsOt7YnRCLqVdBBJ9u8Tn0VRt bc9WfmoDXgOSLeNELvXW7+z7gtngn7XxhfBIBa2fG59LQFoM0y/bRVj3aeCn 8p9O3WRtvzAWl4GkV4AGv15AWvql9bkSzq5dc78ajgU9+7WxeB1IOegiUOuQ LGgivzHiG0DKKzp9FjSR3xrxTSDRX/Sixf3dV8biKpDyIk6fBXme3w/Hgkzr D0Z8q8NEiG3/0x+NxbWO3Ydk0fU9xT8Zi7eB1PV14T8Px4Ke/cVYfA9IcoQk +6828DqQxr78QIL6Nxv4DpCab5o+7TKQDjyf2cAbQMq/noMD340Gdnj2eRsL jo//sMb3S31mMYTi+N8bRxC0UsZ7GSkKz9XuFkPqZb9/VQCkSf2n6wOx/K89 SHxb/m5yymPTPEsVf8wz/6wio8OraWV3Ozl1f0Xs0/ZhQTGtFHjTpyNb/rxC GhxY6vt97/5ve/ABwPtnK6kY+T+R5sdS\ \>"],ImageRangeCache->{{{0., 281.75}, {214.062, 0.}} -> {0., 0., 0., \ 0.}},ExpressionUUID->"50f2320c-5d8a-4ff2-944d-2b00dd49e134"], Cell[BoxData[ TagBox[ RowBox[{"\[SkeletonIndicator]", "Graphics", "\[SkeletonIndicator]"}], False, Editable->False]], "Output",ExpressionUUID->"6658f2ee-a621-42da-9f94-\ 995ea70cfcaf"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Euler Lines", "Section",ExpressionUUID->"21ec0f50-0619-470b-ad53-abfb99f79f45"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.", ",", "0."}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "1.9"}], "}"}], ",", RowBox[{"{", RowBox[{"3.", ",", "0."}], "}"}]}], "}"}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"h", "=", RowBox[{"OrthicTriangle", "[", "t", "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"size", "=", RowBox[{"PointSize", "[", ".015", "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"corner", "=", RowBox[{"Triangle", "/@", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Flatten", "[", RowBox[{"#", ",", "1"}], "]"}], "&"}], "/@", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"List", "/@", RowBox[{"Vertices", "[", "t", "]"}]}], ",", RowBox[{"RotateLeft", "[", RowBox[{"Partition", "[", RowBox[{ RowBox[{"Vertices", "[", "h", "]"}], ",", "2", ",", "1", ",", "1"}], "]"}], "]"}]}], "}"}], "]"}]}], ")"}]}]}], ";"}], "\n", RowBox[{ RowBox[{"euler", "=", RowBox[{ RowBox[{ RowBox[{"EulerLine", "[", RowBox[{"#", ",", "5", ",", "5"}], "]"}], "&"}], "/@", "corner"}]}], ";"}], "\n", RowBox[{"Show", "[", RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", "euler"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Orange", ",", RowBox[{"Altitudes", "[", "t", "]"}]}], "}"}], ",", "\[IndentingNewLine]", "t", ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Point", "/@", RowBox[{"Vertices", "[", "t", "]"}]}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], "}"}], "]"}], ",", RowBox[{"{", "size", "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"DarkGreen", ",", RowBox[{"NinePointCircle", "[", "t", "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Midpoints", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{ "\"\<\!\(\*SubscriptBox[\(M\), \(A\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(M\), \(B\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(M\), \(C\)]\)\>\""}], "}"}]}], "}"}], "]"}], ",", RowBox[{"{", "size", "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Red", ",", "h", ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{ RowBox[{"Orthocenter", "[", "t", "]"}], ",", RowBox[{"Point", "/@", RowBox[{"Vertices", "[", "h", "]"}]}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\<\!\(\*SubscriptBox[\(H\), \(A\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(H\), \(B\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(H\), \(C\)]\)\>\""}], "}"}]}], "}"}], "]"}], ",", RowBox[{"{", "size", "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"EulerPoints", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{ "\"\<\!\(\*SubscriptBox[\(E\), \(A\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(E\), \(B\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(E\), \(C\)]\)\>\""}], "}"}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"Orange", ",", "size"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"PointSize", "[", ".015", "]"}], ",", "Blue", ",", RowBox[{"Intersections", "@@", RowBox[{"Take", "[", RowBox[{"euler", ",", "2"}], "]"}]}]}], "}"}]}], "\[IndentingNewLine]", "}"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}], "]"}]}], "Input",\ ExpressionUUID->"323fc511-22b1-4482-b781-6cecceb34a1c"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.0758 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.370346 0.136281 0.498993 0.136281 [ [ 0 0 0 0 ] [ 1 1.0758 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.0758 L 0 1.0758 L closepath clip newpath 0 0 1 r .5 Mabswid [ ] 0 setdash .08851 1.0758 m .85322 .02561 L s .41151 .04485 m 0 0 rlineto s .41151 .04485 m .60235 1.0758 L s 1 .71375 m .02381 .32354 L s 1 .5 0 r .58581 .70312 m .37035 .49899 L s .53388 .49899 m .53388 .75793 L s .48693 .68358 m .77919 .49899 L s 0 g .37035 .49899 m .53388 .75793 L .77919 .49899 L .37035 .49899 L s 1 1 1 r .37716 .51535 -5.8125 -7 Mabsadd m .37716 .51535 5.8125 -7 Mabsadd L .37716 .51535 5.8125 7 Mabsadd L .37716 .51535 -5.8125 7 Mabsadd L fill 0 g gsave .37716 .51535 -66.8125 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.312 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (A) show 70.625 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .015 w .37035 .49899 Mdot 1 1 1 r .5407 .77428 -5.71875 -7 Mabsadd m .5407 .77428 5.71875 -7 Mabsadd L .5407 .77428 5.71875 7 Mabsadd L .5407 .77428 -5.71875 7 Mabsadd L fill 0 g gsave .5407 .77428 -66.7188 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (B) show 70.438 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .53388 .75793 Mdot 1 1 1 r .786 .51535 -6.0625 -7 Mabsadd m .786 .51535 6.0625 -7 Mabsadd L .786 .51535 6.0625 7 Mabsadd L .786 .51535 -6.0625 7 Mabsadd L fill 0 g gsave .786 .51535 -67.0625 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (C) show 71.125 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .77919 .49899 Mdot 0 .392 0 r .5 Mabswid newpath .55433 .60246 .10547 0 365.73 arc s 1 1 1 r .66335 .64481 -10.4375 -7 Mabsadd m .66335 .64481 10.4375 -7 Mabsadd L .66335 .64481 10.4375 7 Mabsadd L .66335 .64481 -10.4375 7 Mabsadd L fill 0 .392 0 r gsave .66335 .64481 -71.4375 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor 0.000 0.000 rmoveto 63.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor (M) show 73.375 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor (A) show 79.875 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .015 w .65654 .62846 Mdot 1 1 1 r .58158 .51535 -10.375 -7 Mabsadd m .58158 .51535 10.375 -7 Mabsadd L .58158 .51535 10.375 7 Mabsadd L .58158 .51535 -10.375 7 Mabsadd L fill 0 .392 0 r gsave .58158 .51535 -71.375 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor 0.000 0.000 rmoveto 63.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor (M) show 73.250 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor (B) show 79.750 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .57477 .49899 Mdot 1 1 1 r .45893 .64481 -10.6562 -7 Mabsadd m .45893 .64481 10.6562 -7 Mabsadd L .45893 .64481 10.6562 7 Mabsadd L .45893 .64481 -10.6562 7 Mabsadd L fill 0 .392 0 r gsave .45893 .64481 -71.6562 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor 0.000 0.000 rmoveto 63.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor (M) show 73.125 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor (C) show 80.312 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.392 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .45212 .62846 Mdot 1 0 0 r .5 Mabswid .58581 .70312 m .53388 .49899 L .48693 .68358 L .58581 .70312 L s 1 1 1 r .5407 .67028 -6.84375 -7 Mabsadd m .5407 .67028 6.84375 -7 Mabsadd L .5407 .67028 6.84375 7 Mabsadd L .5407 .67028 -6.84375 7 Mabsadd L fill 1 0 0 r gsave .5407 .67028 -67.8438 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 72.688 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .015 w .53388 .65392 Mdot 1 1 1 r .59262 .71947 -9.75 -7 Mabsadd m .59262 .71947 9.75 -7 Mabsadd L .59262 .71947 9.75 7 Mabsadd L .59262 .71947 -9.75 7 Mabsadd L fill 1 0 0 r gsave .59262 .71947 -70.75 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 72.000 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (A) show 78.500 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .58581 .70312 Mdot 1 1 1 r .5407 .51535 -9.6875 -7 Mabsadd m .5407 .51535 9.6875 -7 Mabsadd L .5407 .51535 9.6875 7 Mabsadd L .5407 .51535 -9.6875 7 Mabsadd L fill 1 0 0 r gsave .5407 .51535 -70.6875 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 71.875 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (B) show 78.375 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .53388 .49899 Mdot 1 1 1 r .49374 .69993 -9.96875 -7 Mabsadd m .49374 .69993 9.96875 -7 Mabsadd L .49374 .69993 9.96875 7 Mabsadd L .49374 .69993 -9.96875 7 Mabsadd L fill 1 0 0 r gsave .49374 .69993 -70.9688 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 71.750 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (C) show 78.938 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .48693 .68358 Mdot 1 1 1 r .45893 .59281 -9.03125 -7 Mabsadd m .45893 .59281 9.03125 -7 Mabsadd L .45893 .59281 9.03125 7 Mabsadd L .45893 .59281 -9.03125 7 Mabsadd L fill 1 .5 0 r gsave .45893 .59281 -70.0312 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor (E) show 70.562 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor (A) show 77.062 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .45212 .57646 Mdot 1 1 1 r .5407 .72228 -8.96875 -7 Mabsadd m .5407 .72228 8.96875 -7 Mabsadd L .5407 .72228 8.96875 7 Mabsadd L .5407 .72228 -8.96875 7 Mabsadd L fill 1 .5 0 r gsave .5407 .72228 -69.9688 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor (E) show 70.438 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor (B) show 76.938 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .53388 .70592 Mdot 1 1 1 r .66335 .59281 -9.25 -7 Mabsadd m .66335 .59281 9.25 -7 Mabsadd L .66335 .59281 9.25 7 Mabsadd L .66335 .59281 -9.25 7 Mabsadd L fill 1 .5 0 r gsave .66335 .59281 -70.25 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor (E) show 70.312 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor (C) show 77.500 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.500 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .65654 .57646 Mdot 0 0 1 r .4982 .51317 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{248.688, 170.875}, ImageMargins->{{54, 0}, {0, 0}}, ImageRegion->{{-0.603669, 1.31691}, {-2.05816, 2.46196}},ImageCache->GraphicsData["CompressedBitmap", "\<\ eJzNnPlzFMcVx8faXa1W1+oAdAGS0AFIQlzitI1jV9mEcrli7FSF8gUYJQZX HGNMflalErsqTpzb+SPyt+UP4LfNTr+e1z09n56dZUkqVK126Ot9v++9Pqb7 9b5z/+nDn39x/+mjB/dXbj65//jhowdfr7z15ZNuUu2lJEmedT//WknS5073 0f5ZTTqdTq373DmbPiXm0Tyln2lI+5P5m6ynX0NpzhkoNAVpf5aKmypxq7+K p1XiKSjUhrS/SMVtlbgBhSYh7a9ScVclrkOhcUj7m1Q8pxJX+6t4USUuQ6Ex SPu7VLykEo9CoVFI+4dUvKoSF/ureF0lzkOhEUj7QSq+qhKPQKEmpP1TKi4Y ianbrqnsWSg+HEurpU4/ZVvZT+5qewsiwBBppAkbipG6AAloSN1u2qRtZT/5 WNsTFSVz6VczTXC9gPyvEUtrmm5bSx87XQHpJ2mlf5upvA+1+blQ3s20nq0t Ne0I0JKMtLZ9gtquB5FDDMXQDgmybsa4bWpfpN8JgTrNn1XNkwuRqBHQ/Ie2 XOcgEQHdf3XPEM6VLig1UXoj17bRc/f/NVtqHx3pA8HcFVYLXeq20tGsAqe0 WYGe1mjLUzftdkAi/ciwkLyvzaZKE0VPW/zGtB7+9P/tjNt+Pi/9f01NdSvP w+B05WVgSRYz0WIMU+ZiZs9OS9I6mps9JXUfWPpcV506h87E7lsEdR9x+uz8 6i3QzhDANg3V0yQZbpIltXOgi+6/PSWSObqvTSCiJIcZ75BjlG/GJI1A7utq hHqMTZBGrGd7c82a8hW4q/yNc7WiSmiim2XfgTKyoSqqDJdmvkktN1QtDaBL qrJd/ajavw6Ed9SfTEfK+nnSGY5Sz6fVnfGbORLhd+aH+0lLZb4KiIgKUfbp JXU/K31uQMtb5KKJjEk07RrEw51s+O7BbwaMdlWNNgwMKM2yOmZVlOh6wCdy KkakyCFbMvUy42gevfkeUjvNArfLAIzsNAJpdtY7XqIUv9kNBULzH6WNA8UK tF05R9s87akhm4A5c2insiQ5FKdIJl2LAalA1tg4mHNGFbqbZg6BjHOAhfxy XIllk5XNtAPtGtShAfaE+ElxIk541XcdMO+qMci3NuKAaABcKQFE69yXAdC2 AmqB1E0BtB4DZCouV7R/HdJalkJhRjrwJjm/I6S1N0HgadAPqfhknBF136WK 3EjdI/1ys97uvbLuB6Yw+h4F7DKsJhsVaS2WeE4LqDRjcCOLuE7RUboJNFCs QyvkiWLfZBOyiOB8CUF6DxqE4LDaTXcMPKmrarcxwL4Vp0VD7REQEH2veoEU dZZwexsegmWlOA48toXiyYoUaaQnii/aTcfUiscAwTFohey5I2RPQRaRnS1x 0wkg2ADgNFXR8DKhNqRBbUltONkfrREQP11Cq2zP5HlotdVuC0BrAVqZABay EaqzSC+CbRBVtpZ7UWRn1IbzgOCI2rANPHaF4hZkEcUJEEAUX7SbHlJ70mA3 qxSngMfZOMUWiB8vcVPazK4DXFqXUbkjajka4GagFbKhLHntkNqbYPQVISBG fXIQsvNqQ3qzbKsNp4HH+TjFURCfLSDJhjNAi1yuKq0lteEU0JqEVshJLwjB nYoEpW8WXphp83wQbsfUZNTxx9VkMwD7ojA6U5ERbrd5/QJeGX2ktD1CA86y WmscGLWU0SzA3oszGouK/68zcgd+LWBEgzhZ65Jw241x8/YvC4wOv2BG7iSS 9g0bCucQgJVNnOQsZGV7Xr54wyDbIUqyfZzikUHaEC3VCL47CWoAfOp65GxX 4kQmLEjThPsY0POZiZIceHID2hA9paq3pxvdCkOq8MMA5qrgPAdZRuGNtIkB UW0pKtNa7N3Aq3FNUJ2HLDP4NNN25gZDta0NkV6uV0egPcc0T1N2uXhSgOzq 2GkF1gR9iac3qC1tJThVdUVeiWMYVddYcBi0fbIAYdjWVqgHyV68nYdAvHHu xQHE72grJP6GtLgHWZPao2Q4SJ+yzwwIqgpoE8oJ1fzpU3E956N7LQ68bXuM J8CfLHthHoFya6qLbOEdjs+qJuNoJYgvQZYZgoeVfm1QuCegXE1l0OvMiMhN khDajwT15RjqoB09pgP1ZN8eMzVzVWYragia6PSkNG95b2vHdKH06/U4L9qU o7TpPD7TLA1MxGO5rFxh6i4watpkH3ZmQNulr/S2mPkehBkd1B5VC43FpNVi R3PZMXvSecUnER4zdlwvWRwA6aIindD2aAfJ9Q07YV/N+5NgZEON5mU8J9L4 VlCZr2tRPUXq2PXaNSgUIUDvDK2saN4qZa/xPhu31zNdojQa1I0R9kIjdLSg 4dDw1VDsX8VDjdQS1PcI+2EoN6VSl1XRF0L/9cXpXnhxqhwMndtiuqbqshtL bqBz8yq51fALgDGtMG6oQs7EYQxZkUkoct+bKzyRtAdQdrDl16WD+TaUow1Z mtTd3oM9DrkEQOp9EoyesD0nwQm1x1GgRbE9q2o3ezq3FxUfDM7uvLs4MfOu qt8kLSmIEXVv4kYxSutqMntmfRGAwASbNnzYJucGrCQemVmBipshjlck4F5/ 1+IEggNk02gw7BgYVaFTaAeNB8czXy9sato9KSNqRYBfAOEtAD7nBCmAaLBq BeDDqvPVzM65zSJ5ITYqFj7eG7KTNub5SFrffo6AQHqrqQq2ngdrQj+DaJCL qtilHnBNmOqhvJTcMrA4bvVGSC8UKyrNhXrb4NRzMXAmUnc262Jez+scoLkJ 3wTgM8o7oRLc3GhDM+kOwngAiGMhyt5WS1CZvHWV8IpqyIYv7UKzEwEgmh6K r6VJwtOEB0jTHaAbqqHpOCAX9kyAaDmZePGN4agoGw35NjZUwhuqIZmsk+jt jxo4uOtumZRe9hqNqDNt8KSKeVPVJL3COxgJFllmUKeu473Fai0CNKLoafVj I6HSgUG2amzka/p5TVUnpLzjqXAlyIHaNGnRyE+jAL2kE4Ed6y1BGPMbquBm HPukKpgCuin4lwzhxWQoWmLk3Ij2tlZLsbhw/jfVKDKueee+gT/HYrvZVpPl zMSHDzgIu6bMaE2PE2X12OqbaknJ9cIVHOGZvIx8/DYTJvm035K9snriUqal ETaF8YA22Z4n2tx8bqkLlCmjPPjZBZkSwFHmXPMu89jtXJw1NZaoMM1UABWQ fVuMTjfoZis0OQXw6FaauY7ThsJHgUutguD3BPdJkBXEQgSh25UQy/KbES8C 4nqpSIt1E7BGY+9MRRLfF9YFwDpcKvJ2HOthLeS8m4a1vhDOxxAGgt4VXHRh cweapdfQhl7SCgrPAYZ7Io/ueZ6BJmgzTkJvU6F0KEOHfvdF6BoIDcY08bIk PqIOwR5svneEK7DAJT6IY1ljLHTKSDuPhIpOwMhRLaoTgGojX9w0RZCaqp6m eFfHvydADk0BDwROLhkmdMV3k1VG5/9uHRO/cpZPI8wUJESYP4pjPsmYq8Zw Vb1pQ7M6uTWFrhGjj4XRCjA6nS9umqItPbfgItWWbZnhErsHCep9nwiJZSCx DSSq6tXQMTe46HWPAFNcKwG+K4CPA+AzYXEBrDNk5yA81oqqmXZmqI/TWQuh vhdHbV6sG7Iiy8mjwXyQcCWK+CasdnI4FsNq7lWbcTQY0qq+6tHhDgH5VIDQ 7wqcVSBrFYXSdRoS+kCELoHQcyq04feZXvv2dHEtixPYT34Rl3dePSOIBTUi p0F89IJH+TLSfCwQ+jEG2VxMgRh/N/0622ZwiAQk75hEdRCA+ExALACIl9XP ZBuzo3phkXQl0t04/zwu6HrWaLjblyR+SLwKNSVl/C4cC9CBkVsD/1JA0M9Y XID+lb2x2bbahEXtU1gQZYNhsHHs0PxK0MwBmuzspzgUFS7XTwEqZzD3YxXF barHIp9+m+NydfnRGco4WsN6so3AN7VNj/56YOFqpqZqdMiytaE8viCKRb2i xsvd0DiQT0NRu1+3sI1RqO7VKGpY02XxcfaKuFOVMdXTuJRrFaVMOCnpU8uJ SgX8WgRQVPg16AdtVWsWv6HuZNxOPl9IoxRG/556QXaJPXAi2xXoJ1juWF8+ wNu/NX0qaeLHmhYurTmorO8FrqSZbwuDLoTcAhhBGFo8uKRPLOZjLUI/mPR2 DAtOcPVQTaYQzfBVoZXApesl71SEGyx+g2O2YF4yPf/pQEI7dqAwI1v5D1b0 Yv9EgNAFqZ/Emq35UU70+tRL6FcilC6evRvlEg1YKiAIOuuTuLTb1aXRfd/f SMu0Qfl+zEtN3/9eKtIl359CRfuLWHSb9N/xrJ9FO0rhsI7WL99Iy3RL9071 linm5FtpmX4SRPZjigE0aauZBK98Wu730hoda3+kNXKmDCJsTPZ3g7SiWbYV OsL+JK8Ij1FeObYJOm++a/42TXHvnzaZPv6hR3XzG1i6NsyJpDAdU6cpdXIZ VusUrHSvR51A+qda/I+Y/0Bhf5/l51rdT/+an8Syvxz4TL4+k97m2n0Y8a30 /1Ztj8DUfeXWC8VZnlX559zid5EWn+W+vgTdfztI1mPI+ub/KusryPrd/z7r CWT9tmdW8tJ/AHGvmp8=\ \>"],ImageRangeCache->{{{-150.125, 326.5}, {521.562, -249.812}} -> {0., -9., \ 0., 0.}},ExpressionUUID->"324346fb-0372-4223-ad07-ef842f6d4b3a"], Cell[BoxData[ TagBox[ RowBox[{"\[SkeletonIndicator]", "Graphics", "\[SkeletonIndicator]"}], False, Editable->False]], "Output",ExpressionUUID->"ad08cb7b-fdb9-46de-91ac-\ bbb32977c588"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Sides Parallel to Circumcircle tangents", "Section",ExpressionUUID->"4ababc0c-bae3-4e58-ac8d-45cf40010f8a"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"Triangle", "[", RowBox[{"Reverse", "/@", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.", ",", "0."}], "}"}], ",", RowBox[{"{", RowBox[{"1.2", ",", "2.3"}], "}"}], ",", RowBox[{"{", RowBox[{"3.", ",", "0."}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"v", "=", RowBox[{"Point", "/@", RowBox[{"Vertices", "[", "t", "]"}]}]}], ";"}], "\n", RowBox[{ RowBox[{"h", "=", RowBox[{"OrthicTriangle", "[", "t", "]"}]}], ";"}], "\n", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"t", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ "Red", ",", "\[IndentingNewLine]", "h", ",", "\[IndentingNewLine]", RowBox[{"Dashing", "[", RowBox[{"{", ".02", "}"}], "]"}], ",", RowBox[{"Altitudes", "[", "t", "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Point", "/@", RowBox[{"Vertices", "[", RowBox[{"OrthicTriangle", "[", "t", "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{ "\"\<\!\(\*SubscriptBox[\(H\), \(1\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(H\), \(2\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(H\), \(3\)]\)\>\""}], "}"}]}], "}"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", "\[IndentingNewLine]", RowBox[{"TangentialTriangle", "[", "t", "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Point", "/@", RowBox[{"Vertices", "[", RowBox[{"TangentialTriangle", "[", "t", "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{ "\"\<\!\(\*SubscriptBox[\(T\), \(1\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(T\), \(2\)]\)\>\"", ",", "\"\<\!\(\*SubscriptBox[\(T\), \(3\)]\)\>\""}], "}"}]}], "}"}], "]"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"LimeGreen", ",", "\[IndentingNewLine]", RowBox[{"Circumcircle", "[", "t", "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"Coordinates", "[", "o", "]"}], ",", "#"}], "}"}], "]"}], "&"}], "/@", RowBox[{"Vertices", "[", "t", "]"}]}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"v", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(A\), \(1\)]\)\>\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"v", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(A\), \(2\)]\)\>\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"v", "[", RowBox[{"[", "3", "]"}], "]"}], ",", "\"\<\!\(\*SubscriptBox[\(A\), \(3\)]\)\>\""}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"o", "=", RowBox[{"Circumcenter", "[", "t", "]"}]}], ",", "\"\\"", ",", "LimeGreen"}], "}"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}], "Input",Express\ ionUUID->"acf35294-e5cf-4950-976f-d24a45f0f9a7"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .84946 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.529168 0.152828 0.153101 0.152828 [ [ 0 0 0 0 ] [ 1 .84946 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .84946 L 0 .84946 L closepath clip newpath 0 g .5 Mabswid [ ] 0 setdash .52917 .1531 m .88067 .33649 L .52917 .61159 L .52917 .1531 L s 1 0 0 r .75169 .43744 m .52917 .33649 L .71719 .2512 L .75169 .43744 L s [ .02 ] 0 setdash .75169 .43744 m .52917 .1531 L s .52917 .33649 m .88067 .33649 L s .71719 .2512 m .52917 .61159 L s 1 1 1 r .75933 .45578 -9.15625 -7 Mabsadd m .75933 .45578 9.15625 -7 Mabsadd L .75933 .45578 9.15625 7 Mabsadd L .75933 .45578 -9.15625 7 Mabsadd L fill 1 0 0 r gsave .75933 .45578 -70.1562 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 71.750 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (1) show 77.312 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02 w .75169 .43744 Mdot 1 1 1 r .53681 .35483 -9.15625 -7 Mabsadd m .53681 .35483 9.15625 -7 Mabsadd L .53681 .35483 9.15625 7 Mabsadd L .53681 .35483 -9.15625 7 Mabsadd L fill 1 0 0 r gsave .53681 .35483 -70.1562 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 71.750 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (2) show 77.312 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .52917 .33649 Mdot 1 1 1 r .72484 .26954 -9.15625 -7 Mabsadd m .72484 .26954 9.15625 -7 Mabsadd L .72484 .26954 9.15625 7 Mabsadd L .72484 .26954 -9.15625 7 Mabsadd L fill 1 0 0 r gsave .72484 .26954 -70.1562 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.125 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (H) show 71.750 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor (3) show 77.312 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 1.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .71719 .2512 Mdot 0 0 1 r .5 Mabswid [ ] 0 setdash .96855 .8109 m .02381 .38234 L .82209 .02023 L .96855 .8109 L s 1 1 1 r .97619 .82924 -8.09375 -7 Mabsadd m .97619 .82924 8.09375 -7 Mabsadd L .97619 .82924 8.09375 7 Mabsadd L .97619 .82924 -8.09375 7 Mabsadd L fill 0 0 1 r gsave .97619 .82924 -69.0938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor (T) show 69.625 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor (1) show 75.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02 w .96855 .8109 Mdot 1 1 1 r .03145 .40068 -8.09375 -7 Mabsadd m .03145 .40068 8.09375 -7 Mabsadd L .03145 .40068 8.09375 7 Mabsadd L .03145 .40068 -8.09375 7 Mabsadd L fill 0 0 1 r gsave .03145 .40068 -69.0938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor (T) show 69.625 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor (2) show 75.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .38234 Mdot 1 1 1 r .82973 .03856 -8.09375 -7 Mabsadd m .82973 .03856 8.09375 -7 Mabsadd L .82973 .03856 8.09375 7 Mabsadd L .82973 .03856 -8.09375 7 Mabsadd L fill 0 0 1 r gsave .82973 .03856 -69.0938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor (T) show 69.625 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor (3) show 75.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 1.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .82209 .02023 Mdot .196 .804 .196 r .5 Mabswid newpath .63316 .38234 .25173 0 365.73 arc s .63316 .38234 m .52917 .1531 L s .63316 .38234 m .88067 .33649 L s .63316 .38234 m .52917 .61159 L s 1 1 1 r .53681 .17144 -8.59375 -7 Mabsadd m .53681 .17144 8.59375 -7 Mabsadd L .53681 .17144 8.59375 7 Mabsadd L .53681 .17144 -8.59375 7 Mabsadd L fill 0 g gsave .53681 .17144 -69.5938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.312 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (A) show 70.625 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 76.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02 w .52917 .1531 Mdot 1 1 1 r .88831 .35483 -8.59375 -7 Mabsadd m .88831 .35483 8.59375 -7 Mabsadd L .88831 .35483 8.59375 7 Mabsadd L .88831 .35483 -8.59375 7 Mabsadd L fill 0 g gsave .88831 .35483 -69.5938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.312 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (A) show 70.625 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 76.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .88067 .33649 Mdot 1 1 1 r .53681 .62992 -8.59375 -7 Mabsadd m .53681 .62992 8.59375 -7 Mabsadd L .53681 .62992 8.59375 7 Mabsadd L .53681 .62992 -8.59375 7 Mabsadd L fill 0 g gsave .53681 .62992 -69.5938 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding MacintoshRomanEncoding def currentdict end newfontname exch definefont pop } def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.312 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (A) show 70.625 16.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 76.188 14.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .52917 .61159 Mdot 1 1 1 r .6408 .40068 -6.3125 -7 Mabsadd m .6408 .40068 6.3125 -7 Mabsadd L .6408 .40068 6.3125 7 Mabsadd L .6408 .40068 -6.3125 7 Mabsadd L fill .196 .804 .196 r gsave .6408 .40068 -67.3125 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.196 0.804 0.196 setrgbcolor 0.000 0.000 rmoveto 63.000 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.196 0.804 0.196 setrgbcolor (O) show 71.625 14.000 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.196 0.804 0.196 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .63316 .38234 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{342, 290.438}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}},ImageCache->GraphicsData["CompressedBitmap", "\<\ eJy1XXmIXlcVf51vmS2zZpsmTWeSJm26JE0nW5u1aWqSrnbftzRdEmu6pKmK K6W4IuKKiCsiLlSL+qeIICIiqIggUlwoUlwQKYpIceH53XPv/Z373vvd9+43 Uwe+mTfv/s49v3PefXc5d/muO3r6+MMnj54+cezo3OFTR588fuLY03OHnjjV u9U6I8vOuK33WTeXmes8y/wv+bnd/HL/9Hu90vxqm6z2BHdXmF9dc3d3cHep +dXKfNKgudq28PSWud8ug6bMrwEkCTW5ytrmply5Tyg2AbEBaBEF3WbZMVVp vWGSWgUJza9Vlh6FdNdcdYg0uxdmMZT73IdiWQzECXRBYDQmPVSWaUNmLFlm ADITcHHRseJ+klXlIUsuU8hlEA/Kgf4Dh0iZmQyS/gX5FeWkV5G0NgcJ/5Nd akH/BOicOOgfAG2Ig/4GkufFQa8gpwvioL8CdFEc9BeALiagnRb0J3C6JA76 A3LaFge9DNCOOOj3AF0aB70E0G4CsrlnvwXxvXHQr5HT5XHQiwBdEQf9CqAr 46BfAnQoDvoFiF9FQNst6OfI6do46GcAXR8H/QSgG+KgH4PTTXHQj5DTbQTk XqkfAnRHHPQDgAbN1Uw+/9N59qgd/PuAS40yaOAz5qprrrbHBb8Hs9oGKa9m x1xtict8N0jqIc0nGzC/N5sEyWcTkd5qpb9DpHdY+r3LC+OC35bcTRPdSzc/ Bd27kMX58Sy+JS5xWYTpe8GcVU5O+gXxlW9rbWW+B2pZ1VcjuA+CrGLlgmiw bNvpX1jjBy84SzKbt5l9Q5OKTaD4VFvorJh6AERr8n4+SMJjyXJbJgPe2utQ Lb3PQehYE9fx1TxHGe8htU+Sdcr5yf8drut10LU6ruvLRV3tBeoS61XhmXGF X4LCoHBbfbnrPrXhwAEUAfQfrJZSYVhJ9Nk2LPtiYGBVUJUWbTLXw5aL13uw P72fF0/m0lWtCmpvT/IekZIPVVfAkTUKPgvD2oAPm6suKeDyJg4RBcvjCj4N BR1iQb2qkaKqkux0XOmnoLRLBCXbKSO1BAoOJCqw9Xz2SSgYJIKjUDAOBaz2 mYor+Lj504IC8fIywIHPWLGYhtL9kK1R9VHYMkwyY0rbBLe0qLSUOh5X/2Go HyGCWrLq1TPcnv6IfAhERongikQi/oEEGrJJ+GavveoJ1BD5IIgsIQr0ZVYF 7NXyFVVIREvGXiLhtYWUbEc/e7/5IynjRDCVEvONlpvdRKKG0nvhpUkiOEMo sbqAUVoGSruIhC8chNK7QWmKCGpzVk/Jl6qQ0nJQuoxI+BeHUHoOlKaJ4CpC iVVojNIKULqUSPiqhFB6FpSWEkHtZdRTmoX6nYnqN1v17zR/JGUZETyLqB8i uDmo305Sa9S/HdavIILan6tXvw7qt5HUIeRSUf9WqJ8hgqnq1xPcPMENAlch 8hYQOZMInk0UsNbJvz9hwVwN32ytkSCUnjF/JGUVEZxdBKU1oMS85KtKQulp eGkNEWSUWCPKKJ0NSltqJEJKdpCaPQVKZxPBuURKvmSElGZB6WIiwbzkKD0B SrNEUAeMqoq18MxLa0FpE5GooXQSlOaI4LpESsxLgaxE4HM7Ysyy80kGbYAr DN9g/kjKOiLIGLLeCGMoTuvGKPkWl1A6DqetJ4IaMainJKHQduY5yABsLcEx Ijb4mT0CIhuIIKv9UokwXw8gvwqRh0DkPCLIiIwR3LlFInZUbB+Z/XQWQO1B UNtIBDUuVE/N4/Jg7CdD9XbmeZVSJTpiy0InzMqb5KvO+80fYe7D3k38WNfW 112kMyaezD0t9xHkAK5aizDgXjjYh+Qrz3SBBiyFAfIOtGMky8/F/Cfg9TXs 3bt8N9hvTmQ/kch+Euyl/o2WEXqvXbjnKLrartaeO2EPa5x0+qXeHl/J5+Wq Q24NJtojfwfwNDSqZau5dsGOnoQz4XaY4GdmmkxgIytmwjAeyQhM6Jp/JYyj 0a/ZWn63WEf0brBekq9lmvj5mjjk1wW/JYkulk/X2eHYl/s7Qem4Ca5lwwFG nY0Qp0FT3uRuIk0xR8NyZ5VyDmjeAJo7iHqdCainqS/gJLxZqveEuobvbH+6 8txdS3I9WLGRZCoraV1EubhxqUFrfG+mlsE1VrZ3g434GQM2mh6BX5aDwTiR LQ/8zANyRK6CK1iAJpXIEIj4yEz4MrAum8YXasgdBrl9RKlOLpcaGtZpFnKs wz1J7jHCK0HYR/6MDl872mkxP5WQZXTuJ5VwC4T9UDgkMkHuMdyZIFzWYTzs CB8EYRaP1sk+zbYSw/AtA6umx8k9xlVH0GHp8s61frMBbXln2JxGI1d7n1Ji Nfgwuaej6rAdKNHcB5eyKR9d7FB6o2z3rji3xB71DLmnQ+uwQ1bitQe8Dify 0mqXBf0ZOfb2z4FcOGQpkdsFclcFoDpy4yDHAr++4gqJaAiLjXythA0tCpFr EolIZq3wbWUtcUhkPYiE4RzvEUdku8020+UTYbY6f8/6RMw+RuRcEAkDniUi W+GR1ycSGQQRNj7w9X1TPcH6MOH8R4nmJaB5YyJNbRdYr47RZEV+I3zIyqE1 woaXhNzNieS0DWAtxKQ3IBgm2xStQUOSF4Ake5MdSSncUuJuISBJbdvRvNfl P8sJ3vaY2kWKnN1FYCcrHRwdcHZrN0l1L8EFFs2dqngv1LfJyvZ+7BBEn2F+ J8mMRVXcKp5Sn8K1M/bBSMKwuRJ/DeFe6apTvCeypbUos5YmXtf87kSarGD7 riw8knEviTYR5WxQi+X3NrOxFvnyEgwlWceasWHdtLXWX4ahcAVNXYnhuK61 tvRk749xlUGFlG+/yDPXEQ+eCaPrQwuVDo2s7RqCI6Rw+6BAFmTu3ePIzsKx D8bItsgIiAZQzG/WYQ+iYLi3HJxt25o5GsHyIF3oWtLhqKODlB8jSjfCFQlj zIZ7yJQFPZh1duRoYLZ48XVCLWIgM3ogMBqd1/zhmNHJIZbMUstL1IBMtXYY z7I0VR6o5h5IKKAYWeSPLsJgew8VgYvZ9P5lUVs2uGCjtDFyrwVf6DBD6m9d tdVCWQ9rDekCSK1xotZODTyVwj4lCRZbbDLCyPc+Nqe54rPMnQfrl4I5Y7DG IH/jYh+axFp0yM9m29joid0bxLNhUwstsNLlZs6caZjzeMycvqJZGkphU6xs zMqepljSIQlznq5t5KML0Jx1WL+TP1n7sFgQTKO7bK0HK29isVSNbCDMZsaT jMBStPxUzAiJWE3A9Wx5EyOsbzRbTcPqCrbOQHKeCgiLVbL5xnVxtYebn641 Qfub7nUsFQP/Fks4kBUcdi+6MiTk3LFPogd5M2F4McnCZ2tuGk7CyxKe1/W9 IZFV1rpSdMY5yHV/FkBkjZXowfxEYKiULV6qUa+rjXUfFnt36olIkQ4cBAhb 3cXCaq89G/ZA6oOnIQfdT+Z64K44Z/Jetvrm5TpIvtwMmN9iHeuzs1eXre5s MmIErVts1xWyOtmPMUu0MUBCajjY2xtmartalZD/hsAU3VMX3fBmazc8qL4s cj2aHrYdZOXyqo78cr4GZZpkH5nOCG1jewg71UfnWivXNDzWj3m+d26KXtFn 7cI91ZBn9ImyJlrXzK5utjX+9HgxFYUCP75Yg9k9DWWxEBWzlk0TLdBudJ4t XcwL5o8s1tR28Z6Au9aTeUb7+mzdqMdVG8G+TS1uEsgfSjTwLPcYSmVU/u8S GzWSy8Jl2Hwbm91OsgIzlTTKUNdxqL59tQU05Bx5HUeItln1WR7+GEPWBwb2 uyVXe6UPJNq9uohjJZP5QrBjsJuFuIeJtlnCii2KWlf2gW4oFhcLmkXmUk3s oC0ZQKaF8TlrIsNM5xZgiWxtxgr9/B6SxWZkoarY8llp3aetK/KM9rA7XhGW +vXNFV2x/K7FctVVXrbCrsTOuyS3PomfD7p3EEFGl4XX14NpizPtkIzYCssW cCpslxTZAH9hq24a02qNYUDKuLJLxU+KSDlgix5rSMpMgqSweZ1+SbqIey5R qCwrSfowc6iBrbZ11LbAf2w+jFGbqaEm5UYi+WztZQ2NedC4gQiyma//C41t oHE9EWQ0VtbQuGChNHaARuqkbhoN2wqYm2xNLVtbbytnO90tKWzenRFaUUNI 5whZP4wtia6hthu+OkIE2Uw8299yITyjPmLkWGNVQ24vyB0igowcmyP1/g2J sF10LMrVJ+H9IHwlEUwlzNaDMcKp9/o04gCMYNtzU404z+dCB0aWZqlFc20H K8Fs69OspSvLlCRlfyJdtkGMLZO1wTajg7UKNZQOwYNsRV18DVVxjNEDsOXs LJbAnjrrCdRwPgLObH8t4+xn+KI9gRKehfcZcdbZqiF+NYiznabx1YAVZ5/j M7K92FJ1xlix/YCO1bVgxXZ2MlZ2EMrdybbtsBXJbMeonVmwq3ElhW2sjC9B rbgplQvbUOu43AjnMMH4ymDunDmfG92xWkPjZtBgOwrjNCoumSNQ5mW27dlx uRVc2CL+1MXSjAhzSg0RWQYkKWxDROpqfUaEvQg1RO6CR9gevVQiumiTVWsa tFL1NgKf3QP1bJtO6sYQNq3Hqil2bIAjch+IXEgEU3fcsKk5RmQCuAqRB0CE 7f+Lb1yqvC66QIA1jzUMJIYmKWwEGd/7VWHANsizlfmTwFW4PAxvsL2E8X1y SVyYX9hRHzZYmD0KLqzRj28nrHBh04GMi85dVLicABc2SIrvsaxwmfEZJR/i 4hg8BgasJ3kOBBsZsPMvLidZ6ixVhYvMK0kK21Ud5xLgsnQiOu1XIfIknMJ2 nKduXNbDIdjQQM9SUfU25pmdgvryNibzX+pWbnYaTJ9EToPIaiLImq3U42sY EXZCkyPyJhBJPZWAEdFjVtiAU+fTK+rlnAZJWUkEmXq2YofNz/ZJ5G3wAwss JB0YESyZaCLCzh5zRN4BImx8yIjYQUml2pgiUMaFHbxmy0L2LnBxD7gnF2dQ dIXOsLKgiS53qSjt/wCXgnp7P2i+Fce26LAj7hyR58wfSWE9uqSTZLKMEmEe qSHyHniEdakaT9lxHsEhwBkLseljrah/H9SzxZpMfWEtWqi+hGN7k7TuUyL2 dck+ACJuPrMn16je3VtCcEw9O//RqX9tDs5KJaJtYYWIHCUmKawyTCWi+2dZ NFj7BBX1H4Ef3Oz/fGXhsfzHFvixyV9WHLWDVlH/saL6aN+jngibjWVE2Amk jsgnQISdIMXapOiSR3kMV5NUdvCybcWCQwJZeWctUWE7kHst2VwuKw860K0Q keMQJUUPeWxU7+6xWc4jyIWdP+uUfgbWM6eySrdwtKazPqq+lF8Nkc+BCLOP rbxhZ3zqIQasFLBDs536L0A9y3bMWRmolx/nAzZzq95nhw7b9zw4sNQ+Vcmw 93EKO0xhXFuJdI1eOZi1Za3tiYw634Xa5t0BsVqzCXRrPNOvhMZUo72V7HWK uN6OGpVfC5KcSBBbzuCyVFXsmHOn6vkA7pIrxX5ezm2uqjoM97HTz21HOfs6 QIXXsZh3lgUFa1c8sxdKmWVZZWr8ECB74vl8U63O/I9kxpramnz0jGo9OHh/ A/3SDjqJN0rv/EB/gjuhkZ3OvjwQLO04E3/Jve3I4khDFmPmPtklZBy4BRZc 3ZBL/JRptv/IDVo2Int2LHyYfd2hz1hsWzqLuVxD6eHZEsa/aREq2Z4Iezg1 6uNBNIayg4GdMb+s8iDzqjnoJdiraZPZfSmZRfYJDSO/ZxpyKe3I0S8DebpB MLpjRL+N5KmFZjEBLz/ekIVsn5iGxpMEvrQM191Tj8Xh+t0JJ+Ig/RaGR+Og F2HMQ3HQb5DTMQKy3a3sdwAdjYNeAuj+OEi/9+LeOOhlEL8rDvojcrqTgGyQ IvszQLfHQfr9ILfGQfpNIzfHQa+AOPuOCQf6O3Ji1ZID6feoXEdANm4QfCPL NXHQq+DEqmoH+jdyYk2CA/0XIPbVHw6UA3SQgCYKII9k7VeI1LpvXwNSqzPW 9oZIrahYryFEas10GUGOB0itgHY2ILWeYT2sEKlVzHwDUmsX1tENkQhz55sb kJikyDcR5FiAXAWL2Nf1hEjd3s3GfiFyFshzG5A48DRnA/wQiVUQ9FuMlgTI DbBorgGpJz+waFeI1OMoWKAyROI4i3xVA3IzkCwMHSK3wCI2gzAaIPW4Fjbn EiK3A8mmrELkTiDZtGOIvAxINm8cInfDIjbTPhIg9UAltogkRF4OJFuVEyKv AJItNwuRVwLJ1nWGyEOwSDbchUlSf8tWwOHGuzKqKO0dHOg3Xff9lb5ErYIc RYeqtJOJ6xRg5PvlOItS3pEdYRVZtnEl8p14SbKlXUpJMkOLRPa7N4VnoBs7 KumTwd3sjP8Bw7RJEg==\ \>"],ImageRangeCache->{{{0., 341.}, {289.438, 0.}} -> {-3., -1., 0., \ 0.}},ExpressionUUID->"54c8c3ee-3e9f-4f54-b47e-bf4ea65e74f6"], Cell[BoxData[ TagBox[ RowBox[{"\[SkeletonIndicator]", "Graphics", "\[SkeletonIndicator]"}], False, Editable->False]], "Output",ExpressionUUID->"a4470dde-0608-433c-84fc-\ dc57aabd3251"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Centers", "Section",ExpressionUUID->"6972bc25-391f-4df1-8875-57ac4c8ffd3f"], Cell[BoxData["\<\"Rehashing triangle centers...\"\>"], "Print",ExpressionUUID->"40f3bb70-a1ce-43b7-b96f-16436d3d048b"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"pts", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"#", ",", RowBox[{"KimberlingLookup", "[", RowBox[{"#", "[", "OrthicTriangle", "]"}], "]"}]}], "}"}], "&"}], "/@", RowBox[{"Take", "[", RowBox[{"KimberlingCenters", ",", "All"}], "]"}]}]}], ")"}], ";"}], "//", "Timing"}]], "Input",ExpressionUUID->"38217e2e-5144-45f3-9b3f-\ 58b795caf520"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"1517.0200000000002`", " ", "Second"}], ",", "Null"}], "}"}]], "Output",ExpressionUUID->"518d6629-d90f-4316-9dd8-7cca3074fac9"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"l", "=", RowBox[{"Map", "[", RowBox[{"First", ",", RowBox[{"DeleteCases", "[", RowBox[{"pts", ",", RowBox[{"_", "?", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Last", "[", "#", "]"}], "===", RowBox[{"{", "}"}]}], "&"}], ")"}]}]}], "]"}], ",", RowBox[{"{", "2", "}"}]}], "]"}]}]], "Input",ExpressionUUID->"94839158-\ 754f-41e4-a5c2-024ca20f9c0d"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2503"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "51"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "52"}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "143"}], "}"}], ",", RowBox[{"{", RowBox[{"6", ",", "53"}], "}"}], ",", RowBox[{"{", RowBox[{"30", ",", "1154"}], "}"}], ",", RowBox[{"{", RowBox[{"74", ",", "128"}], "}"}], ",", RowBox[{"{", RowBox[{"98", ",", "129"}], "}"}], ",", RowBox[{"{", RowBox[{"99", ",", "130"}], "}"}], ",", RowBox[{"{", RowBox[{"107", ",", "134"}], "}"}], ",", RowBox[{"{", RowBox[{"110", ",", "137"}], "}"}], ",", RowBox[{"{", RowBox[{"111", ",", "138"}], "}"}], ",", RowBox[{"{", RowBox[{"112", ",", "139"}], "}"}], ",", RowBox[{"{", RowBox[{"399", ",", "1263"}], "}"}], ",", RowBox[{"{", RowBox[{"523", ",", "1510"}], "}"}]}], "}"}]], "Output",ExpressionUUID->\ "3ffeed7f-cb61-437a-b5a9-ac92bd34f70a"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"moses", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "51"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "52"}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "143"}], "}"}], ",", RowBox[{"{", RowBox[{"6", ",", "53"}], "}"}], ",", RowBox[{"{", RowBox[{"7", ",", "1843"}], "}"}], ",", RowBox[{"{", RowBox[{"8", ",", "185"}], "}"}], ",", RowBox[{"{", RowBox[{"9", ",", "6"}], "}"}], ",", RowBox[{"{", RowBox[{"10", ",", "389"}], "}"}], ",", RowBox[{"{", RowBox[{"11", ",", "1112"}], "}"}], ",", RowBox[{"{", RowBox[{"19", ",", "571"}], "}"}], ",", RowBox[{"{", RowBox[{"30", ",", "1154"}], "}"}], ",", RowBox[{"{", RowBox[{"35", ",", "1594"}], "}"}], ",", RowBox[{"{", RowBox[{"36", ",", "403"}], "}"}], ",", RowBox[{"{", RowBox[{"40", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"43", ",", "2052"}], "}"}], ",", RowBox[{"{", RowBox[{"44", ",", "1990"}], "}"}], ",", RowBox[{"{", RowBox[{"46", ",", "24"}], "}"}], ",", RowBox[{"{", RowBox[{"48", ",", "1879"}], "}"}], ",", RowBox[{"{", RowBox[{"55", ",", "427"}], "}"}], ",", RowBox[{"{", RowBox[{"56", ",", "235"}], "}"}], ",", RowBox[{"{", RowBox[{"57", ",", "25"}], "}"}], ",", RowBox[{"{", RowBox[{"63", ",", "184"}], "}"}], ",", RowBox[{"{", RowBox[{"71", ",", "570"}], "}"}], ",", RowBox[{"{", RowBox[{"74", ",", "128"}], "}"}], ",", RowBox[{"{", RowBox[{"80", ",", "1986"}], "}"}], ",", RowBox[{"{", RowBox[{"84", ",", "155"}], "}"}], ",", RowBox[{"{", RowBox[{"90", ",", "2904"}], "}"}], ",", RowBox[{"{", RowBox[{"98", ",", "129"}], "}"}], ",", RowBox[{"{", RowBox[{"99", ",", "130"}], "}"}], ",", RowBox[{"{", RowBox[{"100", ",", "125"}], "}"}], ",", RowBox[{"{", RowBox[{"101", ",", "115"}], "}"}], ",", RowBox[{"{", RowBox[{"102", ",", "131"}], "}"}], ",", RowBox[{"{", RowBox[{"103", ",", "114"}], "}"}], ",", RowBox[{"{", RowBox[{"104", ",", "113"}], "}"}], ",", RowBox[{"{", RowBox[{"105", ",", "132"}], "}"}], ",", RowBox[{"{", RowBox[{"106", ",", "133"}], "}"}], ",", RowBox[{"{", RowBox[{"107", ",", "134"}], "}"}], ",", RowBox[{"{", RowBox[{"108", ",", "135"}], "}"}], ",", RowBox[{"{", RowBox[{"109", ",", "136"}], "}"}], ",", RowBox[{"{", RowBox[{"110", ",", "137"}], "}"}], ",", RowBox[{"{", RowBox[{"111", ",", "138"}], "}"}], ",", RowBox[{"{", RowBox[{"112", ",", "139"}], "}"}], ",", RowBox[{"{", RowBox[{"164", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"165", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"166", ",", "7"}], "}"}], ",", RowBox[{"{", RowBox[{"167", ",", "8"}], "}"}], ",", RowBox[{"{", RowBox[{"168", ",", "9"}], "}"}], ",", RowBox[{"{", RowBox[{"169", ",", "32"}], "}"}], ",", RowBox[{"{", RowBox[{"170", ",", "76"}], "}"}], ",", RowBox[{"{", RowBox[{"173", ",", "19"}], "}"}], ",", RowBox[{"{", RowBox[{"174", ",", "1824"}], "}"}], ",", RowBox[{"{", RowBox[{"177", ",", "1829"}], "}"}], ",", RowBox[{"{", RowBox[{"188", ",", "65"}], "}"}], ",", RowBox[{"{", RowBox[{"191", ",", "54"}], "}"}], ",", RowBox[{"{", RowBox[{"200", ",", "1899"}], "}"}], ",", RowBox[{"{", RowBox[{"236", ",", "2262"}], "}"}], ",", RowBox[{"{", RowBox[{"241", ",", "460"}], "}"}], ",", RowBox[{"{", RowBox[{"258", ",", "33"}], "}"}], ",", RowBox[{"{", RowBox[{"259", ",", "1826"}], "}"}], ",", RowBox[{"{", RowBox[{"260", ",", "429"}], "}"}], ",", RowBox[{"{", RowBox[{"266", ",", "225"}], "}"}], ",", RowBox[{"{", RowBox[{"289", ",", "1856"}], "}"}], ",", RowBox[{"{", RowBox[{"354", ",", "428"}], "}"}], ",", RowBox[{"{", RowBox[{"361", ",", "158"}], "}"}], ",", RowBox[{"{", RowBox[{"362", ",", "31"}], "}"}], ",", RowBox[{"{", RowBox[{"363", ",", "57"}], "}"}], ",", RowBox[{"{", RowBox[{"399", ",", "1263"}], "}"}], ",", RowBox[{"{", RowBox[{"442", ",", "973"}], "}"}], ",", RowBox[{"{", RowBox[{"484", ",", "186"}], "}"}], ",", RowBox[{"{", RowBox[{"503", ",", "92"}], "}"}], ",", RowBox[{"{", RowBox[{"504", ",", "48"}], "}"}], ",", RowBox[{"{", RowBox[{"505", ",", "46"}], "}"}], ",", RowBox[{"{", RowBox[{"513", ",", "523"}], "}"}], ",", RowBox[{"{", RowBox[{"514", ",", "512"}], "}"}], ",", RowBox[{"{", RowBox[{"516", ",", "511"}], "}"}], ",", RowBox[{"{", RowBox[{"517", ",", "30"}], "}"}], ",", RowBox[{"{", RowBox[{"518", ",", "1503"}], "}"}], ",", RowBox[{"{", RowBox[{"522", ",", "924"}], "}"}], ",", RowBox[{"{", RowBox[{"523", ",", "1510"}], "}"}], ",", RowBox[{"{", RowBox[{"527", ",", "2393"}], "}"}], ",", RowBox[{"{", RowBox[{"528", ",", "2781"}], "}"}], ",", RowBox[{"{", RowBox[{"573", ",", "216"}], "}"}], ",", RowBox[{"{", RowBox[{"610", ",", "2165"}], "}"}], ",", RowBox[{"{", RowBox[{"644", ",", "1562"}], "}"}], ",", RowBox[{"{", RowBox[{"649", ",", "647"}], "}"}], ",", RowBox[{"{", RowBox[{"650", ",", "2501"}], "}"}], ",", RowBox[{"{", RowBox[{"657", ",", "2489"}], "}"}], ",", RowBox[{"{", RowBox[{"672", ",", "232"}], "}"}], ",", RowBox[{"{", RowBox[{"844", ",", "75"}], "}"}], ",", RowBox[{"{", RowBox[{"845", ",", "63"}], "}"}], ",", RowBox[{"{", RowBox[{"846", ",", "275"}], "}"}], ",", RowBox[{"{", RowBox[{"900", ",", "526"}], "}"}], ",", RowBox[{"{", RowBox[{"910", ",", "230"}], "}"}], ",", RowBox[{"{", RowBox[{"926", ",", "804"}], "}"}], ",", RowBox[{"{", RowBox[{"927", ",", "2679"}], "}"}], ",", RowBox[{"{", RowBox[{"978", ",", "1093"}], "}"}], ",", RowBox[{"{", RowBox[{"999", ",", "1596"}], "}"}], ",", RowBox[{"{", RowBox[{"1054", ",", "107"}], "}"}], ",", RowBox[{"{", RowBox[{"1128", ",", "1844"}], "}"}], ",", RowBox[{"{", RowBox[{"1130", ",", "1838"}], "}"}], ",", RowBox[{"{", RowBox[{"1145", ",", "974"}], "}"}], ",", RowBox[{"{", RowBox[{"1155", ",", "468"}], "}"}], ",", RowBox[{"{", RowBox[{"1158", ",", "1147"}], "}"}], ",", RowBox[{"{", RowBox[{"1276", ",", "16"}], "}"}], ",", RowBox[{"{", RowBox[{"1277", ",", "15"}], "}"}], ",", RowBox[{"{", RowBox[{"1282", ",", "98"}], "}"}], ",", RowBox[{"{", RowBox[{"1292", ",", "127"}], "}"}], ",", RowBox[{"{", RowBox[{"1293", ",", "122"}], "}"}], ",", RowBox[{"{", RowBox[{"1381", ",", "1312"}], "}"}], ",", RowBox[{"{", RowBox[{"1382", ",", "1313"}], "}"}], ",", RowBox[{"{", RowBox[{"1385", ",", "546"}], "}"}], ",", RowBox[{"{", RowBox[{"1445", ",", "1974"}], "}"}], ",", RowBox[{"{", RowBox[{"1488", ",", "1827"}], "}"}], ",", RowBox[{"{", RowBox[{"1490", ",", "68"}], "}"}], ",", RowBox[{"{", RowBox[{"1507", ",", "1136"}], "}"}], ",", RowBox[{"{", RowBox[{"1635", ",", "1637"}], "}"}], ",", RowBox[{"{", RowBox[{"1697", ",", "1593"}], "}"}], ",", RowBox[{"{", RowBox[{"1709", ",", "1993"}], "}"}], ",", RowBox[{"{", RowBox[{"1721", ",", "317"}], "}"}], ",", RowBox[{"{", RowBox[{"1742", ",", "264"}], "}"}], ",", RowBox[{"{", RowBox[{"1743", ",", "393"}], "}"}], ",", RowBox[{"{", RowBox[{"1745", ",", "847"}], "}"}], ",", RowBox[{"{", RowBox[{"1754", ",", "467"}], "}"}], ",", RowBox[{"{", RowBox[{"1758", ",", "421"}], "}"}], ",", RowBox[{"{", RowBox[{"1763", ",", "2351"}], "}"}], ",", RowBox[{"{", RowBox[{"1764", ",", "418"}], "}"}], ",", RowBox[{"{", RowBox[{"1766", ",", "577"}], "}"}], ",", RowBox[{"{", RowBox[{"1768", ",", "110"}], "}"}], ",", RowBox[{"{", RowBox[{"2077", ",", "2072"}], "}"}], ",", RowBox[{"{", RowBox[{"2082", ",", "1968"}], "}"}], ",", RowBox[{"{", RowBox[{"2089", ",", "1828"}], "}"}], ",", RowBox[{"{", RowBox[{"2136", ",", "64"}], "}"}], ",", RowBox[{"{", RowBox[{"2173", ",", "231"}], "}"}], ",", RowBox[{"{", RowBox[{"2183", ",", "3003"}], "}"}], ",", RowBox[{"{", RowBox[{"2265", ",", "3018"}], "}"}], ",", RowBox[{"{", RowBox[{"2270", ",", "1609"}], "}"}], ",", RowBox[{"{", RowBox[{"2291", ",", "1560"}], "}"}], ",", RowBox[{"{", RowBox[{"2448", ",", "1113"}], "}"}], ",", RowBox[{"{", RowBox[{"2449", ",", "1114"}], "}"}], ",", RowBox[{"{", RowBox[{"2801", ",", "542"}], "}"}], ",", RowBox[{"{", RowBox[{"2802", ",", "2777"}], "}"}], ",", RowBox[{"{", RowBox[{"2808", ",", "2782"}], "}"}], ",", RowBox[{"{", RowBox[{"2809", ",", "2794"}], "}"}], ",", RowBox[{"{", RowBox[{"2810", ",", "2790"}], "}"}], ",", RowBox[{"{", RowBox[{"2820", ",", "2799"}], "}"}], ",", RowBox[{"{", RowBox[{"2821", ",", "2797"}], "}"}], ",", RowBox[{"{", RowBox[{"2832", ",", "2848"}], "}"}], ",", RowBox[{"{", RowBox[{"2938", ",", "95"}], "}"}], ",", RowBox[{"{", RowBox[{"2939", ",", "96"}], "}"}], ",", RowBox[{"{", RowBox[{"2940", ",", "252"}], "}"}], ",", RowBox[{"{", RowBox[{"2941", ",", "97"}], "}"}], ",", RowBox[{"{", RowBox[{"2942", ",", "1799"}], "}"}], ",", RowBox[{"{", RowBox[{"2943", ",", "1105"}], "}"}], ",", RowBox[{"{", RowBox[{"2948", ",", "1141"}], "}"}], ",", RowBox[{"{", RowBox[{"2951", ",", "69"}], "}"}], ",", RowBox[{"{", RowBox[{"2956", ",", "254"}], "}"}], ",", RowBox[{"{", RowBox[{"2957", ",", "250"}], "}"}], ",", RowBox[{"{", RowBox[{"2958", ",", "249"}], "}"}]}], "}"}]}], ";"}]], "Input",Expressi\ onUUID->"005571aa-360a-43b2-b673-f23d7da1fa3c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"Name", "[", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], ",", RowBox[{"X", "[", RowBox[{"#", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], "]"}], ",", RowBox[{"Name", "[", RowBox[{"X", "[", RowBox[{"#", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], "]"}], "]"}]}], "}"}], "&"}], "/@", RowBox[{"Cases", "[", RowBox[{"pts", ",", RowBox[{"_", "?", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Last", "[", "#", "]"}], "=!=", RowBox[{"{", "}"}]}], "&"}], ")"}]}]}], "]"}]}], "//", "TableForm"}]], "Input",ExpressionUUID->"7fe2ead5-4ca7-401d-8ec4-\ d284042a058c"], Cell[BoxData[ TagBox[GridBox[{ { RowBox[{"X", "[", "1", "]"}], "\<\"incenter\"\>", RowBox[{ "X", "[", "2503", "]"}], "\<\"radical center of {circumcircle, Parry circle, Bevan \ circle}\"\>"}, { RowBox[{"X", "[", "2", "]"}], "\<\"centroid\"\>", RowBox[{"X", "[", "51", "]"}], "\<\"centroid of orthic triangle\"\>"}, { RowBox[{"X", "[", "3", "]"}], "\<\"circumcenter\"\>", RowBox[{"X", "[", "5", "]"}], "\<\"nine-point center\"\>"}, { RowBox[{"X", "[", "4", "]"}], "\<\"orthocenter\"\>", RowBox[{ "X", "[", "52", "]"}], "\<\"orthocenter of orthic triangle\"\>"}, { RowBox[{"X", "[", "5", "]"}], "\<\"nine-point center\"\>", RowBox[{ "X", "[", "143", "]"}], "\<\"nine-point center of orthic triangle\"\>"}, { RowBox[{ "X", "[", "6", "]"}], "\<\"symmedian point (Lemoine point, Grebe point)\"\>", RowBox[{ "X", "[", "53", "]"}], "\<\"symmedian point of orthic triangle\"\>"}, { RowBox[{"X", "[", "30", "]"}], "\<\"Euler infinity point\"\>", RowBox[{"X", "[", "1154", "]"}], "\<\"isogonal conjugate of X(1141)\"\>"}, { RowBox[{"X", "[", "74", "]"}], "\<\"X(74)\"\>", RowBox[{"X", "[", "128", "]"}], "\<\"X(74)-of-orthic-triangle\"\>"}, { RowBox[{"X", "[", "98", "]"}], "\<\"Tarry point\"\>", RowBox[{"X", "[", "129", "]"}], "\<\"X(98)-of-orthic-triangle\"\>"}, { RowBox[{"X", "[", "99", "]"}], "\<\"Steiner point\"\>", RowBox[{"X", "[", "130", "]"}], "\<\"X(99)-of-orthic-triangle\"\>"}, { RowBox[{ "X", "[", "107", "]"}], "\<\"ψ(symmedian point, orthocenter)\"\>", RowBox[{"X", "[", "134", "]"}], "\<\"X(107)-of-orthic-triangle\"\>"}, { RowBox[{"X", "[", "110", "]"}], "\<\"focus of Kiepert parabola\"\>", RowBox[{"X", "[", "137", "]"}], "\<\"X(110)-of-orthic-triangle\"\>"}, { RowBox[{"X", "[", "111", "]"}], "\<\"Parry point\"\>", RowBox[{"X", "[", "138", "]"}], "\<\"X(111)-of-orthic-triangle\"\>"}, { RowBox[{ "X", "[", "112", "]"}], "\<\"ψ(orthocenter, symmedian point)\"\>", RowBox[{"X", "[", "139", "]"}], "\<\"X(112)-of-orthic-triangle\"\>"}, { RowBox[{"X", "[", "399", "]"}], "\<\"Parry reflection point\"\>", RowBox[{"X", "[", "1263", "]"}], "\<\"isogonal conjugate of X(1157)\"\>"}, { RowBox[{"X", "[", "523", "]"}], "\<\"isogonal conjugate of X(110)\"\>", RowBox[{"X", "[", "1510", "]"}], "\<\"Napoleon crossdifference\"\>"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output",ExpressionUUID->"d14ea725-be36-4bf0-\ 98e1-df14a061627a"] }, Open ]], Cell[CellGroupData[{ Cell["X[1]", "Subsection",ExpressionUUID->"506a729a-5cfa-4316-b575-095088035656"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"KimberlingLookup", "[", RowBox[{ RowBox[{"X", "[", "1", "]"}], "[", "OrthicTriangle", "]"}], "]"}]], "Input",\ ExpressionUUID->"07d2a761-189a-465c-ade8-ead17c5febad"], Cell[BoxData[ RowBox[{"{", "2503", "}"}]], "Output",ExpressionUUID->"5dfff70c-e086-4216-97a0-b3de59460bdf"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"expr", "=", RowBox[{"-", RowBox[{"ToAngles", "[", RowBox[{"Symmetrize", "[", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Together", "//@", RowBox[{"ToSidelengths", "[", RowBox[{ RowBox[{"X", "[", "1", "]"}], "[", "OrthicTriangle", "]"}], "]"}]}], "/.", RowBox[{ RowBox[{"Sqrt", "[", "s_", "]"}], "\[RuleDelayed]", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", "s", "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}]}]}], "]"}], "]"}], "]"}]}]}]], "Input",ExpressionUUID->"979c90e8-5e01-4c18-ad46-\ 593fbfa511fe"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ FractionBox["1", RowBox[{"a", " ", "b", " ", "c"}]], RowBox[{"(", RowBox[{ RowBox[{"Abs", "[", RowBox[{"b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}]}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "c", " ", RowBox[{"Cos", "[", "B", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["b", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "c", " ", RowBox[{"Cos", "[", "B", "]"}]}], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "c", " ", RowBox[{"Cos", "[", "B", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "b", " ", RowBox[{"Cos", "[", "C", "]"}]}], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["b", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "b", " ", RowBox[{"Cos", "[", "C", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "b", " ", RowBox[{"Cos", "[", "C", "]"}]}], "]"}]}]}], ")"}], " ", RowBox[{"Sec", "[", "A", "]"}]}], ")"}]}], ",", RowBox[{ FractionBox["1", RowBox[{"a", " ", "b", " ", "c"}]], RowBox[{"(", RowBox[{ RowBox[{"Abs", "[", RowBox[{"a", " ", "c", " ", RowBox[{"Cos", "[", "B", "]"}]}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", RowBox[{"Abs", "[", RowBox[{"b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["b", "2"], " ", RowBox[{"Abs", "[", RowBox[{"b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}]}], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Abs", "[", RowBox[{"b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}]}], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "b", " ", RowBox[{"Cos", "[", "C", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["b", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "b", " ", RowBox[{"Cos", "[", "C", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "b", " ", RowBox[{"Cos", "[", "C", "]"}]}], "]"}]}]}], ")"}], " ", RowBox[{"Sec", "[", "B", "]"}]}], ")"}]}], ",", RowBox[{ FractionBox["1", RowBox[{"a", " ", "b", " ", "c"}]], RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", RowBox[{"Abs", "[", RowBox[{"b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}]}], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["b", "2"], " ", RowBox[{"Abs", "[", RowBox[{"b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Abs", "[", RowBox[{"b", " ", "c", " ", RowBox[{"Cos", "[", "A", "]"}]}], "]"}]}], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "c", " ", RowBox[{"Cos", "[", "B", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["b", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "c", " ", RowBox[{"Cos", "[", "B", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", SuperscriptBox["c", "2"], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "c", " ", RowBox[{"Cos", "[", "B", "]"}]}], "]"}]}]}], ")"}], " ", RowBox[{"Abs", "[", RowBox[{"a", " ", "b", " ", RowBox[{"Cos", "[", "C", "]"}]}], "]"}], " ", RowBox[{"Sec", "[", "C", "]"}]}], ")"}]}]}], "}"}]], "Output",Expression\ UUID->"c436e36e-b8a7-49b3-8fc1-3bbd88e7b96f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"KimberlingLookup", "[", "%", "]"}]], "Input",ExpressionUUID->"b27dec37-0ebb-487e-bd8a-45b4c56ce13d"], Cell[BoxData[ RowBox[{"{", "2503", "}"}]], "Output",ExpressionUUID->"ed25ed99-c6a3-4a41-970e-e8188180a6b1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Symmetrize", "[", RowBox[{"ToAngles", "[", RowBox[{"Simplify", "[", RowBox[{"expr", ",", RowBox[{ RowBox[{"AcuteQ", "[", "]"}], "&&", RowBox[{"TriangleQ", "[", "]"}]}]}], "]"}], "]"}], "]"}]], "Input",Expre\ ssionUUID->"4c7d8a26-77cf-446c-8397-fb151da77e56"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"Sec", "[", "A", "]"}], ",", RowBox[{"Sec", "[", "B", "]"}], ",", RowBox[{"Sec", "[", "C", "]"}]}], "}"}]], "Output",ExpressionUUID->\ "524ecadf-f57e-416c-9389-85f19a5738ca"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"KimberlingLookup", "[", "%", "]"}]], "Input",ExpressionUUID->"4f9e1434-7fef-46df-8997-b3f4926a7a94"], Cell[BoxData[ RowBox[{"{", "4", "}"}]], "Output",ExpressionUUID->"0ded6ecf-6fbe-4f3f-9441-24f3a8dd32aa"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Acute-Only", "Subsection",ExpressionUUID->"c0481605-2fc1-421b-95b8-c72d23216c10"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"KimberlingLookup", "[", RowBox[{ RowBox[{"X", "[", "7", "]"}], "[", "OrthicTriangle", "]"}], "]"}]], "Input",\ ExpressionUUID->"e317dc81-06ec-4ca0-9a53-5e7ccae6f7b4"], Cell[BoxData[ RowBox[{"{", "}"}]], "Output",ExpressionUUID->"f747c7c8-de4a-4624-994e-eb6702087fd1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AcuteQ", "[", "]"}]], "Input",ExpressionUUID->"c18a94a5-dc95-475c-90f1-8b20dd028630"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]}], ">", SuperscriptBox["c", "2"]}], "&&", RowBox[{ RowBox[{ SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ">", SuperscriptBox["a", "2"]}], "&&", RowBox[{ RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["c", "2"]}], ">", SuperscriptBox["b", "2"]}], "&&", RowBox[{"0", "<", "A", "<", FractionBox["\[Pi]", "2"]}], "&&", RowBox[{"0", "<", "B", "<", FractionBox["\[Pi]", "2"]}], "&&", RowBox[{"0", "<", "C", "<", FractionBox["\[Pi]", "2"]}]}]], "Output",ExpressionUUID->"e1ded302-6c00-\ 4a9b-a17d-3991274a0586"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{"Together", "//@", RowBox[{"ToSidelengths", "[", RowBox[{ RowBox[{"X", "[", "7", "]"}], "[", "OrthicTriangle", "]"}], "]"}]}], "/.", RowBox[{ RowBox[{"Sqrt", "[", "s_", "]"}], "\[RuleDelayed]", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Sqrt", "[", "s", "]"}], ",", RowBox[{ RowBox[{"TriangleQ", "[", "]"}], "&&", RowBox[{"AcuteQ", "[", "]"}]}]}], "]"}]}]}], ",", RowBox[{ RowBox[{"TriangleQ", "[", "]"}], "&&", RowBox[{"AcuteQ", "[", "]"}]}]}], "]"}]], "Input",ExpressionUUID->\ "90630de4-77b4-43ea-ae2d-dcc33d64167b"], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox[ RowBox[{"512", " ", SuperscriptBox["a", "9"], " ", SuperscriptBox["b", "8"], " ", SuperscriptBox["c", "8"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], "4"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "4"], "-", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}], "2"]}], ")"}], "3"]}]], ",", RowBox[{"-", FractionBox[ RowBox[{"512", " ", SuperscriptBox["a", "8"], " ", SuperscriptBox["b", "9"], " ", SuperscriptBox["c", "8"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["c", "2"]}], ")"}]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], "4"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "4"], "-", SuperscriptBox["b", "4"], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "2"]}], "+", SuperscriptBox["c", "4"]}], ")"}], "3"]}]]}], ",", RowBox[{"-", FractionBox[ RowBox[{"512", " ", SuperscriptBox["a", "8"], " ", SuperscriptBox["b", "8"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]}], ")"}], " ", SuperscriptBox["c", "9"]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}], "4"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "4"], "-", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", SuperscriptBox["b", "4"], "-", SuperscriptBox["c", "4"]}], ")"}], "3"]}]]}]}], "}"}]], "Output",Expr\ essionUUID->"3ee5c7f1-ae6f-4f15-9075-38a0d898ed0f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["Symmetrize"], "Input",ExpressionUUID->"231a569e-ea9e-4290-b0b3-a8ccce3aedc4"], Cell[BoxData["Symmetrize"], "Output",ExpressionUUID->"aefae39f-1174-40f6-ba99-454daac4b7e2"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{"%49", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["a", "2"]}], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], "3"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}], "3"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], "3"]}], RowBox[{"512", " ", SuperscriptBox["a", "8"], " ", SuperscriptBox["b", "8"], " ", SuperscriptBox["c", "8"]}]]}], "]"}]], "Input",ExpressionUUID->"a3e5ba17-\ 1f5b-472b-8072-198127cd9698"], Cell[BoxData[ RowBox[{"-", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}], "3"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}], "3"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], "3"], " ", "%49"}], RowBox[{"512", " ", SuperscriptBox["a", "8"], " ", SuperscriptBox["b", "8"], " ", SuperscriptBox["c", "8"]}]]}]], "Output",ExpressionUUID->"e9842f3f-ea8c-\ 4f4a-89a5-8f475d4c657e"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{913, 671}, WindowMargins->{{3, Automatic}, {Automatic, 4}}, ShowSelection->True, FrontEndVersion->"11.1 for Mac OS X x86 (32-bit, 64-bit Kernel) (June 2, \ 2017)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 87, 0, 92, "Title", "ExpressionUUID" -> \ "c12f3fc0-466a-4170-b0d9-48cb6898bf5f"], Cell[CellGroupData[{ Cell[692, 26, 83, 0, 44, "Subsection", "ExpressionUUID" -> \ "6590cf23-08b2-4d4a-a77e-2205a6c3c6f9"], Cell[778, 28, 110, 3, 49, "Text", "ExpressionUUID" -> \ "b2f404bb-e7b7-43fa-97d3-8fe2f5985ef8"], Cell[891, 33, 344, 9, 30, "Text", "ExpressionUUID" -> \ "dcee03b9-a778-4cd5-8015-183f9360eab2"], Cell[1238, 44, 358, 10, 30, "Text", "ExpressionUUID" -> \ "8aa6672a-75c7-4db7-97a7-1ec663559008"], Cell[1599, 56, 154, 2, 30, "Text", "ExpressionUUID" -> \ "1beec0f9-8b9a-48c4-9ff8-f7edc8daecea"] }, Open ]], Cell[CellGroupData[{ Cell[1790, 63, 80, 0, 64, "Section", "ExpressionUUID" -> \ "dadb3a0a-3ea8-4a63-94e8-8f04c22d038a"], Cell[CellGroupData[{ Cell[1895, 67, 2953, 74, 369, "Input", "ExpressionUUID" -> \ "a7db8556-d7f6-4745-9e55-207bdb5c9e32"], Cell[4851, 143, 18740, 632, 222, 13855, 549, "GraphicsData", "PostScript", \ "Graphics", "ExpressionUUID" -> "e746970f-1fa0-4382-b175-90b51459bb21"], Cell[23594, 777, 191, 5, 70, "Output", "ExpressionUUID" -> \ "212edaee-d5cb-48a9-9e81-1908c6e9ae03"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[23834, 788, 82, 0, 70, "Section", "ExpressionUUID" -> \ "8e6ce092-5333-4037-961b-e8800b057a38"], Cell[23919, 790, 121, 1, 70, "Input", "ExpressionUUID" -> \ "c8a946cb-e041-4e2f-adcd-2e30421a1aa7"], Cell[CellGroupData[{ Cell[24065, 795, 209, 5, 70, "Input", "ExpressionUUID" -> \ "bdd4f038-0851-4676-8222-bee189063644"], Cell[24277, 802, 462, 16, 70, "Output", "ExpressionUUID" -> \ "1029c11c-b437-4cfb-9ebc-cb34e1d70a02"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[24788, 824, 86, 0, 70, "Section", "ExpressionUUID" -> \ "62909f42-a1dd-4e89-996d-f076f78f0c8a"], Cell[CellGroupData[{ Cell[24899, 828, 317, 7, 70, "Input", "ExpressionUUID" -> \ "6af1546f-8463-429c-b221-ce20b7a223ad"], Cell[25219, 837, 3309, 103, 70, "Output", "ExpressionUUID" -> \ "888a7cd5-a746-4d8f-bc87-8d6622ed0bdb"] }, Open ]], Cell[CellGroupData[{ Cell[28565, 945, 208, 5, 70, "Input", "ExpressionUUID" -> \ "bbc04a1f-6e8f-40cc-b2ab-d51e5a11322c"], Cell[28776, 952, 881, 28, 70, "Output", "ExpressionUUID" -> \ "9b0249c9-8222-497c-a735-bffcf7933205"] }, Open ]], Cell[CellGroupData[{ Cell[29694, 985, 241, 6, 70, "Input", "ExpressionUUID" -> \ "416509cd-3fee-497f-af2f-6a6692a0e801"], Cell[29938, 993, 407, 12, 70, "Output", "ExpressionUUID" -> \ "3866edde-c60a-416b-a490-e1b7e617549f"] }, Open ]], Cell[CellGroupData[{ Cell[30382, 1010, 82, 0, 70, "Subsection", "ExpressionUUID" -> \ "5decba0b-dbf9-497a-a983-9e25650118e5"], Cell[CellGroupData[{ Cell[30489, 1014, 176, 4, 70, "Input", "ExpressionUUID" -> \ "55800865-3f7b-4114-adf8-9cfda5d9fdf5"], Cell[30668, 1020, 308, 9, 70, "Output", "ExpressionUUID" -> \ "0bd40363-6858-40ca-8664-34a1e04b3765"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[31037, 1036, 87, 0, 70, "Section", "ExpressionUUID" -> \ "db0e2772-8d34-4931-b14c-cd87f2f356c3"], Cell[CellGroupData[{ Cell[31149, 1040, 318, 8, 70, "Input", "ExpressionUUID" -> \ "4229ea00-49ca-41f1-bd49-8f229da8489a"], Cell[31470, 1050, 810, 26, 70, "Output", "ExpressionUUID" -> \ "cce216c4-2104-4db7-b9a0-6aa72eb1c231"] }, Open ]], Cell[CellGroupData[{ Cell[32317, 1081, 244, 6, 70, "Input", "ExpressionUUID" -> \ "3719391d-8161-4e07-9a92-2fa0286fae7f"], Cell[32564, 1089, 461, 14, 70, "Output", "ExpressionUUID" -> \ "5906de36-3de5-4f4d-9478-a0753e90953a"] }, Open ]], Cell[CellGroupData[{ Cell[33062, 1108, 552, 14, 70, "Input", "ExpressionUUID" -> \ "8066e823-0ab2-42e4-98a8-e28dc2a281d6"], Cell[33617, 1124, 177, 4, 70, "Output", "ExpressionUUID" -> \ "09bb5cbb-ec63-44f9-a8e6-0aab27eb2d87"] }, Open ]], Cell[CellGroupData[{ Cell[33831, 1133, 552, 14, 70, "Input", "ExpressionUUID" -> \ "2a671ee2-e594-4155-ab11-e8ccf6f2d306"], Cell[34386, 1149, 177, 4, 70, "Output", "ExpressionUUID" -> \ "ceb5861e-7028-4483-9316-13b2040a0303"] }, Open ]], Cell[CellGroupData[{ Cell[34600, 1158, 552, 14, 70, "Input", "ExpressionUUID" -> \ "944f1535-3d58-4e86-b3a6-611fce50030f"], Cell[35155, 1174, 177, 4, 70, "Output", "ExpressionUUID" -> \ "64b6f29c-e185-45d0-9919-81925d7e7459"] }, Open ]], Cell[CellGroupData[{ Cell[35369, 1183, 82, 0, 70, "Subsection", "ExpressionUUID" -> \ "916e9202-56a1-4252-913b-bcecd094d0e3"], Cell[CellGroupData[{ Cell[35476, 1187, 380, 10, 70, "Input", "ExpressionUUID" -> \ "659aed88-fe96-408a-b35b-5eb8f93c9dbf"], Cell[35859, 1199, 117, 1, 70, "Output", "ExpressionUUID" -> \ "65abedcc-71cc-42cd-84d6-9472ef9a7ee5"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[36037, 1207, 86, 0, 70, "Section", "ExpressionUUID" -> \ "43d00bc1-fe07-44ef-8408-5660b09cf3a6"], Cell[CellGroupData[{ Cell[36148, 1211, 1146, 31, 70, "Input", "ExpressionUUID" -> \ "d6d2d2bd-d9c3-442b-a811-5e99ee3909bf"], Cell[37297, 1244, 103, 1, 70, "Output", "ExpressionUUID" -> \ "be9f99ea-d490-4db4-a25d-c22d22ac0a8a"] }, Open ]], Cell[CellGroupData[{ Cell[37437, 1250, 82, 0, 70, "Subsection", "ExpressionUUID" -> \ "1032a1e1-d300-4a02-a6a4-ddc21949f69b"], Cell[CellGroupData[{ Cell[37544, 1254, 593, 16, 70, "Input", "ExpressionUUID" -> \ "1e92700f-3515-493f-9866-4978a5ad9c3f"], Cell[38140, 1272, 103, 1, 70, "Output", "ExpressionUUID" -> \ "2cc55769-6716-4caa-ad71-ec4091966955"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[38304, 1280, 82, 0, 70, "Section", "ExpressionUUID" -> \ "3a266e72-ea14-4b61-965e-8e5932f7314f"], Cell[CellGroupData[{ Cell[38411, 1284, 572, 15, 70, "Input", "ExpressionUUID" -> \ "f518e683-ad90-4ad4-80a0-497fec804edc"], Cell[38986, 1301, 320, 8, 70, "Output", "ExpressionUUID" -> \ "e14f9aee-c996-42c2-acee-12de2b09037b"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[39355, 1315, 78, 0, 70, "Section", "ExpressionUUID" -> \ "546c42ef-2324-469d-ae4a-5f98606b7413"], Cell[CellGroupData[{ Cell[39458, 1319, 348, 8, 70, "Input", "ExpressionUUID" -> \ "53aae19c-3c6d-414a-b218-aef5ebf6b68e"], Cell[39809, 1329, 1288, 39, 70, "Output", "ExpressionUUID" -> \ "3c7603d7-ab31-4ffb-aed1-d99157ab2134"] }, Open ]], Cell[CellGroupData[{ Cell[41134, 1373, 307, 8, 70, "Input", "ExpressionUUID" -> \ "74fb2ae5-f94c-4d81-8510-d4b2b6c66442"], Cell[41444, 1383, 380, 10, 70, "Output", "ExpressionUUID" -> \ "9a2fb4ec-4e05-4064-a10d-60e58fa24da3"] }, Open ]], Cell[CellGroupData[{ Cell[41861, 1398, 82, 0, 70, "Subsection", "ExpressionUUID" -> \ "cfd11433-f4eb-4864-81d1-054e69b2676e"], Cell[CellGroupData[{ Cell[41968, 1402, 174, 4, 70, "Input", "ExpressionUUID" -> \ "b5b5f2aa-faca-4304-b1ee-e5f802ff063c"], Cell[42145, 1408, 284, 7, 70, "Output", "ExpressionUUID" -> \ "7b7ebb9a-33d6-42ff-9c1e-696c02f3e893"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[42490, 1422, 80, 0, 70, "Section", "ExpressionUUID" -> \ "09e989de-a244-419c-8e42-990ba6e6ed5c"], Cell[42573, 1424, 118, 0, 70, "Print", "ExpressionUUID" -> \ "e4d91556-6716-4a1b-acb6-c2b3c1a18d9a"], Cell[CellGroupData[{ Cell[42716, 1428, 85, 0, 70, "Subsection", "ExpressionUUID" -> \ "31681a80-ba49-4aac-837c-f56002bed697"], Cell[CellGroupData[{ Cell[42826, 1432, 129, 1, 70, "Input", "ExpressionUUID" -> \ "a033d69c-0452-46bd-8b39-6fd52afe60ae"], Cell[42958, 1435, 6006, 172, 70, "Output", "ExpressionUUID" -> \ "2570b415-1c91-43a4-86a4-76498e2da926"] }, Open ]], Cell[CellGroupData[{ Cell[49001, 1612, 381, 10, 70, "Input", "ExpressionUUID" -> \ "33144581-c433-4577-bb23-67329c2e5d18"], Cell[49385, 1624, 464, 15, 70, "Output", "ExpressionUUID" -> \ "b782cf12-9ef7-42e4-a535-ab39e0bc9615"] }, Open ]], Cell[CellGroupData[{ Cell[49886, 1644, 194, 4, 70, "Input", "ExpressionUUID" -> \ "dedc52f6-2ce8-4d8c-b450-92dc646951fe"], Cell[50083, 1650, 232, 6, 70, "Output", "ExpressionUUID" -> \ "16ac69b5-efc6-4fa1-a2a8-a46b222cc8e0"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[50364, 1662, 89, 0, 70, "Subsection", "ExpressionUUID" -> \ "4b651366-10b3-4f6d-aed4-fbf7cdfaec33"], Cell[CellGroupData[{ Cell[50478, 1666, 133, 1, 70, "Input", "ExpressionUUID" -> \ "3fba3f26-5748-4577-a49b-ea3f4a8521c7"], Cell[50614, 1669, 141777, 3495, 70, "Output", "ExpressionUUID" -> \ "a64a6893-2f84-4ec0-be4f-18d317f6c3f3"] }, Closed]], Cell[CellGroupData[{ Cell[192428, 5169, 346, 9, 70, "Input", "ExpressionUUID" -> \ "790953ab-7e59-4f09-9cf1-25780cb3536d"], Cell[192777, 5180, 308, 9, 70, "Output", "ExpressionUUID" -> \ "db5935dd-926f-4635-8520-8b550c051ac3"] }, Open ]], Cell[CellGroupData[{ Cell[193122, 5194, 194, 4, 70, "Input", "ExpressionUUID" -> \ "a501b8aa-b505-4f92-98ee-2aa7145cbfbe"], Cell[193319, 5200, 230, 6, 70, "Output", "ExpressionUUID" -> \ "b1d7f841-c160-4c41-80f3-1efb159483a1"] }, Open ]], Cell[CellGroupData[{ Cell[193586, 5211, 142, 3, 70, "Input", "ExpressionUUID" -> \ "55cbdf54-6483-4143-bb9f-7fdf3aeff994"], Cell[193731, 5216, 107, 0, 70, "Output", "ExpressionUUID" -> \ "8068163a-e98f-4b7b-a539-0cd2b1dcc6c9"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[193887, 5222, 85, 0, 70, "Subsection", "ExpressionUUID" -> \ "75b79556-59fd-4fcb-a2d8-1faad31d819c"], Cell[CellGroupData[{ Cell[193997, 5226, 129, 1, 70, "Input", "ExpressionUUID" -> \ "f2719b48-017b-4f56-825f-b876e8037d28"], Cell[194129, 5229, 130, 1, 70, "Output", "ExpressionUUID" -> \ "c50057e2-19f1-40ed-8d82-f5aef678cdf2"] }, Open ]], Cell[CellGroupData[{ Cell[194296, 5235, 496, 15, 70, "Input", "ExpressionUUID" -> \ "506cdab6-cac5-42e1-ad7a-c8777bb329fb"], Cell[194795, 5252, 202, 4, 70, "Output", "ExpressionUUID" -> \ "3d9f4e63-eb6b-4284-b933-ed6e70dd9f58"] }, Open ]], Cell[CellGroupData[{ Cell[195034, 5261, 119, 1, 70, "Input", "ExpressionUUID" -> \ "b083376f-172a-49d7-b7df-f131078bb9c1"], Cell[195156, 5264, 186, 4, 70, "Output", "ExpressionUUID" -> \ "4593346d-24a9-4ce7-b727-56c376e5dde8"] }, Open ]], Cell[195357, 5271, 82, 0, 70, "Text", "ExpressionUUID" -> \ "cb5532bf-e19a-4058-9d18-1c285cf39e2c"], Cell[CellGroupData[{ Cell[195464, 5275, 132, 1, 70, "Input", "ExpressionUUID" -> \ "fd5b75ca-fa32-4276-9e4c-e73e55585dee"], Cell[195599, 5278, 112, 1, 70, "Output", "ExpressionUUID" -> \ "92d91bd6-b471-4dc9-bf96-c42fce85f94e"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[195760, 5285, 88, 0, 70, "Subsection", "ExpressionUUID" -> \ "44120aaf-5774-4c46-9fa5-007d56b162d5"], Cell[CellGroupData[{ Cell[195873, 5289, 321, 8, 70, "Input", "ExpressionUUID" -> \ "41b6adb0-8a8d-4529-8648-556cd001ac33"], Cell[196197, 5299, 560, 18, 70, "Output", "ExpressionUUID" -> \ "d61da313-8fa0-40c4-935f-b507a40a114e"] }, Open ]], Cell[CellGroupData[{ Cell[196794, 5322, 194, 4, 70, "Input", "ExpressionUUID" -> \ "897c24f9-ccbc-4092-84ef-577e675c3e5a"], Cell[196991, 5328, 231, 6, 70, "Output", "ExpressionUUID" -> \ "b381d548-03b1-45ac-855e-4a885d254554"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[197271, 5340, 92, 0, 70, "Subsection", "ExpressionUUID" -> \ "d1287cbb-b4c4-401c-94a2-cbdbc3d7b444"], Cell[197366, 5342, 95, 0, 70, "Text", "ExpressionUUID" -> \ "6cc78935-b428-4452-b8ec-a4950c17b1a0"], Cell[197464, 5344, 117, 1, 70, "Input", "ExpressionUUID" -> \ "0f993b02-12e4-49ff-9f05-2594c1be4a8e"], Cell[CellGroupData[{ Cell[197606, 5349, 1142, 28, 70, "Input", "ExpressionUUID" -> \ "753e6e09-371a-498e-8c46-c0c330b8adeb"], Cell[198751, 5379, 7227, 229, 70, 3904, 173, "GraphicsData", "PostScript", \ "Graphics", "ExpressionUUID" -> "d80e64c9-5376-491e-bbac-f81b5d59f6ef"], Cell[205981, 5610, 191, 5, 70, "Output", "ExpressionUUID" -> \ "2fec26ae-8417-40f0-a653-55d6255b204f"] }, Open ]], Cell[CellGroupData[{ Cell[206209, 5620, 749, 20, 70, "Input", "ExpressionUUID" -> \ "ed86bfad-f025-421c-bd99-03a1e3c32edc"], Cell[206961, 5642, 957, 15, 70, "Message", "ExpressionUUID" -> \ "913feb94-ff6e-4e9e-a369-300806422ddb"], Cell[207921, 5659, 909, 14, 70, "Message", "ExpressionUUID" -> \ "a801aec8-a18b-4c5e-897e-72594656c335"] }, Open ]], Cell[208845, 5676, 388, 12, 70, "Input", "ExpressionUUID" -> \ "8adb164e-7191-432e-a96a-c196384f1639"], Cell[CellGroupData[{ Cell[209258, 5692, 165, 3, 70, "Input", "ExpressionUUID" -> \ "179d9c4a-5423-4591-a89a-f14562237a88"], Cell[209426, 5697, 199, 4, 70, "Output", "ExpressionUUID" -> \ "54c4f805-47aa-4ba8-bc93-a0b8f7564313"] }, Open ]], Cell[CellGroupData[{ Cell[209662, 5706, 147, 3, 70, "Input", "ExpressionUUID" -> \ "5c92f545-8e23-4096-8fe5-c5370fb37907"], Cell[209812, 5711, 200, 4, 70, "Output", "ExpressionUUID" -> \ "85cb5545-1a2f-4685-91f3-6846c0e9af62"] }, Open ]], Cell[CellGroupData[{ Cell[210049, 5720, 305, 8, 70, "Input", "ExpressionUUID" -> \ "dfeac559-e2f2-45cd-8392-f5ffa68ba4e8"], Cell[210357, 5730, 200, 4, 70, "Output", "ExpressionUUID" -> \ "59b2fb80-2787-4457-83e7-6be1e6527a6e"] }, Open ]], Cell[CellGroupData[{ Cell[210594, 5739, 357, 9, 70, "Input", "ExpressionUUID" -> \ "291dcf51-5693-4085-8351-ccef6b9ced49"], Cell[210954, 5750, 231, 6, 70, "Output", "ExpressionUUID" -> \ "b7819e0c-b3ed-48cf-b342-b8b38cd219c8"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[211246, 5763, 90, 0, 70, "Section", "ExpressionUUID" -> \ "20b41ab3-72f9-40d2-aede-aebee7a1c1d0"], Cell[CellGroupData[{ Cell[211361, 5767, 4499, 126, 70, "Input", "ExpressionUUID" -> \ "6c0679b9-2360-4683-8e90-d3781318f2c6"], Cell[215863, 5895, 26391, 911, 70, 21379, 827, "GraphicsData", "PostScript", \ "Graphics", "ExpressionUUID" -> "50f2320c-5d8a-4ff2-944d-2b00dd49e134"], Cell[242257, 6808, 191, 5, 70, "Output", "ExpressionUUID" -> \ "6658f2ee-a621-42da-9f94-995ea70cfcaf"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[242497, 6819, 85, 0, 70, "Section", "ExpressionUUID" -> \ "21ec0f50-0619-470b-ad53-abfb99f79f45"], Cell[CellGroupData[{ Cell[242607, 6823, 4767, 127, 70, "Input", "ExpressionUUID" -> \ "323fc511-22b1-4482-b781-6cecceb34a1c"], Cell[247377, 6952, 32525, 1146, 70, 27546, 1063, "GraphicsData", \ "PostScript", "Graphics", "ExpressionUUID" -> \ "324346fb-0372-4223-ad07-ef842f6d4b3a"], Cell[279905, 8100, 191, 5, 70, "Output", "ExpressionUUID" -> \ "ad08cb7b-fdb9-46de-91ac-bbb32977c588"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[280145, 8111, 113, 0, 70, "Section", "ExpressionUUID" -> \ "4ababc0c-bae3-4e58-ac8d-45cf40010f8a"], Cell[CellGroupData[{ Cell[280283, 8115, 3952, 100, 70, "Input", "ExpressionUUID" -> \ "acf35294-e5cf-4950-976f-d24a45f0f9a7"], Cell[284238, 8217, 29836, 1010, 70, 23070, 897, "GraphicsData", "PostScript", \ "Graphics", "ExpressionUUID" -> "54c8c3ee-3e9f-4f54-b47e-bf4ea65e74f6"], Cell[314077, 9229, 191, 5, 70, "Output", "ExpressionUUID" -> \ "a4470dde-0608-433c-84fc-dc57aabd3251"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[314317, 9240, 81, 0, 70, "Section", "ExpressionUUID" -> \ "6972bc25-391f-4df1-8875-57ac4c8ffd3f"], Cell[314401, 9242, 118, 0, 70, "Print", "ExpressionUUID" -> \ "40f3bb70-a1ce-43b7-b96f-16436d3d048b"], Cell[CellGroupData[{ Cell[314544, 9246, 470, 14, 70, "Input", "ExpressionUUID" -> \ "38217e2e-5144-45f3-9b3f-58b795caf520"], Cell[315017, 9262, 181, 4, 70, "Output", "ExpressionUUID" -> \ "518d6629-d90f-4316-9dd8-7cca3074fac9"] }, Open ]], Cell[CellGroupData[{ Cell[315235, 9271, 443, 13, 70, "Input", "ExpressionUUID" -> \ "94839158-754f-41e4-a5c2-024ca20f9c0d"], Cell[315681, 9286, 1101, 35, 70, "Output", "ExpressionUUID" -> \ "3ffeed7f-cb61-437a-b5a9-ac92bd34f70a"] }, Open ]], Cell[316797, 9324, 10910, 325, 70, "Input", "ExpressionUUID" -> \ "005571aa-360a-43b2-b673-f23d7da1fa3c"], Cell[CellGroupData[{ Cell[327732, 9653, 910, 30, 70, "Input", "ExpressionUUID" -> \ "7fe2ead5-4ca7-401d-8ec4-d284042a058c"], Cell[328645, 9685, 3044, 73, 70, "Output", "ExpressionUUID" -> \ "d14ea725-be36-4bf0-98e1-df14a061627a"] }, Open ]], Cell[CellGroupData[{ Cell[331726, 9763, 81, 0, 70, "Subsection", "ExpressionUUID" -> \ "506a729a-5cfa-4316-b575-095088035656"], Cell[CellGroupData[{ Cell[331832, 9767, 196, 4, 70, "Input", "ExpressionUUID" -> \ "07d2a761-189a-465c-ade8-ead17c5febad"], Cell[332031, 9773, 108, 1, 70, "Output", "ExpressionUUID" -> \ "5dfff70c-e086-4216-97a0-b3de59460bdf"] }, Open ]], Cell[CellGroupData[{ Cell[332176, 9779, 676, 19, 70, "Input", "ExpressionUUID" -> \ "979c90e8-5e01-4c18-ad46-593fbfa511fe"], Cell[332855, 9800, 4634, 126, 70, "Output", "ExpressionUUID" -> \ "c436e36e-b8a7-49b3-8fc1-3bbd88e7b96f"] }, Open ]], Cell[CellGroupData[{ Cell[337526, 9931, 124, 1, 70, "Input", "ExpressionUUID" -> \ "b27dec37-0ebb-487e-bd8a-45b4c56ce13d"], Cell[337653, 9934, 108, 1, 70, "Output", "ExpressionUUID" -> \ "ed25ed99-c6a3-4a41-970e-e8188180a6b1"] }, Open ]], Cell[CellGroupData[{ Cell[337798, 9940, 313, 8, 70, "Input", "ExpressionUUID" -> \ "4c7d8a26-77cf-446c-8397-fb151da77e56"], Cell[338114, 9950, 233, 6, 70, "Output", "ExpressionUUID" -> \ "524ecadf-f57e-416c-9389-85f19a5738ca"] }, Open ]], Cell[CellGroupData[{ Cell[338384, 9961, 124, 1, 70, "Input", "ExpressionUUID" -> \ "4f9e1434-7fef-46df-8997-b3f4926a7a94"], Cell[338511, 9964, 105, 1, 70, "Output", "ExpressionUUID" -> \ "0ded6ecf-6fbe-4f3f-9441-24f3a8dd32aa"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[338665, 9971, 87, 0, 70, "Subsection", "ExpressionUUID" -> \ "c0481605-2fc1-421b-95b8-c72d23216c10"], Cell[CellGroupData[{ Cell[338777, 9975, 196, 4, 70, "Input", "ExpressionUUID" -> \ "e317dc81-06ec-4ca0-9a53-5e7ccae6f7b4"], Cell[338976, 9981, 100, 1, 70, "Output", "ExpressionUUID" -> \ "f747c7c8-de4a-4624-994e-eb6702087fd1"] }, Open ]], Cell[CellGroupData[{ Cell[339113, 9987, 109, 1, 70, "Input", "ExpressionUUID" -> \ "c18a94a5-dc95-475c-90f1-8b20dd028630"], Cell[339225, 9990, 701, 23, 70, "Output", "ExpressionUUID" -> \ "e1ded302-6c00-4a9b-a17d-3991274a0586"] }, Open ]], Cell[CellGroupData[{ Cell[339963, 10018, 683, 19, 70, "Input", "ExpressionUUID" -> \ "90630de4-77b4-43ea-ae2d-dcc33d64167b"], Cell[340649, 10039, 2542, 81, 70, "Output", "ExpressionUUID" -> \ "3ee5c7f1-ae6f-4f15-9075-38a0d898ed0f"] }, Open ]], Cell[CellGroupData[{ Cell[343228, 10125, 91, 0, 70, "Input", "ExpressionUUID" -> \ "231a569e-ea9e-4290-b0b3-a8ccce3aedc4"], Cell[343322, 10127, 92, 0, 70, "Output", "ExpressionUUID" -> \ "aefae39f-1174-40f6-ba99-454daac4b7e2"] }, Open ]], Cell[CellGroupData[{ Cell[343451, 10132, 892, 28, 70, "Input", "ExpressionUUID" -> \ "a3e5ba17-1f5b-472b-8072-198127cd9698"], Cell[344346, 10162, 821, 26, 70, "Output", "ExpressionUUID" -> \ "e9842f3f-ea8c-4f4a-89a5-8f475d4c657e"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)