(* 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[ 150419, 4045] NotebookOptionsPosition[ 132438, 3644] NotebookOutlinePosition[ 132925, 3664] CellTagsIndexPosition[ 132882, 3661] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Euler Line", "Title",ExpressionUUID->"1908b17e-9c90-45b2-91e6-766f2b0badf8"], Cell[CellGroupData[{ Cell["Author", "Subsection",ExpressionUUID->"5e0a3ccc-a8f7-4a2a-a990-4f3dcc06f469"], Cell["\<\ Eric W. Weisstein August 2, 2007\ \>", "Text",ExpressionUUID->"4174208d-520e-4352-9cc4-08b19d2e47f7"], Cell[TextData[{ "This notebook downloaded from ", ButtonBox["http://mathworld.wolfram.com/notebooks/PlaneGeometry/EulerLine.nb", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://mathworld.wolfram.com/notebooks/PlaneGeometry/EulerLine.nb"], None}], "." }], "Text",ExpressionUUID->"3884f925-f756-45b1-b9aa-51fa8d00853d"], Cell[TextData[{ "For more information, see Eric's ", StyleBox["MathWorld", FontSlant->"Italic"], " entry ", ButtonBox["http://mathworld.wolfram.com/EulerLine.html", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://mathworld.wolfram.com/EulerLine.html"], None}], "." }], "Text",ExpressionUUID->"5310b6f5-0ba7-45c9-874a-2a2be97d259f"], Cell["\<\ \[Copyright]2007 Wolfram Research, Inc. except for portions noted otherwise\ \>", "Text",ExpressionUUID->"06697f88-1730-4761-972f-451cae7ed1bb"] }, Open ]], Cell[CellGroupData[{ Cell["Line Equation", "Section",ExpressionUUID->"7201e03b-5bc3-43e2-8f86-548c7d5d85e9"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LineEquation", "[", "EulerLine", "]"}]], "Input",ExpressionUUID->"359228d3-7d3d-4e1e-a621-4bcdf17173ad"], Cell[BoxData[ RowBox[{ RowBox[{"\[Gamma]", " ", RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"Cos", "[", "A", "]"}], "2"], "-", SuperscriptBox[ RowBox[{"Cos", "[", "B", "]"}], "2"]}], ")"}], " ", RowBox[{"Cos", "[", "C", "]"}]}], "+", RowBox[{"\[Alpha]", " ", RowBox[{"Cos", "[", "A", "]"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"Cos", "[", "B", "]"}], "2"], "-", SuperscriptBox[ RowBox[{"Cos", "[", "C", "]"}], "2"]}], ")"}]}], "+", RowBox[{"\[Beta]", " ", RowBox[{"Cos", "[", "B", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox[ RowBox[{"Cos", "[", "A", "]"}], "2"]}], "+", SuperscriptBox[ RowBox[{"Cos", "[", "C", "]"}], "2"]}], ")"}]}]}]], "Output",ExpressionU\ UID->"313c1a33-0ba2-4f55-b533-206944fcf54d"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Symmetrize", "[", RowBox[{"Factor", "[", RowBox[{"ToSidelengths", "[", RowBox[{"LineEquation", "[", "EulerLine", "]"}], "]"}], "]"}], "]"}]], "Input",ExpressionUUID->"e3ce8ce3-58c0-45bc-9bea-24ec17898b27"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "3"]}], " ", SuperscriptBox["b", "2"], " ", "\[Alpha]"}], "+", RowBox[{"a", " ", SuperscriptBox["b", "4"], " ", "\[Alpha]"}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Alpha]"}], "-", RowBox[{"a", " ", SuperscriptBox["c", "4"], " ", "\[Alpha]"}], "-", RowBox[{ SuperscriptBox["a", "4"], " ", "b", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "3"], " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["b", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Beta]"}], "+", RowBox[{"b", " ", SuperscriptBox["c", "4"], " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", "c", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["b", "4"], " ", "c", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Gamma]"}]}]], "Output",ExpressionUUID->\ "7b045710-42e7-4799-b4ee-10626137a4f9"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "/@", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Coefficient", "[", RowBox[{"%", ",", "#"}], "]"}], "&"}], "/@", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}]}], ")"}]}]], "Input",ExpressionUUID->"56d5cfeb-2ee1-40fb-8ba3-aef2e073c396"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", RowBox[{"(", RowBox[{"b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}]}], ",", RowBox[{ RowBox[{"-", "b"}], " ", RowBox[{"(", RowBox[{"a", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"a", "-", "b"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}], " ", "c", " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}]}]}], "}"}]], "Output",ExpressionUUID->\ "e9638785-752b-4d51-8a70-d1084d25a9ee"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Complement and Anticomplement", "Section",ExpressionUUID->"d9d8c96a-7c26-4b10-9cc8-8f87a827e259"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Symmetrize", "[", RowBox[{"ToSidelengths", "[", RowBox[{ RowBox[{"Line", "[", "EulerLine", "]"}], "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "]"}], "]"}]], "Input",ExpressionU\ UID->"aed2a39d-590a-438c-8c57-0ae6571efda9"], Cell[BoxData[ RowBox[{ RowBox[{"-", "a"}], " ", RowBox[{"(", RowBox[{"b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}]}]], "Output",ExpressionUUID->"64bfc9bc-\ e27a-48e8-b5d9-bcc6b40f60b8"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Symmetrize", "[", RowBox[{"ToSidelengths", "[", RowBox[{ RowBox[{"TrilinearComplement", "[", "EulerLine", "]"}], "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "]"}], "]"}]], "Input",ExpressionU\ UID->"92a50f4f-5837-4c31-a41f-3a5c90e60284"], Cell[BoxData[ RowBox[{"a", " ", RowBox[{"(", RowBox[{"b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}]}]], "Output",ExpressionUUID->"3131b535-\ 0ce3-4f4f-9740-dc3a1bae1326"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Symmetrize", "[", RowBox[{"ToSidelengths", "[", RowBox[{ RowBox[{"Anticomplement", "[", "EulerLine", "]"}], "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "]"}], "]"}]], "Input",ExpressionU\ UID->"a3da9feb-c2d4-42a7-a33d-f70369b2114d"], Cell[BoxData[ RowBox[{"a", " ", RowBox[{"(", RowBox[{"b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]}], ")"}]}]], "Output",ExpressionUUID->"284dc485-\ a1d6-4e2d-9734-cbb0a7222227"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Figure", "Section",ExpressionUUID->"b0714851-0c8e-48db-b76d-7f3d6b756a03"], Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"Triangle", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", RowBox[{ RowBox[{"-", "2"}], "/", "10"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"5", "/", "2"}]}], "}"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"pts", "=", RowBox[{"{", "\n", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Centroid", "[", "t", "]"}], ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Circumcenter", "[", "t", "]"}], ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"DeLongchampsPoint", "[", "t", "]"}], ",", "\"\\""}], "}"}], ",", "\n", RowBox[{"{", RowBox[{ RowBox[{"NinePointCenter", "[", "t", "]"}], ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Orthocenter", "[", "t", "]"}], ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"TangentialTriangleCircumcenter", "[", "t", "]"}], ",", "\"\<\!\(\*SubscriptBox[\(O\), \(t\)]\)\>\""}], "}"}]}], "}"}]}], ";"}]}], "Input",ExpressionUUID->"1292f6fb-e599-4e82-b358-fe7eeaae5f6f"], Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"t", ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"VertexPoints", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "\[IndentingNewLine]", RowBox[{"PointLabels", "[", "pts", "]"}], ",", "\[IndentingNewLine]", "Red", ",", RowBox[{"LongestLine", "[", RowBox[{"Coordinates", "/@", RowBox[{"First", "/@", "pts"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}]], "Input",ExpressionUUID->"8b4165e2-4b6c-42d0-9e4f-\ f436ce5025bf"], Cell[BoxData[ GraphicsBox[{ LineBox[NCache[{{0, 0}, {3, Rational[-1, 5]}, {1, Rational[5, 2]}, {0, 0}}, {{0, 0}, {3, -0.2}, {1, 2.5}, {0, 0}}]], { {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"A\"\>", TraditionalForm], TraditionalForm, Editable->True], {0.05, 0.12}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[{0, 0}]}, {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"B\"\>", TraditionalForm], TraditionalForm, Editable->True], {3.05, -0.08000000000000002}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{3, Rational[-1, 5]}, {3, -0.2}]]}, {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"C\"\>", TraditionalForm], TraditionalForm, Editable->True], {1.05, 2.62}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{1, Rational[5, 2]}, {1, 2.5}]]}}, {RGBColor[1, 0, 0], {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"G\"\>", TraditionalForm], TraditionalForm, Editable->True], {1.3833333333333335, 0.8866666666666667}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{ Rational[ 77, 1356] + ((15 226^Rational[-1, 2])/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ( Rational[-154, 3] 1129^Rational[-1, 2] + (Rational[-77, 6] 226^Rational[-1, 2]) ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])), Rational[385, 452] - (226^Rational[-1, 2]/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ( Rational[-154, 3] 1129^Rational[-1, 2] + (Rational[-77, 6] 226^Rational[-1, 2]) ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2]))}, {1.3333333333333337`, 0.7666666666666667}]]}, {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"O\"\>", TraditionalForm], TraditionalForm, Editable->True], {1.6116883116883116, 0.9453246753246755}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{ Rational[1463, 2] (7399466^Rational[-1, 2]/( 19 Rational[226, 32741]^Rational[1, 2] + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) + (Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))) + ((15 226^Rational[-1, 2])/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[ 77, 10] ((15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])/( 19 Rational[226, 32741]^Rational[1, 2] + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) + (Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))) + (Rational[-1463, 2] 32741^Rational[-1, 2]) (((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])/( 19 Rational[226, 32741]^Rational[1, 2] + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) + (Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))), Rational[21945, 2] (7399466^Rational[-1, 2]/( 19 Rational[226, 32741]^Rational[1, 2] + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) + (Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))) - (226^Rational[-1, 2]/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[ 77, 10] ((15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])/( 19 Rational[226, 32741]^Rational[1, 2] + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) + (Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))) + (Rational[-1463, 2] 32741^Rational[-1, 2]) (((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])/( 19 Rational[226, 32741]^Rational[1, 2] + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) + (Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))))}, {1.5616883116883118`, 0.8253246753246755}]]}, {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"Z\"\>", TraditionalForm], TraditionalForm, Editable->True], {2.296753246753247, 1.1212987012987012}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{(Rational[77, 10] 226^Rational[-1, 2]) (( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))/((Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + (Rational[1, 10] 1129^Rational[1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])) + (Rational[1, 5] 226^Rational[1, 2]) ( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) + ((15 226^Rational[-1, 2])/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[ 77, 10] ((15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))/((Rational[1, 2] 29^Rational[1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])) + (Rational[1, 5] 226^Rational[1, 2]) ( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) + ( Rational[-77, 10] ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])) (( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))/((Rational[1, 2] 29^Rational[1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + (Rational[1, 10] 1129^Rational[1, 2]) (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])) + (Rational[1, 5] 226^Rational[1, 2]) ( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))))), (Rational[231, 2] 226^Rational[-1, 2]) (( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))/((Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + (Rational[1, 10] 1129^Rational[1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])) + (Rational[1, 5] 226^Rational[1, 2]) ( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) - (226^Rational[-1, 2]/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[ 77, 10] ((15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))/((Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + (Rational[1, 10] 1129^Rational[1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])) + (Rational[1, 5] 226^Rational[1, 2]) ( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) + ( Rational[-77, 10] ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])) (( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))/((Rational[1, 2] 29^Rational[1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + (Rational[1, 10] 1129^Rational[1, 2]) ( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2] - (95 32741^Rational[-1, 2]) ( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])) + (Rational[1, 5] 226^Rational[1, 2]) ( 95 32741^Rational[-1, 2] - (15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]) (150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))))}, {2.2467532467532467`, 1.0012987012987014`}]]}, {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"N\"\>", TraditionalForm], TraditionalForm, Editable->True], {1.2691558441558446, 0.8573376623376624}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{(Rational[77, 10] 226^Rational[-1, 2]) ( Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]/((Rational[1, 2] 29^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + (Rational[1, 10] 1129^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]] + (Rational[1, 5] 226^Rational[1, 2]) Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])) + ((15 226^Rational[-1, 2])/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[77, 10] ( Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]/((Rational[1, 2] 29^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + (Rational[1, 10] 1129^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]] + (Rational[1, 5] 226^Rational[1, 2]) Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])) + ( Rational[-77, 10] ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])) ( Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]/((Rational[1, 2] 29^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + (Rational[1, 10] 1129^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]] + (Rational[1, 5] 226^Rational[1, 2]) Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]))), (Rational[231, 2] 226^Rational[-1, 2]) ( Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]/((Rational[1, 2] 29^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + (Rational[1, 10] 1129^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]] + (Rational[1, 5] 226^Rational[1, 2]) Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])) - (226^Rational[-1, 2]/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[77, 10] ( Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]/((Rational[1, 2] 29^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + (Rational[1, 10] 1129^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]] + (Rational[1, 5] 226^Rational[1, 2]) Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])) + ( Rational[-77, 10] ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])) ( Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]/((Rational[1, 2] 29^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + (Rational[1, 10] 1129^Rational[1, 2]) Cos[ArcCos[95 32741^Rational[-1, 2]] - ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]] + (Rational[1, 5] 226^Rational[1, 2]) Cos[ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]] - ArcCos[150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])))}, {1.2191558441558445`, 0.7373376623376624}]]}, {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"H\"\>", TraditionalForm], TraditionalForm, Editable->True], {0.9266233766233771, 0.7693506493506493}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{ Rational[77, 950] (Rational[32741, 226]^Rational[1, 2]/( Rational[1, 475] 7399466^Rational[1, 2] + Rational[1, 10] (1129^Rational[1, 2]/( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + Rational[1, 2] (29^Rational[1, 2]/( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) + ((15 226^Rational[-1, 2])/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[ 77, 10] ((15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])^(-1)/( Rational[1, 475] 7399466^Rational[1, 2] + Rational[1, 10] (1129^Rational[1, 2]/( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + Rational[1, 2] (29^Rational[1, 2]/( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) + (Rational[-77, 950] 32741^Rational[1, 2]) (((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])/( Rational[1, 475] 7399466^Rational[1, 2] + Rational[1, 10] (1129^Rational[1, 2]/( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + Rational[1, 2] (29^Rational[1, 2]/( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]))))), Rational[231, 190] (Rational[32741, 226]^Rational[1, 2]/( Rational[1, 475] 7399466^Rational[1, 2] + Rational[1, 10] (1129^Rational[1, 2]/( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + Rational[1, 2] (29^Rational[1, 2]/( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) - (226^Rational[-1, 2]/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + Rational[ 77, 10] ((15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])^(-1)/( Rational[1, 475] 7399466^Rational[1, 2] + Rational[1, 10] (1129^Rational[1, 2]/( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + Rational[1, 2] (29^Rational[1, 2]/( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))) + (Rational[-77, 950] 32741^Rational[1, 2]) (((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])/( Rational[1, 475] 7399466^Rational[1, 2] + Rational[1, 10] (1129^Rational[1, 2]/( 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2])) + Rational[1, 2] (29^Rational[1, 2]/( 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2])))))}, {0.8766233766233771, 0.6493506493506493}]]}, {PointSize[0.02], InsetBox[ TagBox[ FormBox["\<\"\\!\\(\\*SubscriptBox[\\(O\\), \\(t\\)]\\)\"\>", TraditionalForm], TraditionalForm, Editable->True], {3.2434651328069948, 1.3644825127873899}, Background->GrayLevel[1], BaseStyle->{{FontFamily -> "Times", FontSlant -> "Italic"}}], PointBox[NCache[{ Rational[ 77, 50] (( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])/( Rational[29, 4] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[-29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[1129, 100] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[226, 25] ( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]))) + ((15 226^Rational[-1, 2])/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + (Rational[77, 100] 1129^Rational[1, 2]) (( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])/( Rational[29, 4] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[-29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[1129, 100] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[226, 25] ( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]))) + ((Rational[-77, 25] Rational[113, 2]^Rational[1, 2]) ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])) (( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])/( Rational[29, 4] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[-29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[1129, 100] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[226, 25] ( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])))), Rational[ 231, 10] (( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])/( Rational[29, 4] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[-29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[1129, 100] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[226, 25] ( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]))) - (226^Rational[-1, 2]/( 10 Rational[2, 127577]^Rational[1, 2] - 405 255154^Rational[-1, 2])) ((-77) 1129^Rational[-1, 2] + (Rational[77, 100] 1129^Rational[1, 2]) (( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])/( Rational[29, 4] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[-29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[1129, 100] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[226, 25] ( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]))) + ((Rational[-77, 25] Rational[113, 2]^Rational[1, 2]) ((-150) Rational[2, 127577]^Rational[1, 2] - 27 255154^Rational[-1, 2])) (( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]])/( Rational[29, 4] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[-29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[1129, 100] ( Rational[226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[-1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]) + Rational[226, 25] ( Rational[-226, 25] Cos[2 ArcCos[95 32741^Rational[-1, 2]]] + Rational[1129, 100] Cos[2 ArcCos[ 15 Rational[2, 3277]^Rational[1, 2] - 5 6554^Rational[-1, 2]]] + Rational[29, 4] Cos[2 ArcCos[ 150 Rational[2, 127577]^Rational[1, 2] + 27 255154^Rational[-1, 2]]]))))}, {3.193465132806995, 1.2444825127873897`}]]}}, {RGBColor[1, 0, 0], LineBox[{{-0.2244831776941718, 0.3670156354230725}, {3.5040336481273284`, 1.319771849834743}}]}}, ImagePadding->{{0., 1.}, {1., 0.}}, PlotRange->{{-0.067572, 3.311037}, {-0.264869, 2.684869}}, PlotRangePadding->Automatic]], "Input",ExpressionUUID->"2887c6ba-db78-4e33-\ b6aa-06c81e7c0153"] }, Open ]], Cell[CellGroupData[{ Cell["Isotomic Conjugate", "Section",ExpressionUUID->"419ad808-d06c-4e2b-b68c-34570cca0693"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{"ToSidelengths", "[", RowBox[{ RowBox[{"TrilinearEquation", "[", "EulerLine", "]"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "->", RowBox[{"IsotomicConjugate", "[", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "]"}]}], "]"}]}], "]"}], "]"}]], "Input",ExpressionUUID->"68e261f6-f01d-4d4c-\ bdbf-0a46518cca04"], Cell[BoxData[ RowBox[{ FractionBox["1", RowBox[{"8", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["b", "4"], " ", SuperscriptBox["c", "4"], " ", "\[Alpha]", " ", "\[Beta]", " ", "\[Gamma]"}]], RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"a", "-", "b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "-", "b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["a", "5"], " ", "b", " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{"a", " ", SuperscriptBox["b", "5"], " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["a", "5"], " ", "c", " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "2"], " ", "c", " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{"a", " ", SuperscriptBox["c", "5"], " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "3"], " ", "c", " ", "\[Beta]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["b", "5"], " ", "c", " ", "\[Beta]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", SuperscriptBox["c", "3"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{"b", " ", SuperscriptBox["c", "5"], " ", "\[Beta]", " ", "\[Gamma]"}]}], ")"}]}], ")"}]}]], "Output",ExpressionUUID->"0713ae50-badd-4bae-a733-d98e887b4c86"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"isotomic", "=", RowBox[{ RowBox[{ SuperscriptBox["a", "5"], " ", "b", " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{"a", " ", SuperscriptBox["b", "5"], " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", "b", " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{"a", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["a", "5"], " ", "c", " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "2"], " ", "c", " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{"a", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{"a", " ", SuperscriptBox["c", "5"], " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "3"], " ", "c", " ", "\[Beta]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["b", "5"], " ", "c", " ", "\[Beta]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", "b", " ", SuperscriptBox["c", "3"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{"b", " ", SuperscriptBox["c", "5"], " ", "\[Beta]", " ", "\[Gamma]"}]}]}], ";"}]], "Input",ExpressionUUID->"2f75df4e-4908-4c35-861a-7ae3e36442b4"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"IncidentCenters", "[", RowBox[{"KimberlingCenters", ",", "isotomic"}], "]"}]], "Input",ExpressionUU\ ID->"55122cb2-fe0c-48d0-a6f2-37169fc82758"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"X", "[", "2", "]"}], ",", RowBox[{"X", "[", "69", "]"}], ",", RowBox[{"X", "[", "95", "]"}], ",", RowBox[{"X", "[", "253", "]"}], ",", RowBox[{"X", "[", "264", "]"}], ",", RowBox[{"X", "[", "287", "]"}], ",", RowBox[{"X", "[", "305", "]"}], ",", RowBox[{"X", "[", "306", "]"}], ",", RowBox[{"X", "[", "307", "]"}], ",", RowBox[{"X", "[", "328", "]"}], ",", RowBox[{"X", "[", "1441", "]"}], ",", RowBox[{"X", "[", "1494", "]"}], ",", RowBox[{"X", "[", "1799", "]"}], ",", RowBox[{"X", "[", "1972", "]"}], ",", RowBox[{"X", "[", "2373", "]"}], ",", RowBox[{"X", "[", "2419", "]"}]}], "}"}]], "Output",ExpressionUUID->\ "dd55f720-f5a6-4cd4-a42d-c2246c31eeae"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Isogonal Conjugate", "Section",ExpressionUUID->"5c227374-5726-4a36-b9a1-7de1e2925e5f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{"ToSidelengths", "[", RowBox[{ RowBox[{"TrilinearEquation", "[", "EulerLine", "]"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "->", RowBox[{"IsogonalConjugate", "[", RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "]"}]}], "]"}]}], "]"}], "]"}]], "Input",ExpressionUUID->"05488949-05e1-4664-\ b22a-9689ed7af365"], Cell[BoxData[ RowBox[{"-", RowBox[{ FractionBox["1", RowBox[{"8", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "3"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Beta]", " ", "\[Gamma]"}]], RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "a"}], "+", "b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "a"}], "+", "b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "4"]}], " ", "c", " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", "c", " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", "b", " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "3"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{"b", " ", SuperscriptBox["c", "4"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "2"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{"a", " ", SuperscriptBox["b", "4"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Beta]", " ", "\[Gamma]"}], "+", RowBox[{"a", " ", SuperscriptBox["c", "4"], " ", "\[Beta]", " ", "\[Gamma]"}]}], ")"}]}], ")"}]}]}]], "Output",ExpressionUUID->"ae3bb75d-df5a-4a38-b2f2-\ 51ec819bb113"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"isogonal", "=", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "4"]}], " ", "c", " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", "c", " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", "b", " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "3"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{"b", " ", SuperscriptBox["c", "4"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "2"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{"a", " ", SuperscriptBox["b", "4"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Beta]", " ", "\[Gamma]"}], "+", RowBox[{"a", " ", SuperscriptBox["c", "4"], " ", "\[Beta]", " ", "\[Gamma]"}]}]}], ";"}]], "Input",ExpressionUUID->"dfba3c9c-34ca-45dc-a5e6-b22dfa3d32b1"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"ToSidelengths", "[", RowBox[{"TrigExpand", "[", RowBox[{"TrilinearEquation", "[", "JerabekHyperbola", "]"}], "]"}], "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], "]"}]], "Input",ExpressionUUID->\ "de930920-a4b1-48d1-8aec-5c5a2a27dc9a"], Cell[BoxData[ RowBox[{ FractionBox["1", RowBox[{"2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Beta]", " ", "\[Gamma]"}]], 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[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["a", "4"]}], " ", "c", " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["b", "4"], " ", "c", " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Beta]"}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "3"], " ", "\[Alpha]", " ", "\[Beta]"}], "+", RowBox[{ SuperscriptBox["a", "4"], " ", "b", " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "3"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["b", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Alpha]", " ", "\[Gamma]"}], "-", RowBox[{"b", " ", SuperscriptBox["c", "4"], " ", "\[Alpha]", " ", "\[Gamma]"}], "+", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "2"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{"a", " ", SuperscriptBox["b", "4"], " ", "\[Beta]", " ", "\[Gamma]"}], "-", RowBox[{ SuperscriptBox["a", "3"], " ", SuperscriptBox["c", "2"], " ", "\[Beta]", " ", "\[Gamma]"}], "+", RowBox[{"a", " ", SuperscriptBox["c", "4"], " ", "\[Beta]", " ", "\[Gamma]"}]}], ")"}]}], ")"}]}]], "Output",ExpressionUUID->"d976c86c-6379-45f3-8dea-629471f8a172"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"IncidentCenters", "[", RowBox[{"KimberlingCenters", ",", "isogonal"}], "]"}]], "Input",ExpressionUU\ ID->"c302268d-1ebe-4cc4-bf5b-d88b5c6a4053"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"X", "[", "3", "]"}], ",", RowBox[{"X", "[", "4", "]"}], ",", RowBox[{"X", "[", "6", "]"}], ",", RowBox[{"X", "[", "54", "]"}], ",", RowBox[{"X", "[", "64", "]"}], ",", RowBox[{"X", "[", "65", "]"}], ",", RowBox[{"X", "[", "66", "]"}], ",", RowBox[{"X", "[", "67", "]"}], ",", RowBox[{"X", "[", "68", "]"}], ",", RowBox[{"X", "[", "69", "]"}], ",", RowBox[{"X", "[", "70", "]"}], ",", RowBox[{"X", "[", "71", "]"}], ",", RowBox[{"X", "[", "72", "]"}], ",", RowBox[{"X", "[", "73", "]"}], ",", RowBox[{"X", "[", "74", "]"}], ",", RowBox[{"X", "[", "248", "]"}], ",", RowBox[{"X", "[", "265", "]"}], ",", RowBox[{"X", "[", "290", "]"}], ",", RowBox[{"X", "[", "695", "]"}], ",", RowBox[{"X", "[", "879", "]"}], ",", RowBox[{"X", "[", "895", "]"}], ",", RowBox[{"X", "[", "1173", "]"}], ",", RowBox[{"X", "[", "1175", "]"}], ",", RowBox[{"X", "[", "1176", "]"}], ",", RowBox[{"X", "[", "1177", "]"}], ",", RowBox[{"X", "[", "1242", "]"}], ",", RowBox[{"X", "[", "1243", "]"}], ",", RowBox[{"X", "[", "1244", "]"}], ",", RowBox[{"X", "[", "1245", "]"}], ",", RowBox[{"X", "[", "1246", "]"}], ",", RowBox[{"X", "[", "1439", "]"}], ",", RowBox[{"X", "[", "1798", "]"}], ",", RowBox[{"X", "[", "1903", "]"}], ",", RowBox[{"X", "[", "1942", "]"}], ",", RowBox[{"X", "[", "1987", "]"}], ",", RowBox[{"X", "[", "2213", "]"}], ",", RowBox[{"X", "[", "2435", "]"}], ",", RowBox[{"X", "[", "2574", "]"}], ",", RowBox[{"X", "[", "2575", "]"}], ",", RowBox[{"X", "[", "2992", "]"}], ",", RowBox[{"X", "[", "2993", "]"}]}], "}"}]], "Output",ExpressionUUID->\ "0f832a8d-849d-431c-997c-503f36c8abae"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Incident Centers", "Section",ExpressionUUID->"182e7303-2435-42d9-bc5a-8ee8cd81443a"], Cell[BoxData["\<\"Rehashing triangle centers...\"\>"], "Print",ExpressionUUID->"eec3ca60-909d-41b2-aa4c-1bcce010fa68"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"ctrs", "=", RowBox[{"IncidentCenters", "[", RowBox[{"KimberlingCenters", ",", "EulerLine"}], "]"}]}], ")"}], "//", "Timing"}]], "Input",ExpressionUUID->"2919102e-8a2e-4b20-b1b9-3c69fccf0a1c"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"14.170898999999991`", " ", "Second"}], ",", RowBox[{"{", RowBox[{ RowBox[{"X", "[", "2", "]"}], ",", RowBox[{"X", "[", "3", "]"}], ",", RowBox[{"X", "[", "4", "]"}], ",", RowBox[{"X", "[", "5", "]"}], ",", RowBox[{"X", "[", "20", "]"}], ",", RowBox[{"X", "[", "21", "]"}], ",", RowBox[{"X", "[", "22", "]"}], ",", RowBox[{"X", "[", "23", "]"}], ",", RowBox[{"X", "[", "24", "]"}], ",", RowBox[{"X", "[", "25", "]"}], ",", RowBox[{"X", "[", "26", "]"}], ",", RowBox[{"X", "[", "27", "]"}], ",", RowBox[{"X", "[", "28", "]"}], ",", RowBox[{"X", "[", "29", "]"}], ",", RowBox[{"X", "[", "30", "]"}], ",", RowBox[{"X", "[", "140", "]"}], ",", RowBox[{"X", "[", "186", "]"}], ",", RowBox[{"X", "[", "199", "]"}], ",", RowBox[{"X", "[", "235", "]"}], ",", RowBox[{"X", "[", "237", "]"}], ",", RowBox[{"X", "[", "297", "]"}], ",", RowBox[{"X", "[", "376", "]"}], ",", RowBox[{"X", "[", "377", "]"}], ",", RowBox[{"X", "[", "378", "]"}], ",", RowBox[{"X", "[", "379", "]"}], ",", RowBox[{"X", "[", "381", "]"}], ",", RowBox[{"X", "[", "382", "]"}], ",", RowBox[{"X", "[", "383", "]"}], ",", RowBox[{"X", "[", "384", "]"}], ",", RowBox[{"X", "[", "401", "]"}], ",", RowBox[{"X", "[", "402", "]"}], ",", RowBox[{"X", "[", "403", "]"}], ",", RowBox[{"X", "[", "404", "]"}], ",", RowBox[{"X", "[", "405", "]"}], ",", RowBox[{"X", "[", "406", "]"}], ",", RowBox[{"X", "[", "407", "]"}], ",", RowBox[{"X", "[", "408", "]"}], ",", RowBox[{"X", "[", "409", "]"}], ",", RowBox[{"X", "[", "410", "]"}], ",", RowBox[{"X", "[", "411", "]"}], ",", RowBox[{"X", "[", "412", "]"}], ",", RowBox[{"X", "[", "413", "]"}], ",", RowBox[{"X", "[", "414", "]"}], ",", RowBox[{"X", "[", "415", "]"}], ",", RowBox[{"X", "[", "416", "]"}], ",", RowBox[{"X", "[", "417", "]"}], ",", RowBox[{"X", "[", "418", "]"}], ",", RowBox[{"X", "[", "419", "]"}], ",", RowBox[{"X", "[", "420", "]"}], ",", RowBox[{"X", "[", "421", "]"}], ",", RowBox[{"X", "[", "422", "]"}], ",", RowBox[{"X", "[", "423", "]"}], ",", RowBox[{"X", "[", "424", "]"}], ",", RowBox[{"X", "[", "425", "]"}], ",", RowBox[{"X", "[", "426", "]"}], ",", RowBox[{"X", "[", "427", "]"}], ",", RowBox[{"X", "[", "428", "]"}], ",", RowBox[{"X", "[", "429", "]"}], ",", RowBox[{"X", "[", "430", "]"}], ",", RowBox[{"X", "[", "431", "]"}], ",", RowBox[{"X", "[", "432", "]"}], ",", RowBox[{"X", "[", "433", "]"}], ",", RowBox[{"X", "[", "434", "]"}], ",", RowBox[{"X", "[", "435", "]"}], ",", RowBox[{"X", "[", "436", "]"}], ",", RowBox[{"X", "[", "437", "]"}], ",", RowBox[{"X", "[", "438", "]"}], ",", RowBox[{"X", "[", "439", "]"}], ",", RowBox[{"X", "[", "440", "]"}], ",", RowBox[{"X", "[", "441", "]"}], ",", RowBox[{"X", "[", "442", "]"}], ",", RowBox[{"X", "[", "443", "]"}], ",", RowBox[{"X", "[", "444", "]"}], ",", RowBox[{"X", "[", "445", "]"}], ",", RowBox[{"X", "[", "446", "]"}], ",", RowBox[{"X", "[", "447", "]"}], ",", RowBox[{"X", "[", "448", "]"}], ",", RowBox[{"X", "[", "449", "]"}], ",", RowBox[{"X", "[", "450", "]"}], ",", RowBox[{"X", "[", "451", "]"}], ",", RowBox[{"X", "[", "452", "]"}], ",", RowBox[{"X", "[", "453", "]"}], ",", RowBox[{"X", "[", "454", "]"}], ",", RowBox[{"X", "[", "455", "]"}], ",", RowBox[{"X", "[", "456", "]"}], ",", RowBox[{"X", "[", "457", "]"}], ",", RowBox[{"X", "[", "458", "]"}], ",", RowBox[{"X", "[", "459", "]"}], ",", RowBox[{"X", "[", "460", "]"}], ",", RowBox[{"X", "[", "461", "]"}], ",", RowBox[{"X", "[", "462", "]"}], ",", RowBox[{"X", "[", "463", "]"}], ",", RowBox[{"X", "[", "464", "]"}], ",", RowBox[{"X", "[", "465", "]"}], ",", RowBox[{"X", "[", "466", "]"}], ",", RowBox[{"X", "[", "467", "]"}], ",", RowBox[{"X", "[", "468", "]"}], ",", RowBox[{"X", "[", "469", "]"}], ",", RowBox[{"X", "[", "470", "]"}], ",", RowBox[{"X", "[", "471", "]"}], ",", RowBox[{"X", "[", "472", "]"}], ",", RowBox[{"X", "[", "473", "]"}], ",", RowBox[{"X", "[", "474", "]"}], ",", RowBox[{"X", "[", "475", "]"}], ",", RowBox[{"X", "[", "546", "]"}], ",", RowBox[{"X", "[", "547", "]"}], ",", RowBox[{"X", "[", "548", "]"}], ",", RowBox[{"X", "[", "549", "]"}], ",", RowBox[{"X", "[", "550", "]"}], ",", RowBox[{"X", "[", "631", "]"}], ",", RowBox[{"X", "[", "632", "]"}], ",", RowBox[{"X", "[", "851", "]"}], ",", RowBox[{"X", "[", "852", "]"}], ",", RowBox[{"X", "[", "853", "]"}], ",", RowBox[{"X", "[", "854", "]"}], ",", RowBox[{"X", "[", "855", "]"}], ",", RowBox[{"X", "[", "856", "]"}], ",", RowBox[{"X", "[", "857", "]"}], ",", RowBox[{"X", "[", "858", "]"}], ",", RowBox[{"X", "[", "859", "]"}], ",", RowBox[{"X", "[", "860", "]"}], ",", RowBox[{"X", "[", "861", "]"}], ",", RowBox[{"X", "[", "862", "]"}], ",", RowBox[{"X", "[", "863", "]"}], ",", RowBox[{"X", "[", "864", "]"}], ",", RowBox[{"X", "[", "865", "]"}], ",", RowBox[{"X", "[", "866", "]"}], ",", RowBox[{"X", "[", "867", "]"}], ",", RowBox[{"X", "[", "868", "]"}], ",", RowBox[{"X", "[", "964", "]"}], ",", RowBox[{"X", "[", "1003", "]"}], ",", RowBox[{"X", "[", "1004", "]"}], ",", RowBox[{"X", "[", "1005", "]"}], ",", RowBox[{"X", "[", "1006", "]"}], ",", RowBox[{"X", "[", "1008", "]"}], ",", RowBox[{"X", "[", "1009", "]"}], ",", RowBox[{"X", "[", "1010", "]"}], ",", RowBox[{"X", "[", "1011", "]"}], ",", RowBox[{"X", "[", "1012", "]"}], ",", RowBox[{"X", "[", "1013", "]"}], ",", RowBox[{"X", "[", "1080", "]"}], ",", RowBox[{"X", "[", "1113", "]"}], ",", RowBox[{"X", "[", "1114", "]"}], ",", RowBox[{"X", "[", "1312", "]"}], ",", RowBox[{"X", "[", "1313", "]"}], ",", RowBox[{"X", "[", "1314", "]"}], ",", RowBox[{"X", "[", "1315", "]"}], ",", RowBox[{"X", "[", "1316", "]"}], ",", RowBox[{"X", "[", "1325", "]"}], ",", RowBox[{"X", "[", "1344", "]"}], ",", RowBox[{"X", "[", "1345", "]"}], ",", RowBox[{"X", "[", "1346", "]"}], ",", RowBox[{"X", "[", "1347", "]"}], ",", RowBox[{"X", "[", "1368", "]"}], ",", RowBox[{"X", "[", "1370", "]"}], ",", RowBox[{"X", "[", "1375", "]"}], ",", RowBox[{"X", "[", "1513", "]"}], ",", RowBox[{"X", "[", "1529", "]"}], ",", RowBox[{"X", "[", "1532", "]"}], ",", RowBox[{"X", "[", "1536", "]"}], ",", RowBox[{"X", "[", "1551", "]"}], ",", RowBox[{"X", "[", "1556", "]"}], ",", RowBox[{"X", "[", "1557", "]"}], ",", RowBox[{"X", "[", "1559", "]"}], ",", RowBox[{"X", "[", "1563", "]"}], ",", RowBox[{"X", "[", "1564", "]"}], ",", RowBox[{"X", "[", "1567", "]"}], ",", RowBox[{"X", "[", "1583", "]"}], ",", RowBox[{"X", "[", "1584", "]"}], ",", RowBox[{"X", "[", "1585", "]"}], ",", RowBox[{"X", "[", "1586", "]"}], ",", RowBox[{"X", "[", "1589", "]"}], ",", RowBox[{"X", "[", "1590", "]"}], ",", RowBox[{"X", "[", "1591", "]"}], ",", RowBox[{"X", "[", "1592", "]"}], ",", RowBox[{"X", "[", "1593", "]"}], ",", RowBox[{"X", "[", "1594", "]"}], ",", RowBox[{"X", "[", "1595", "]"}], ",", RowBox[{"X", "[", "1596", "]"}], ",", RowBox[{"X", "[", "1597", "]"}], ",", RowBox[{"X", "[", "1598", "]"}], ",", RowBox[{"X", "[", "1599", "]"}], ",", RowBox[{"X", "[", "1600", "]"}], ",", RowBox[{"X", "[", "1628", "]"}], ",", RowBox[{"X", "[", "1650", "]"}], ",", RowBox[{"X", "[", "1651", "]"}], ",", RowBox[{"X", "[", "1656", "]"}], ",", RowBox[{"X", "[", "1657", "]"}], ",", RowBox[{"X", "[", "1658", "]"}], ",", RowBox[{"X", "[", "1816", "]"}], ",", RowBox[{"X", "[", "1817", "]"}], ",", RowBox[{"X", "[", "1883", "]"}], ",", RowBox[{"X", "[", "1884", "]"}], ",", RowBox[{"X", "[", "1885", "]"}], ",", RowBox[{"X", "[", "1889", "]"}], ",", RowBox[{"X", "[", "1894", "]"}], ",", RowBox[{"X", "[", "1904", "]"}], ",", RowBox[{"X", "[", "1906", "]"}], ",", RowBox[{"X", "[", "1907", "]"}], ",", RowBox[{"X", "[", "1981", "]"}], ",", RowBox[{"X", "[", "1982", "]"}], ",", RowBox[{"X", "[", "1984", "]"}], ",", RowBox[{"X", "[", "1985", "]"}], ",", RowBox[{"X", "[", "1995", "]"}], ",", RowBox[{"X", "[", "2041", "]"}], ",", RowBox[{"X", "[", "2042", "]"}], ",", RowBox[{"X", "[", "2043", "]"}], ",", RowBox[{"X", "[", "2044", "]"}], ",", RowBox[{"X", "[", "2045", "]"}], ",", RowBox[{"X", "[", "2046", "]"}], ",", RowBox[{"X", "[", "2047", "]"}], ",", RowBox[{"X", "[", "2048", "]"}], ",", RowBox[{"X", "[", "2049", "]"}], ",", RowBox[{"X", "[", "2050", "]"}], ",", RowBox[{"X", "[", "2060", "]"}], ",", RowBox[{"X", "[", "2070", "]"}], ",", RowBox[{"X", "[", "2071", "]"}], ",", RowBox[{"X", "[", "2072", "]"}], ",", RowBox[{"X", "[", "2073", "]"}], ",", RowBox[{"X", "[", "2074", "]"}], ",", RowBox[{"X", "[", "2075", "]"}], ",", RowBox[{"X", "[", "2409", "]"}], ",", RowBox[{"X", "[", "2450", "]"}], ",", RowBox[{"X", "[", "2454", "]"}], ",", RowBox[{"X", "[", "2455", "]"}], ",", RowBox[{"X", "[", "2475", "]"}], ",", RowBox[{"X", "[", "2476", "]"}], ",", RowBox[{"X", "[", "2478", "]"}], ",", RowBox[{"X", "[", "2479", "]"}], ",", RowBox[{"X", "[", "2480", "]"}], ",", RowBox[{"X", "[", "2552", "]"}], ",", RowBox[{"X", "[", "2553", "]"}], ",", RowBox[{"X", "[", "2554", "]"}], ",", RowBox[{"X", "[", "2555", "]"}], ",", RowBox[{"X", "[", "2566", "]"}], ",", RowBox[{"X", "[", "2567", "]"}], ",", RowBox[{"X", "[", "2570", "]"}], ",", RowBox[{"X", "[", "2571", "]"}], ",", RowBox[{"X", "[", "2675", "]"}], ",", RowBox[{"X", "[", "2676", "]"}], ",", RowBox[{"X", "[", "2915", "]"}], ",", RowBox[{"X", "[", "2937", "]"}]}], "}"}]}], "}"}]], "Output",ExpressionUU\ ID->"f9319699-2eec-4bcd-9faa-abae0dd1b312"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"First", "/@", "ctrs"}]], "Input",ExpressionUUID->"ccbf56d7-41b7-4412-bced-2d3ae717625d"], Cell[BoxData[ RowBox[{"{", RowBox[{ "2", ",", "3", ",", "4", ",", "5", ",", "20", ",", "21", ",", "22", ",", "23", ",", "24", ",", "25", ",", "26", ",", "27", ",", "28", ",", "29", ",", "30", ",", "140", ",", "186", ",", "199", ",", "235", ",", "237", ",", "297", ",", "376", ",", "377", ",", "378", ",", "379", ",", "381", ",", "382", ",", "383", ",", "384", ",", "401", ",", "402", ",", "403", ",", "404", ",", "405", ",", "406", ",", "407", ",", "408", ",", "409", ",", "410", ",", "411", ",", "412", ",", "413", ",", "414", ",", "415", ",", "416", ",", "417", ",", "418", ",", "419", ",", "420", ",", "421", ",", "422", ",", "423", ",", "424", ",", "425", ",", "426", ",", "427", ",", "428", ",", "429", ",", "430", ",", "431", ",", "432", ",", "433", ",", "434", ",", "435", ",", "436", ",", "437", ",", "438", ",", "439", ",", "440", ",", "441", ",", "442", ",", "443", ",", "444", ",", "445", ",", "446", ",", "447", ",", "448", ",", "449", ",", "450", ",", "451", ",", "452", ",", "453", ",", "454", ",", "455", ",", "456", ",", "457", ",", "458", ",", "459", ",", "460", ",", "461", ",", "462", ",", "463", ",", "464", ",", "465", ",", "466", ",", "467", ",", "468", ",", "469", ",", "470", ",", "471", ",", "472", ",", "473", ",", "474", ",", "475", ",", "546", ",", "547", ",", "548", ",", "549", ",", "550", ",", "631", ",", "632", ",", "851", ",", "852", ",", "853", ",", "854", ",", "855", ",", "856", ",", "857", ",", "858", ",", "859", ",", "860", ",", "861", ",", "862", ",", "863", ",", "864", ",", "865", ",", "866", ",", "867", ",", "868", ",", "964", ",", "1003", ",", "1004", ",", "1005", ",", "1006", ",", "1008", ",", "1009", ",", "1010", ",", "1011", ",", "1012", ",", "1013", ",", "1080", ",", "1113", ",", "1114", ",", "1312", ",", "1313", ",", "1314", ",", "1315", ",", "1316", ",", "1325", ",", "1344", ",", "1345", ",", "1346", ",", "1347", ",", "1368", ",", "1370", ",", "1375", ",", "1513", ",", "1529", ",", "1532", ",", "1536", ",", "1551", ",", "1556", ",", "1557", ",", "1559", ",", "1563", ",", "1564", ",", "1567", ",", "1583", ",", "1584", ",", "1585", ",", "1586", ",", "1589", ",", "1590", ",", "1591", ",", "1592", ",", "1593", ",", "1594", ",", "1595", ",", "1596", ",", "1597", ",", "1598", ",", "1599", ",", "1600", ",", "1628", ",", "1650", ",", "1651", ",", "1656", ",", "1657", ",", "1658", ",", "1816", ",", "1817", ",", "1883", ",", "1884", ",", "1885", ",", "1889", ",", "1894", ",", "1904", ",", "1906", ",", "1907", ",", "1981", ",", "1982", ",", "1984", ",", "1985", ",", "1995", ",", "2041", ",", "2042", ",", "2043", ",", "2044", ",", "2045", ",", "2046", ",", "2047", ",", "2048", ",", "2049", ",", "2050", ",", "2060", ",", "2070", ",", "2071", ",", "2072", ",", "2073", ",", "2074", ",", "2075", ",", "2409", ",", "2450", ",", "2454", ",", "2455", ",", "2475", ",", "2476", ",", "2478", ",", "2479", ",", "2480", ",", "2552", ",", "2553", ",", "2554", ",", "2555", ",", "2566", ",", "2567", ",", "2570", ",", "2571", ",", "2675", ",", "2676", ",", "2915", ",", "2937"}], "}"}]], "Output",ExpressionUUID->\ "1a7efc0b-2805-4a34-ace8-bb9e4cd78791"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Length", "[", "ctrs", "]"}]], "Input",ExpressionUUID->"8375da95-1b8b-4603-9f92-bea96d2d1874"], Cell[BoxData["242"], "Output",ExpressionUUID->"3de5ff5d-b959-4524-a2d1-97fbe4ea5c2d"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"#", ",", RowBox[{"CenterName", "[", "#", "]"}]}], "}"}], "&"}], "/@", "ctrs"}], "//", "TableForm"}]], "Input",ExpressionUUID->"337a2f66-1770-4d44-bea4-\ 3ef02776efd3"], Cell[BoxData[ TagBox[GridBox[{ { RowBox[{"X", "[", "2", "]"}], "\<\"centroid\"\>"}, { RowBox[{"X", "[", "3", "]"}], "\<\"circumcenter\"\>"}, { RowBox[{"X", "[", "4", "]"}], "\<\"orthocenter\"\>"}, { RowBox[{"X", "[", "5", "]"}], "\<\"nine-point center\"\>"}, { RowBox[{"X", "[", "20", "]"}], "\<\"de Longchamps point\"\>"}, { RowBox[{"X", "[", "21", "]"}], "\<\"Schiffler point\"\>"}, { RowBox[{"X", "[", "22", "]"}], "\<\"Exeter point\"\>"}, { RowBox[{"X", "[", "23", "]"}], "\<\"far-out point\"\>"}, { RowBox[{ "X", "[", "24", "]"}], "\<\"perspector of abc and orthic-of-orthic triangle\"\>"}, { RowBox[{ "X", "[", "25", "]"}], "\<\"homothetic center of orthic and tangential triangles\"\>"}, { RowBox[{ "X", "[", "26", "]"}], "\<\"circumcenter of the tangential triangle\"\>"}, { RowBox[{ "X", "[", "27", "]"}], "\<\"Cevapoint of orthocenter and Clawson center\"\>"}, { RowBox[{"X", "[", "28", "]"}], "\<\"Cevapoint of X(19) and X(25)\"\>"}, { RowBox[{ "X", "[", "29", "]"}], "\<\"Cevapoint of incenter and orthocenter\"\>"}, { RowBox[{"X", "[", "30", "]"}], "\<\"Euler infinity point\"\>"}, { RowBox[{"X", "[", "140", "]"}], "\<\"midpoint of X(3) and X(5)\"\>"}, { RowBox[{ "X", "[", "186", "]"}], "\<\"inverse-in-circumcircle of X(4)\"\>"}, { RowBox[{"X", "[", "199", "]"}], "\<\"X(10)-Ceva conjugate of X(6)\"\>"}, { RowBox[{ "X", "[", "235", "]"}], "\<\"X(4)-Ceva conjugate of X(185)\"\>"}, { RowBox[{"X", "[", "237", "]"}], "\<\"X(3)-line conjugate of X(2)\"\>"}, { RowBox[{"X", "[", "297", "]"}], "\<\"X(2)-Hirst inverse of X(4)\"\>"}, { RowBox[{ "X", "[", "376", "]"}], "\<\"centroid of the antipedal triangle of X(2)\"\>"}, { RowBox[{ "X", "[", "377", "]"}], "\<\"Euler line intercept of line X(7)X(8)\"\>"}, { RowBox[{"X", "[", "378", "]"}], "\<\"reflection of X(22) in X(3)\"\>"}, { RowBox[{ "X", "[", "379", "]"}], "\<\"Euler line intercept of line X(6)X(7)\"\>"}, { RowBox[{"X", "[", "381", "]"}], "\<\"midpoint of X(2) and X(4)\"\>"}, { RowBox[{ "X", "[", "382", "]"}], "\<\"reflection of circumcenter in orthocenter\"\>"}, { RowBox[{ "X", "[", "383", "]"}], "\<\"Euler line intercept of line X(14)X(98)\"\>"}, { RowBox[{ "X", "[", "384", "]"}], "\<\"Euler line intercept of line X(32)X(76)\"\>"}, { RowBox[{"X", "[", "401", "]"}], "\<\"Bailey point\"\>"}, { RowBox[{"X", "[", "402", "]"}], "\<\"Zeeman-Gossard perspector\"\>"}, { RowBox[{"X", "[", "403", "]"}], "\<\"X(36) of the orthic triangle\"\>"}, { RowBox[{ "X", "[", "404", "]"}], "\<\"{X(2),X(3)}-harmonic conjugate of X(21)\"\>"}, { RowBox[{ "X", "[", "405", "]"}], "\<\"Euler line intercept of line X(1)X(6)\"\>"}, { RowBox[{ "X", "[", "406", "]"}], "\<\"Euler line intercept of line X(10)X(33)\"\>"}, { RowBox[{ "X", "[", "407", "]"}], "\<\"crosspoint of X(4) and X(225)\"\>"}, { RowBox[{ "X", "[", "408", "]"}], "\<\"Euler line intercept of line X(73)X(228)\"\>"}, { RowBox[{ "X", "[", "409", "]"}], "\<\"Euler X(21)-1st-substitution point\"\>"}, { RowBox[{ "X", "[", "410", "]"}], "\<\"Euler X(29)-1st-substitution point\"\>"}, { RowBox[{ "X", "[", "411", "]"}], "\<\"Euler X(21)-2nd-substitution point\"\>"}, { RowBox[{ "X", "[", "412", "]"}], "\<\"Euler X(29)-2nd-substitution point\"\>"}, { RowBox[{ "X", "[", "413", "]"}], "\<\"Euler X(21)-3rd-substitution point\"\>"}, { RowBox[{ "X", "[", "414", "]"}], "\<\"Euler X(29)-3rd-substitution point\"\>"}, { RowBox[{"X", "[", "415", "]"}], "\<\"X(4)-Hirst inverse of X(29)\"\>"}, { RowBox[{"X", "[", "416", "]"}], "\<\"X(3)-Hirst inverse of X(21)\"\>"}, { RowBox[{ "X", "[", "417", "]"}], "\<\"X(3)-Ceva conjugate of X(185)\"\>"}, { RowBox[{ "X", "[", "418", "]"}], "\<\"X(3)-Ceva-conjugate of X(216)\"\>"}, { RowBox[{"X", "[", "419", "]"}], "\<\"X(4)-Hirst inverse of X(25)\"\>"}, { RowBox[{"X", "[", "420", "]"}], "\<\"X(4)-Hirst inverse of X(427)\"\>"}, { RowBox[{"X", "[", "421", "]"}], "\<\"X(4)-Hirst inverse of X(24)\"\>"}, { RowBox[{"X", "[", "422", "]"}], "\<\"X(4)-Hirst inverse of X(28)\"\>"}, { RowBox[{"X", "[", "423", "]"}], "\<\"X(4)-Hirst inverse of X(27)\"\>"}, { RowBox[{"X", "[", "424", "]"}], "\<\"X(4)-Hirst inverse of X(451)\"\>"}, { RowBox[{"X", "[", "425", "]"}], "\<\"X(4)-Hirst inverse of X(21)\"\>"}, { RowBox[{ "X", "[", "426", "]"}], "\<\"Euler X(19)-4th-substitution point\"\>"}, { RowBox[{"X", "[", "427", "]"}], "\<\"complement of X(22)\"\>"}, { RowBox[{ "X", "[", "428", "]"}], "\<\"Euler X(38)-5th-substitution point\"\>"}, { RowBox[{ "X", "[", "429", "]"}], "\<\"Euler X(58)-5th-substitution point\"\>"}, { RowBox[{ "X", "[", "430", "]"}], "\<\"Euler X(81)-5th-substitution point\"\>"}, { RowBox[{ "X", "[", "431", "]"}], "\<\"Euler X(283)-5th-substitution point\"\>"}, { RowBox[{ "X", "[", "432", "]"}], "\<\"Euler X(155)-6th-substitution point\"\>"}, { RowBox[{ "X", "[", "433", "]"}], "\<\"Euler X(159)-6th-substitution point\"\>"}, { RowBox[{ "X", "[", "434", "]"}], "\<\"Euler X(195)-6th-substitution point\"\>"}, { RowBox[{ "X", "[", "435", "]"}], "\<\"Euler X(399)-6th-substitution point\"\>"}, { RowBox[{ "X", "[", "436", "]"}], "\<\"Euler X(48)-7th-substitution point\"\>"}, { RowBox[{ "X", "[", "437", "]"}], "\<\"Euler X(214)-8th-substitution point\"\>"}, { RowBox[{ "X", "[", "438", "]"}], "\<\"Euler X(204)-9th-substitution point\"\>"}, { RowBox[{ "X", "[", "439", "]"}], "\<\"Euler X(193)-10th-substitution point\"\>"}, { RowBox[{"X", "[", "440", "]"}], "\<\"complement of X(27)\"\>"}, { RowBox[{"X", "[", "441", "]"}], "\<\"complement of X(297)\"\>"}, { RowBox[{ "X", "[", "442", "]"}], "\<\"complement of Schiffler point\"\>"}, { RowBox[{"X", "[", "443", "]"}], "\<\"complement of X(452)\"\>"}, { RowBox[{ "X", "[", "444", "]"}], "\<\"Euler line intercept of line X(19)X(232)\"\>"}, { RowBox[{ "X", "[", "445", "]"}], "\<\"Euler X(79)-11th-substitution point\"\>"}, { RowBox[{"X", "[", "446", "]"}], "\<\"crosspoint of X(98) and X(511)\"\>"}, { RowBox[{"X", "[", "447", "]"}], "\<\"X(2)-Hirst inverse of X(27)\"\>"}, { RowBox[{"X", "[", "448", "]"}], "\<\"X(2)-Hirst inverse of X(21)\"\>"}, { RowBox[{"X", "[", "449", "]"}], "\<\"X(2)-Hirst inverse of X(452)\"\>"}, { RowBox[{"X", "[", "450", "]"}], "\<\"X(3)-Hirst inverse of X(4)\"\>"}, { RowBox[{"X", "[", "451", "]"}], "\<\"X(4)-Hirst inverse of X(424)\"\>"}, { RowBox[{"X", "[", "452", "]"}], "\<\"X(2)-Hirst inverse of X(449)\"\>"}, { RowBox[{ "X", "[", "453", "]"}], "\<\"X(46)-Hirst inverse of X(452)\"\>"}, { RowBox[{ "X", "[", "454", "]"}], "\<\"Euler X(155)-12th-substitution point\"\>"}, { RowBox[{ "X", "[", "455", "]"}], "\<\"Euler X(159)-13th-substitution point\"\>"}, { RowBox[{ "X", "[", "456", "]"}], "\<\"Euler X(195)-13th-substitution point\"\>"}, { RowBox[{ "X", "[", "457", "]"}], "\<\"Euler X(399)-12th-substitution point\"\>"}, { RowBox[{ "X", "[", "458", "]"}], "\<\"Euler line intercept of line X(76)X(275)\"\>"}, { RowBox[{"X", "[", "459", "]"}], "\<\"X(393)-cross conjugate of X(4)\"\>"}, { RowBox[{"X", "[", "460", "]"}], "\<\"X(4)-Hirst inverse of X(459)\"\>"}, { RowBox[{ "X", "[", "461", "]"}], "\<\"Euler line intercept of line X(33)X(200)\"\>"}, { RowBox[{ "X", "[", "462", "]"}], "\<\"Euler line intercept of line X(51)X(397)\"\>"}, { RowBox[{ "X", "[", "463", "]"}], "\<\"Euler line intercept of line X(51)X(398)\"\>"}, { RowBox[{ "X", "[", "464", "]"}], "\<\"Euler line intercept of line X(63)X(69)\"\>"}, { RowBox[{ "X", "[", "465", "]"}], "\<\"Euler line intercept of line X(216)X(395)\"\>"}, { RowBox[{ "X", "[", "466", "]"}], "\<\"Euler line intercept of line X(216)X(396)\"\>"}, { RowBox[{ "X", "[", "467", "]"}], "\<\"Euler line intercept of line X(53)X(311)\"\>"}, { RowBox[{"X", "[", "468", "]"}], "\<\"X(2)-line conjugate of X(3)\"\>"}, { RowBox[{ "X", "[", "469", "]"}], "\<\"Euler line intercept of line X(92)X(264)\"\>"}, { RowBox[{ "X", "[", "470", "]"}], "\<\"X(15)-cross conjugate of X(298)\"\>"}, { RowBox[{ "X", "[", "471", "]"}], "\<\"X(16)-cross conjugate of X(299)\"\>"}, { RowBox[{ "X", "[", "472", "]"}], "\<\"X(62)-cross conjugate of X(303)\"\>"}, { RowBox[{ "X", "[", "473", "]"}], "\<\"X(61)-cross conjugate of X(302)\"\>"}, { RowBox[{ "X", "[", "474", "]"}], "\<\"Euler line intercept of line X(10)X(56)\"\>"}, { RowBox[{ "X", "[", "475", "]"}], "\<\"Euler line intercept of line X(10)X(34)\"\>"}, { RowBox[{"X", "[", "546", "]"}], "\<\"midpoint of X(4) and X(5)\"\>"}, { RowBox[{"X", "[", "547", "]"}], "\<\"midpoint of X(2) and X(5)\"\>"}, { RowBox[{"X", "[", "548", "]"}], "\<\"midpoint of X(5) and X(20)\"\>"}, { RowBox[{"X", "[", "549", "]"}], "\<\"midpoint of X(2) and X(3)\"\>"}, { RowBox[{"X", "[", "550", "]"}], "\<\"midpoint of X(3) and X(20)\"\>"}, { RowBox[{"X", "[", "631", "]"}], "\<\"3/5*og\"\>"}, { RowBox[{"X", "[", "632", "]"}], "\<\"9/10*og\"\>"}, { RowBox[{"X", "[", "851", "]"}], "\<\"X(65)-Hirst inverse of X(73)\"\>"}, { RowBox[{"X", "[", "852", "]"}], "\<\"X(2)-line conjugate of X(4)\"\>"}, { RowBox[{ "X", "[", "853", "]"}], "\<\"intercept of Euler line and trilinear pole of X(55)\"\>"}, { RowBox[{ "X", "[", "854", "]"}], "\<\"intercept of Euler line and trilinear pole of X(56)\"\>"}, { RowBox[{ "X", "[", "855", "]"}], "\<\"intercept of Euler line and trilinear pole of X(57)\"\>"}, { RowBox[{ "X", "[", "856", "]"}], "\<\"intercept of Euler line and trilinear pole of X(63)\"\>"}, { RowBox[{ "X", "[", "857", "]"}], "\<\"intercept of Euler line and trilinear pole of X(75)\"\>"}, { RowBox[{"X", "[", "858", "]"}], "\<\"complement of X(23)\"\>"}, { RowBox[{ "X", "[", "859", "]"}], "\<\"intercept of Euler line and trilinear pole of X(81)\"\>"}, { RowBox[{ "X", "[", "860", "]"}], "\<\"intercept of Euler line and trilinear pole of X(92)\"\>"}, { RowBox[{ "X", "[", "861", "]"}], "\<\"intercept of Euler line and trilinear pole of X(9)\"\>"}, { RowBox[{ "X", "[", "862", "]"}], "\<\"intercept of Euler line and trilinear pole of X(19)\"\>"}, { RowBox[{ "X", "[", "863", "]"}], "\<\"intercept of Euler line and pole of trilinear X(31)\"\>"}, { RowBox[{ "X", "[", "864", "]"}], "\<\"intercept of Euler line and trilinear pole of X(32)\"\>"}, { RowBox[{ "X", "[", "865", "]"}], "\<\"intercept of Euler line and trilinear pole of X(512)\"\>"}, { RowBox[{ "X", "[", "866", "]"}], "\<\"intercept of Euler line and trilinear pole of X(513)\"\>"}, { RowBox[{ "X", "[", "867", "]"}], "\<\"intercept of Euler line and trilinear pole of X(514)\"\>"}, { RowBox[{"X", "[", "868", "]"}], "\<\"crosspoint of X(98) and X(523)\"\>"}, { RowBox[{ "X", "[", "964", "]"}], "\<\"intercept of Euler line and line X(6)X(8)\"\>"}, { RowBox[{ "X", "[", "1003", "]"}], "\<\"intercept of Euler line and line X(6)X(99)\"\>"}, { RowBox[{ "X", "[", "1004", "]"}], "\<\"intercept of Euler line and line X(7)X(100)\"\>"}, { RowBox[{ "X", "[", "1005", "]"}], "\<\"intercept of Euler line and line X(9)X(100)\"\>"}, { RowBox[{ "X", "[", "1006", "]"}], "\<\"intercept of Euler line and line X(9)X(48)\"\>"}, { RowBox[{ "X", "[", "1008", "]"}], "\<\"intercept of Euler line and line X(1)X(76)\"\>"}, { RowBox[{ "X", "[", "1009", "]"}], "\<\"intercept of Euler line and line X(1)X(39)\"\>"}, { RowBox[{ "X", "[", "1010", "]"}], "\<\"intercept of Euler line and line X(1)X(75)\"\>"}, { RowBox[{ "X", "[", "1011", "]"}], "\<\"intercept of Euler line and line X(6)X(31)\"\>"}, { RowBox[{ "X", "[", "1012", "]"}], "\<\"intercept of Euler line and line X(1)X(84)\"\>"}, { RowBox[{ "X", "[", "1013", "]"}], "\<\"intercept of Euler line and line X(7)X(108)\"\>"}, { RowBox[{ "X", "[", "1080", "]"}], "\<\"intercept of Euler line and line X(13)X(98)\"\>"}, { RowBox[{ "X", "[", "1113", "]"}], "\<\"1st Euler-line-circumcircle intersection\"\>"}, { RowBox[{ "X", "[", "1114", "]"}], "\<\"2nd Euler-line-circumcircle intersection\"\>"}, { RowBox[{"X", "[", "1312", "]"}], "\<\"1st Moses intersection\"\>"}, { RowBox[{"X", "[", "1313", "]"}], "\<\"2nd Moses intersection\"\>"}, { RowBox[{"X", "[", "1314", "]"}], "\<\"3rd Moses intersection\"\>"}, { RowBox[{"X", "[", "1315", "]"}], "\<\"4th Moses intersection\"\>"}, { RowBox[{"X", "[", "1316", "]"}], "\<\"5th Moses intersection\"\>"}, { RowBox[{ "X", "[", "1325", "]"}], "\<\"inverse-in-circumcircle of X(21)\"\>"}, { RowBox[{ "X", "[", "1344", "]"}], "\<\"insimilicenter(circumcircle, orthocentroidal circle)\"\>"}, { RowBox[{ "X", "[", "1345", "]"}], "\<\"exsimilicenter(circumcircle, orthocentroidal circle)\"\>"}, { RowBox[{ "X", "[", "1346", "]"}], "\<\"insimilicenter(nine-point circle, orthocentroidal circle)\"\ \>"}, { RowBox[{ "X", "[", "1347", "]"}], "\<\"exsimilicenter(nine-point circle, orthocentroidal \ circle)\"\>"}, { RowBox[{ "X", "[", "1368", "]"}], "\<\"complementary conjugate of X(6)\"\>"}, { RowBox[{"X", "[", "1370", "]"}], "\<\"anticomplement of X(25)\"\>"}, { RowBox[{"X", "[", "1375", "]"}], "\<\"Evans point\"\>"}, { RowBox[{"X", "[", "1513", "]"}], "\<\"orthojoin of X(2)\"\>"}, { RowBox[{"X", "[", "1529", "]"}], "\<\"orthojoin of X(25)\"\>"}, { RowBox[{"X", "[", "1532", "]"}], "\<\"orthojoin of X(37)\"\>"}, { RowBox[{"X", "[", "1536", "]"}], "\<\"orthojoin of X(42)\"\>"}, { RowBox[{"X", "[", "1551", "]"}], "\<\"orthojoin of X(111)\"\>"}, { RowBox[{"X", "[", "1556", "]"}], "\<\"orthojoin of X(251)\"\>"}, { RowBox[{"X", "[", "1557", "]"}], "\<\"orthojoin of X(263)\"\>"}, { RowBox[{"X", "[", "1559", "]"}], "\<\"orthojoin of X(393)\"\>"}, { RowBox[{"X", "[", "1563", "]"}], "\<\"orthojoin of X(588)\"\>"}, { RowBox[{"X", "[", "1564", "]"}], "\<\"orthojoin of X(589)\"\>"}, { RowBox[{"X", "[", "1567", "]"}], "\<\"orthojoin of X(694)\"\>"}, { RowBox[{"X", "[", "1583", "]"}], "\<\"point capella i\"\>"}, { RowBox[{"X", "[", "1584", "]"}], "\<\"point capella ii\"\>"}, { RowBox[{"X", "[", "1585", "]"}], "\<\"point caph i\"\>"}, { RowBox[{"X", "[", "1586", "]"}], "\<\"point caph ii\"\>"}, { RowBox[{"X", "[", "1589", "]"}], "\<\"point chara i\"\>"}, { RowBox[{"X", "[", "1590", "]"}], "\<\"point chara ii\"\>"}, { RowBox[{"X", "[", "1591", "]"}], "\<\"point chara iii\"\>"}, { RowBox[{"X", "[", "1592", "]"}], "\<\"point chara iv\"\>"}, { RowBox[{"X", "[", "1593", "]"}], "\<\"point cebalrai\"\>"}, { RowBox[{"X", "[", "1594", "]"}], "\<\"Rigby-lalescu orthopole\"\>"}, { RowBox[{"X", "[", "1595", "]"}], "\<\"point cheleb i\"\>"}, { RowBox[{"X", "[", "1596", "]"}], "\<\"point cheleb ii\"\>"}, { RowBox[{"X", "[", "1597", "]"}], "\<\"point chertan i\"\>"}, { RowBox[{"X", "[", "1598", "]"}], "\<\"point chertan ii\"\>"}, { RowBox[{"X", "[", "1599", "]"}], "\<\"point chort i\"\>"}, { RowBox[{"X", "[", "1600", "]"}], "\<\"point chort ii\"\>"}, { RowBox[{"X", "[", "1628", "]"}], "\<\"Tcc-perspector of X(254)\"\>"}, { RowBox[{"X", "[", "1650", "]"}], "\<\"tripolar centroid of X(525)\"\>"}, { RowBox[{"X", "[", "1651", "]"}], "\<\"tripolar centroid of X(648)\"\>"}, { RowBox[{ "X", "[", "1656", "]"}], "\<\"intersection of Euler line and line X(17)X(18)\"\>"}, { RowBox[{ "X", "[", "1657", "]"}], "\<\"{X(3),X(4)}-harmonic conjugate of X(1656)\"\>"}, { RowBox[{ "X", "[", "1658", "]"}], "\<\"circumcenter of Kosnita triangle\"\>"}, { RowBox[{ "X", "[", "1816", "]"}], "\<\"inverse Mimosa transform of X(1075)\"\>"}, { RowBox[{ "X", "[", "1817", "]"}], "\<\"inverse Mimosa transform of X(1249)\"\>"}, { RowBox[{"X", "[", "1883", "]"}], "\<\"Zosma transform of X(595)\"\>"}, { RowBox[{"X", "[", "1884", "]"}], "\<\"Zosma transform of X(758)\"\>"}, { RowBox[{"X", "[", "1885", "]"}], "\<\"Zosma transform of X(774)\"\>"}, { RowBox[{"X", "[", "1889", "]"}], "\<\"Zosma transform of X(968)\"\>"}, { RowBox[{"X", "[", "1894", "]"}], "\<\"Zosma transform of X(993)\"\>"}, { RowBox[{"X", "[", "1904", "]"}], "\<\"Zosma transform of X(1468)\"\>"}, { RowBox[{"X", "[", "1906", "]"}], "\<\"Zosma transform of X(1496)\"\>"}, { RowBox[{"X", "[", "1907", "]"}], "\<\"Zosma transform of X(1497)\"\>"}, { RowBox[{"X", "[", "1981", "]"}], "\<\"vega transform of X(647)\"\>"}, { RowBox[{ "X", "[", "1982", "]"}], "\<\"pu(22)-harmonic conjugate of X(1981)\"\>"}, { RowBox[{"X", "[", "1984", "]"}], "\<\"vega transform of X(1020)\"\>"}, { RowBox[{ "X", "[", "1985", "]"}], "\<\"Euler intercept of line X(6)X(11)\"\>"}, { RowBox[{"X", "[", "1995", "]"}], "\<\"orthocorrespondent of X(6)\"\>"}, { RowBox[{"X", "[", "2041", "]"}], "\<\"1st Euler-Vecten-Gibert point\"\>"}, { RowBox[{"X", "[", "2042", "]"}], "\<\"2nd Euler-Vecten-Gibert point\"\>"}, { RowBox[{"X", "[", "2043", "]"}], "\<\"3rd Euler-Vecten-Gibert point\"\>"}, { RowBox[{"X", "[", "2044", "]"}], "\<\"4th Euler-Vecten-Gibert point\"\>"}, { RowBox[{"X", "[", "2045", "]"}], "\<\"5th Euler-Vecten-Gibert point\"\>"}, { RowBox[{"X", "[", "2046", "]"}], "\<\"6th Euler-Vecten-Gibert point\"\>"}, { RowBox[{ "X", "[", "2047", "]"}], "\<\"Euler line intercept of line X(10)X(485)\"\>"}, { RowBox[{ "X", "[", "2048", "]"}], "\<\"{X(3),X(5)}-harmonic conjugate of X(2047)\"\>"}, { RowBox[{ "X", "[", "2049", "]"}], "\<\"Euler line intercept of line X(6)X(10)\"\>"}, { RowBox[{ "X", "[", "2050", "]"}], "\<\"{X(3),X(5)}-harmonic conjugate of X(2049)\"\>"}, { RowBox[{"X", "[", "2060", "]"}], "\<\"Orion transform of X(20)\"\>"}, { RowBox[{ "X", "[", "2070", "]"}], "\<\"inverse-in-circumcircle of X(5)\"\>"}, { RowBox[{ "X", "[", "2071", "]"}], "\<\"inverse-in-circumcircle of X(20)\"\>"}, { RowBox[{ "X", "[", "2072", "]"}], "\<\"inverse-in-circumcircle of X(26)\"\>"}, { RowBox[{ "X", "[", "2073", "]"}], "\<\"inverse-in-circumcircle of X(27)\"\>"}, { RowBox[{ "X", "[", "2074", "]"}], "\<\"inverse-in-circumcircle of X(28)\"\>"}, { RowBox[{ "X", "[", "2075", "]"}], "\<\"inverse-in-circumcircle of X(29)\"\>"}, { RowBox[{ "X", "[", "2409", "]"}], "\<\"Gibert-Simson transform of X(112)\"\>"}, { RowBox[{ "X", "[", "2450", "]"}], "\<\"inverse-in-nine-point-circle of X(1316)\"\>"}, { RowBox[{ "X", "[", "2454", "]"}], "\<\"1st intersection(Euler line, Steiner inellipse)\"\>"}, { RowBox[{ "X", "[", "2455", "]"}], "\<\"2nd intersection(Euler line, Steiner inellipse)\"\>"}, { RowBox[{"X", "[", "2475", "]"}], "\<\"anticomplement of X(21)\"\>"}, { RowBox[{ "X", "[", "2476", "]"}], "\<\"inverse-in-orthocentroidal-circle of X(21)\"\>"}, { RowBox[{ "X", "[", "2478", "]"}], "\<\"inverse-in-orthocentroidal-circle of X(377)\"\>"}, { RowBox[{ "X", "[", "2479", "]"}], "\<\"1st intersection(Euler line, Steiner circumellipse)\"\>"}, { RowBox[{ "X", "[", "2480", "]"}], "\<\"2nd intersection(Euler line, Steiner circumellipse)\"\>"}, { RowBox[{ "X", "[", "2552", "]"}], "\<\"insimilicenter(orthocentroidal circle, (X(4),2r))\"\>"}, { RowBox[{ "X", "[", "2553", "]"}], "\<\"exsimilicenter(orthocentroidal circle, (X(4),2r))\"\>"}, { RowBox[{ "X", "[", "2554", "]"}], "\<\"1st intersection(Euler line, 2nd Brocard circle)\"\>"}, { RowBox[{ "X", "[", "2555", "]"}], "\<\"2nd intersection(Euler line, 2nd Brocard circle)\"\>"}, { RowBox[{ "X", "[", "2566", "]"}], "\<\"insimilicenter(nine-point circle, 2nd Brocard \ circle)\"\>"}, { RowBox[{ "X", "[", "2567", "]"}], "\<\"exsimilicenter(nine-point circle, 2nd Brocard \ circle)\"\>"}, { RowBox[{ "X", "[", "2570", "]"}], "\<\"insimilicenter(orthocentroidal circle, 2nd Brocard \ circle)\"\>"}, { RowBox[{ "X", "[", "2571", "]"}], "\<\"exsimilicenter(orthocentroidal circle, 2nd Brocard \ circle)\"\>"}, { RowBox[{ "X", "[", "2675", "]"}], "\<\"intersection of lines X(2671)X(2673) and \ X(2672)X(2674)\"\>"}, { RowBox[{ "X", "[", "2676", "]"}], "\<\"intersection of Euler line and line X(2671)X(2672)\"\>"}, { RowBox[{ "X", "[", "2915", "]"}], "\<\"tangential isogonal conjugate of X(1)\"\>"}, { RowBox[{ "X", "[", "2937", "]"}], "\<\"tangential isogonal conjugate of X(195)\"\>"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[2.0999999999999996`]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output",ExpressionUUID->"4cf606dd-587f-44be-\ 9831-27b498913884"] }, Open ]], Cell[CellGroupData[{ Cell["Check", "Subsection",ExpressionUUID->"c3099dc0-948e-4217-914f-47d6634a2bec"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Do", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"{", RowBox[{"i", ",", RowBox[{"ctrs", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"TimeConstrained", "[", RowBox[{ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"DistanceTrilinears", "[", RowBox[{"TrigExpand", "[", RowBox[{ RowBox[{"LineEquation", "[", "EulerLine", "]"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "->", RowBox[{"Trilinears", "[", RowBox[{"ctrs", "[", RowBox[{"[", "i", "]"}], "]"}], "]"}]}], "]"}]}], "]"}], "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], ",", "100"}], "]"}], "//", "Timing"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{"Length", "[", "ctrs", "]"}]}], "}"}]}], "]"}]], "Input",Expressi\ onUUID->"2d307a8b-ad07-40e0-83f2-1dce1cfd0138"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", RowBox[{"X", "[", "2", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.10000000000000142`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"48fe9ade-ea21-4027-a1ad-9dc870b21e9f"], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", RowBox[{"X", "[", "3", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.05000000000000071`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"f651c55c-c3f2-4c99-be75-ce5cece30276"], Cell[BoxData[ RowBox[{"{", RowBox[{"3", ",", RowBox[{"X", "[", "4", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.05999999999999872`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"b5851ae4-d3ca-4b5c-9f46-2c985a26f935"], Cell[BoxData[ RowBox[{"{", RowBox[{"4", ",", RowBox[{"X", "[", "5", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"9.979999999999997`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"33070451-953e-4342-861c-b3a925f5f891"], Cell[BoxData[ RowBox[{"{", RowBox[{"5", ",", RowBox[{"X", "[", "20", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07000000000000384`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"43bb3d6a-4dfc-4926-8a7f-73d9e2e8b8c6"], Cell[BoxData[ RowBox[{"{", RowBox[{"6", ",", RowBox[{"X", "[", "21", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.10999999999999943`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"40248b57-d54c-40ad-a4a4-84574b9d1a9f"], Cell[BoxData[ RowBox[{"{", RowBox[{"7", ",", RowBox[{"X", "[", "22", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.120000000000001`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"b4e98f5a-1f59-49dc-a7f5-c0a2bf65b97e"], Cell[BoxData[ RowBox[{"{", RowBox[{"8", ",", RowBox[{"X", "[", "23", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.14999999999999858`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"dbc4212f-d8df-415e-9fa4-e84812c07647"], Cell[BoxData[ RowBox[{"{", RowBox[{"9", ",", RowBox[{"X", "[", "24", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.05999999999999872`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"1d61ee37-60e9-462d-9c10-521e898f810c"], Cell[BoxData[ RowBox[{"{", RowBox[{"10", ",", RowBox[{"X", "[", "25", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.060000000000002274`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"ea5f2649-df88-4ef2-bfd5-62aea5775beb"], Cell[BoxData[ RowBox[{"{", RowBox[{"11", ",", RowBox[{"X", "[", "26", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.28999999999999915`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"2b33b26a-1f69-4eda-8e18-d1004ebb2e44"], Cell[BoxData[ RowBox[{"{", RowBox[{"12", ",", RowBox[{"X", "[", "27", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.08999999999999986`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"7d324b89-56cb-4afd-9759-574d5dbe7ee9"], Cell[BoxData[ RowBox[{"{", RowBox[{"13", ",", RowBox[{"X", "[", "28", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"5.6000000000000085`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"62c49b0c-b164-4eff-bd55-969f89c03676"], Cell[BoxData[ RowBox[{"{", RowBox[{"14", ",", RowBox[{"X", "[", "29", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.0799999999999983`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"f46adf42-59a1-4c4f-8960-c612f6f2c162"], Cell[BoxData[ RowBox[{"{", RowBox[{"15", ",", RowBox[{"X", "[", "30", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07000000000000028`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"972943f9-75ee-41ab-867c-5db2c88422bd"], Cell[BoxData[ RowBox[{"{", RowBox[{"16", ",", RowBox[{"X", "[", "140", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07000000000000028`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"f61affda-72bf-4445-bf4b-a32f7c6cf90a"], Cell[BoxData[ RowBox[{"{", RowBox[{"17", ",", RowBox[{"X", "[", "186", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07000000000000028`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"99aed333-dc86-479b-8eda-72c2377a8154"], Cell[BoxData[ RowBox[{"{", RowBox[{"18", ",", RowBox[{"X", "[", "199", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.3499999999999943`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"4bf73b09-2407-4b06-9e65-08ffbdebe779"], Cell[BoxData[ RowBox[{"{", RowBox[{"19", ",", RowBox[{"X", "[", "235", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"7.210000000000001`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"aa767476-b40a-4eb8-ba61-a683f00363ee"], Cell[BoxData[ RowBox[{"{", RowBox[{"20", ",", RowBox[{"X", "[", "237", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"7.559999999999995`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"519f78d4-09c9-470e-bc62-619d4bb1a963"], Cell[BoxData[ RowBox[{"{", RowBox[{"21", ",", RowBox[{"X", "[", "297", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"11.650000000000006`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"3b2589dc-3081-4219-8714-fea7581778b1"], Cell[BoxData[ RowBox[{"{", RowBox[{"22", ",", RowBox[{"X", "[", "376", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.0899999999999963`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"8a704008-4494-4111-a4a2-20bb6b9bf477"], Cell[BoxData[ RowBox[{"{", RowBox[{"23", ",", RowBox[{"X", "[", "377", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.21999999999999886`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"212f3736-c6c7-4fd5-ad8c-07b4c33226f1"], Cell[BoxData[ RowBox[{"{", RowBox[{"24", ",", RowBox[{"X", "[", "378", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.0800000000000054`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"4f1e9b9b-be9b-42d4-bfcd-a3dd9a901924"], Cell[BoxData[ RowBox[{"{", RowBox[{"25", ",", RowBox[{"X", "[", "379", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.29999999999999716`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"0d6c19b5-e5b6-40ed-96f9-c4c7ea979aea"], Cell[BoxData[ RowBox[{"{", RowBox[{"26", ",", RowBox[{"X", "[", "381", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"2.1199999999999974`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"e43b93c4-8d31-428a-861c-47d78fcf4873"], Cell[BoxData[ RowBox[{"{", RowBox[{"27", ",", RowBox[{"X", "[", "382", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07000000000000028`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"2bd3f4f2-08c1-4855-a003-8abd66288e6b"], Cell[BoxData[ RowBox[{"{", RowBox[{"28", ",", RowBox[{"X", "[", "383", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"10.760000000000005`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"78605ebc-fad4-4cb7-b3c2-61e6a4a76fb4"], Cell[BoxData[ RowBox[{"{", RowBox[{"29", ",", RowBox[{"X", "[", "384", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.09999999999999432`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"c41aacd4-5398-4d64-9316-d290ca877b2e"], Cell[BoxData[ RowBox[{"{", RowBox[{"30", ",", RowBox[{"X", "[", "401", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"29.5`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",Ex\ pressionUUID->"147ffdec-4ad8-4ed6-8c7e-d5d5d3d10b6d"], Cell[BoxData[ RowBox[{"{", RowBox[{"31", ",", RowBox[{"X", "[", "403", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.06999999999999318`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"65d6820d-d1c1-4b5f-ba84-9d6e9abce493"], Cell[BoxData[ RowBox[{"{", RowBox[{"32", ",", RowBox[{"X", "[", "404", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.20000000000000284`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"410cc8d6-bcbb-486f-95d5-8207b50bf77c"], Cell[BoxData[ RowBox[{"{", RowBox[{"33", ",", RowBox[{"X", "[", "405", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.12999999999999545`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"a5ea103d-5ad9-413e-8b65-fffd88bb4615"], Cell[BoxData[ RowBox[{"{", RowBox[{"34", ",", RowBox[{"X", "[", "406", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.12000000000000455`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"f4f3b2d9-be39-4f04-8cd3-c7c4800fd115"], Cell[BoxData[ RowBox[{"{", RowBox[{"35", ",", RowBox[{"X", "[", "417", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.10999999999999943`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"92d7173f-d8a0-4f00-b67a-d726c9fcafdb"], Cell[BoxData[ RowBox[{"{", RowBox[{"36", ",", RowBox[{"X", "[", "418", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.710000000000008`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"e77afdf9-3900-4600-8fb7-ab4eb4fcebf7"], Cell[BoxData[ RowBox[{"{", RowBox[{"37", ",", RowBox[{"X", "[", "427", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.09999999999999432`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"f3f71a73-f8be-407b-972e-733b98ffc99d"], Cell[BoxData[ RowBox[{"{", RowBox[{"38", ",", RowBox[{"X", "[", "450", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.0799999999999983`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"10852e87-80d5-4659-b058-c6d1d31d21dd"], Cell[BoxData[ RowBox[{"{", RowBox[{"39", ",", RowBox[{"X", "[", "470", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"3.510000000000005`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"65e4dd4e-d6c9-4bb1-b3fc-f38f340e7bc4"], Cell[BoxData[ RowBox[{"{", RowBox[{"40", ",", RowBox[{"X", "[", "471", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1.8299999999999983`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"774a9057-b975-4049-b31d-73b51f954cc6"], Cell[BoxData[ RowBox[{"{", RowBox[{"41", ",", RowBox[{"X", "[", "472", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.7800000000000011`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"fd610d50-eb93-4e65-8bca-1b4fffb6b11b"], Cell[BoxData[ RowBox[{"{", RowBox[{"42", ",", RowBox[{"X", "[", "473", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.18000000000000682`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"04bb7906-e6eb-4c8a-82e4-c6385ef76ca6"], Cell[BoxData[ RowBox[{"{", RowBox[{"43", ",", RowBox[{"X", "[", "474", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.11999999999999034`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"c1128e86-940b-48ae-b057-30e484075448"], Cell[BoxData[ RowBox[{"{", RowBox[{"44", ",", RowBox[{"X", "[", "475", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.10999999999999943`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"62e93ae5-f10a-4a29-ae5f-0f113a9fe23e"], Cell[BoxData[ RowBox[{"{", RowBox[{"45", ",", RowBox[{"X", "[", "546", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"8.090000000000003`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"e94215ff-c17d-4d48-a623-f2ef4cff0d26"], Cell[BoxData[ RowBox[{"{", RowBox[{"46", ",", RowBox[{"X", "[", "547", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"7.939999999999998`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"02767b3b-1ebd-4af7-9074-b4c315005ece"], Cell[BoxData[ RowBox[{"{", RowBox[{"47", ",", RowBox[{"X", "[", "548", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07999999999998408`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"33cfc7c6-48a1-4c41-baef-3e5cdf7b933c"], Cell[BoxData[ RowBox[{"{", RowBox[{"48", ",", RowBox[{"X", "[", "549", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.09000000000000341`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"16772ceb-6afa-4914-9810-18d218d18ed3"], Cell[BoxData[ RowBox[{"{", RowBox[{"49", ",", RowBox[{"X", "[", "550", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.09000000000000341`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"b0f2b90a-65be-4ae0-96e4-b02ab524d0cf"], Cell[BoxData[ RowBox[{"{", RowBox[{"50", ",", RowBox[{"X", "[", "631", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.06999999999999318`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"ec21db35-64ad-4da9-a8de-c8a0651acd6c"], Cell[BoxData[ RowBox[{"{", RowBox[{"51", ",", RowBox[{"X", "[", "851", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"34.19999999999999`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"0379f5b1-14e4-4849-be27-8eb58347ea46"], Cell[BoxData[ RowBox[{"{", RowBox[{"52", ",", RowBox[{"X", "[", "852", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"31.02000000000004`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"7de4e347-fbbf-410f-b8a7-b4b2e727d997"], Cell[BoxData[ RowBox[{"{", RowBox[{"53", ",", RowBox[{"X", "[", "853", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"49.18000000000001`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"0181dcf4-8129-4018-929a-\ 7f122ff260f5"], Cell[BoxData[ RowBox[{"{", RowBox[{"54", ",", RowBox[{"X", "[", "854", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"49.23999999999998`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"4fd4f25d-c723-4a51-9a37-\ c7beb25e107c"], Cell[BoxData[ RowBox[{"{", RowBox[{"55", ",", RowBox[{"X", "[", "855", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"49.31`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"b2dc57be-ab4d-455c-83e8-05dbd784eb8d"], Cell[BoxData[ RowBox[{"{", RowBox[{"56", ",", RowBox[{"X", "[", "856", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"48.64000000000004`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"634c0438-b304-44c8-a727-\ c613bc1ba107"], Cell[BoxData[ RowBox[{"{", RowBox[{"57", ",", RowBox[{"X", "[", "857", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"48.809999999999945`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"25b3dbf3-0eab-4d0c-b496-\ 283a84e102e9"], Cell[BoxData[ RowBox[{"{", RowBox[{"58", ",", RowBox[{"X", "[", "858", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"35.960000000000036`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"978e5aee-c2b4-4a46-88f5-d18eabf052c9"], Cell[BoxData[ RowBox[{"{", RowBox[{"59", ",", RowBox[{"X", "[", "859", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"48.82000000000005`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"095477af-fb87-44ce-a4fc-\ b560ae4f7251"], Cell[BoxData[ RowBox[{"{", RowBox[{"60", ",", RowBox[{"X", "[", "860", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"49.6099999999999`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"0fd6374b-0c9b-486c-a067-466f2f0f31d5"], Cell[BoxData[ RowBox[{"{", RowBox[{"61", ",", RowBox[{"X", "[", "861", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"48.950000000000045`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"a8d4e028-746d-4f4b-98b5-\ 20ef0caaa855"], Cell[BoxData[ RowBox[{"{", RowBox[{"62", ",", RowBox[{"X", "[", "862", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"49.25999999999999`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"b952bd01-5e57-4393-9e0d-\ 8245fdee203e"], Cell[BoxData[ RowBox[{"{", RowBox[{"63", ",", RowBox[{"X", "[", "863", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"42.17999999999995`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"d8dfce08-f363-4266-b21e-c6d98e87a979"], Cell[BoxData[ RowBox[{"{", RowBox[{"64", ",", RowBox[{"X", "[", "864", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"48.80000000000007`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"4b5ae0a4-a5c5-49ed-8ea6-\ 4b9d1a111276"], Cell[BoxData[ RowBox[{"{", RowBox[{"65", ",", RowBox[{"X", "[", "865", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"48.97000000000003`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"0796971c-737d-4874-999f-\ b21af6d1ff2c"], Cell[BoxData[ RowBox[{"{", RowBox[{"66", ",", RowBox[{"X", "[", "866", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"49.33000000000004`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"138318e6-e3ad-4498-9d7f-\ b1c653777720"], Cell[BoxData[ RowBox[{"{", RowBox[{"67", ",", RowBox[{"X", "[", "867", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"66.37`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"3624523f-5061-40ae-ac64-8ad098d6c357"], Cell[BoxData[ RowBox[{"{", RowBox[{"68", ",", RowBox[{"X", "[", "868", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"65.06000000000006`", " ", "Second"}], ",", "$Aborted"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"ebb003a2-6c09-404c-ba29-\ cb9b88b98fa6"], Cell[BoxData[ RowBox[{"{", RowBox[{"69", ",", RowBox[{"X", "[", "964", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.40999999999996817`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"264c6b1e-cfdd-46d6-930b-6a853c2b1daa"], Cell[BoxData[ RowBox[{"{", RowBox[{"70", ",", RowBox[{"X", "[", "1003", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.17999999999994998`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"67acb04e-bd6b-42a9-acf1-11a0ea96c66f"], Cell[BoxData[ RowBox[{"{", RowBox[{"71", ",", RowBox[{"X", "[", "1004", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.36000000000001364`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"ae34169a-29f0-4818-b04b-fe9cf407ed9d"], Cell[BoxData[ RowBox[{"{", RowBox[{"72", ",", RowBox[{"X", "[", "1006", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.6600000000000819`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"fef8e6c0-ac75-43df-a258-e8105381cc7e"], Cell[BoxData[ RowBox[{"{", RowBox[{"73", ",", RowBox[{"X", "[", "1008", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.75`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",Ex\ pressionUUID->"8ab3e4a3-9dd8-4186-9a12-9ec6bf43d590"], Cell[BoxData[ RowBox[{"{", RowBox[{"74", ",", RowBox[{"X", "[", "1009", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.2899999999999636`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"8411acd9-fc1c-40f6-b186-bffd86c1b2bf"], Cell[BoxData[ RowBox[{"{", RowBox[{"75", ",", RowBox[{"X", "[", "1010", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.2400000000000091`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"fa9d2135-c0da-4d8c-bf87-b58d751bfa56"], Cell[BoxData[ RowBox[{"{", RowBox[{"76", ",", RowBox[{"X", "[", "1011", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.31999999999993634`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"a9f5f51b-3480-4548-8177-608a2730bc6d"], Cell[BoxData[ RowBox[{"{", RowBox[{"77", ",", RowBox[{"X", "[", "1013", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.11000000000001364`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"66c33157-efff-4766-adf1-2f8f12e5c3b0"], Cell[BoxData[ RowBox[{"{", RowBox[{"78", ",", RowBox[{"X", "[", "1080", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1.6000000000000227`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"ad0b61a4-ab7a-4e31-940a-1b98f5c4ac5a"], Cell[BoxData[ RowBox[{"{", RowBox[{"79", ",", RowBox[{"X", "[", "1113", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.21000000000003638`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"7110059c-9cc2-47da-a3ea-6e9b13cd8f75"], Cell[BoxData[ RowBox[{"{", RowBox[{"80", ",", RowBox[{"X", "[", "1114", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.2300000000000182`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"15a405fa-37a6-407a-9688-b325dcd951dc"], Cell[BoxData[ RowBox[{"{", RowBox[{"81", ",", RowBox[{"X", "[", "1325", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.37000000000000455`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"de10e7e6-1a34-4b85-b1cc-90210ef29de9"], Cell[BoxData[ RowBox[{"{", RowBox[{"82", ",", RowBox[{"X", "[", "1368", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.16999999999995907`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"aded7e2b-d549-4b92-b37f-2837381767cd"], Cell[BoxData[ RowBox[{"{", RowBox[{"83", ",", RowBox[{"X", "[", "1370", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.18999999999994088`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"acd6c5e7-8b55-45ae-96a2-7d30bbb75862"], Cell[BoxData[ RowBox[{"{", RowBox[{"84", ",", RowBox[{"X", "[", "1375", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.5`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",Exp\ ressionUUID->"40232e4f-24e5-4309-97b6-0ee02297b008"], Cell[BoxData[ RowBox[{"{", RowBox[{"85", ",", RowBox[{"X", "[", "1513", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.41000000000008185`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"82403384-4c4d-40b8-ae6b-30f57391906a"], Cell[BoxData[ RowBox[{"{", RowBox[{"86", ",", RowBox[{"X", "[", "1583", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.7300000000000182`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"fd7e48cf-f31b-4801-bff1-f8eaaaacbf05"], Cell[BoxData[ RowBox[{"{", RowBox[{"87", ",", RowBox[{"X", "[", "1584", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.09999999999990905`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"01592913-ef19-4bcf-ad2b-358afd607160"], Cell[BoxData[ RowBox[{"{", RowBox[{"88", ",", RowBox[{"X", "[", "1585", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.12999999999999545`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"ac3d5863-aa1a-48cd-b218-43d43bac31a7"], Cell[BoxData[ RowBox[{"{", RowBox[{"89", ",", RowBox[{"X", "[", "1586", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.12000000000000455`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"9d4e5106-15ff-41b3-973e-15d1b16c13b1"], Cell[BoxData[ RowBox[{"{", RowBox[{"90", ",", RowBox[{"X", "[", "1589", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.7300000000000182`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"11aff9e3-3a9e-4c77-9d17-7b56ccb918ec"], Cell[BoxData[ RowBox[{"{", RowBox[{"91", ",", RowBox[{"X", "[", "1590", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.7400000000000091`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"805389a9-3577-42fb-880d-f5881d33cec2"], Cell[BoxData[ RowBox[{"{", RowBox[{"92", ",", RowBox[{"X", "[", "1591", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"10.129999999999995`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"05d2a480-55cb-451d-8bec-96e0b52e1da1"], Cell[BoxData[ RowBox[{"{", RowBox[{"93", ",", RowBox[{"X", "[", "1592", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"8.459999999999923`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"42396cdf-df24-41c6-96ef-a8a77dbe4626"], Cell[BoxData[ RowBox[{"{", RowBox[{"94", ",", RowBox[{"X", "[", "1593", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07000000000005002`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"d3358b2a-328c-40ad-8432-5cc86e2d7476"], Cell[BoxData[ RowBox[{"{", RowBox[{"95", ",", RowBox[{"X", "[", "1594", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.09000000000003183`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"889bd10a-8b87-450f-865e-041875b68f9f"], Cell[BoxData[ RowBox[{"{", RowBox[{"96", ",", RowBox[{"X", "[", "1595", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.07999999999992724`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"16d70c6d-748e-425c-b5c7-0ef7017e1c1b"], Cell[BoxData[ RowBox[{"{", RowBox[{"97", ",", RowBox[{"X", "[", "1596", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.09000000000003183`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"a4e3ce2c-b42d-4640-aba8-41572e1bc8f9"], Cell[BoxData[ RowBox[{"{", RowBox[{"98", ",", RowBox[{"X", "[", "1597", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.06999999999993634`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"4e015284-c5c6-466f-8fcc-6bf5845af4eb"], Cell[BoxData[ RowBox[{"{", RowBox[{"99", ",", RowBox[{"X", "[", "1598", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.08000000000004093`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"8610fe28-7b44-4f57-b8a6-9835fcb600f5"], Cell[BoxData[ RowBox[{"{", RowBox[{"100", ",", RowBox[{"X", "[", "1599", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.10000000000002274`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"e1a27fcd-e2e4-41a4-b0db-8b3a5af2f036"], Cell[BoxData[ RowBox[{"{", RowBox[{"101", ",", RowBox[{"X", "[", "1600", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.10000000000002274`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"18a3d478-38e9-49f7-98c8-bc1df8ef91e7"], Cell[BoxData[ RowBox[{"{", RowBox[{"102", ",", RowBox[{"X", "[", "1656", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.06999999999993634`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"1554335e-4aef-44a0-83a5-68f0e861373f"], Cell[BoxData[ RowBox[{"{", RowBox[{"103", ",", RowBox[{"X", "[", "1657", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.06000000000005912`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"a94039ce-e8cf-42a5-9141-fd4a23f03090"], Cell[BoxData[ RowBox[{"{", RowBox[{"104", ",", RowBox[{"X", "[", "1984", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1.7899999999999636`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"85a0fa1b-0729-4efc-9140-466bf5ba45c9"], Cell[BoxData[ RowBox[{"{", RowBox[{"105", ",", RowBox[{"X", "[", "1995", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"0.14999999999997726`", " ", "Second"}], ",", "0"}], "}"}]}], "}"}]], "Print",ExpressionUUID->"1af62b27-b29b-4473-bd77-6ca75149d088"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"DistanceTrilinears", "[", RowBox[{ RowBox[{ RowBox[{"LineEquation", "[", "SoddyLine", "]"}], "/.", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]"}], "}"}], "->", RowBox[{"Trilinears", "[", "#", "]"}]}], "]"}]}], "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"x_", "-", "y_"}], "]"}], "\[RuleDelayed]", RowBox[{"TrigExpand", "[", RowBox[{"Sin", "[", RowBox[{"x", "-", "y"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Sin", "[", RowBox[{"2", "x_"}], "]"}], "\[RuleDelayed]", RowBox[{"TrigExpand", "[", RowBox[{"2", "x"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Sec", "[", RowBox[{"x_", "/", "2"}], "]"}], "\[RuleDelayed]", RowBox[{"Sqrt", "[", RowBox[{"2", "/", RowBox[{"(", RowBox[{"1", "+", RowBox[{"Cos", "[", "x", "]"}]}], ")"}]}], "]"}]}]}], "\[IndentingNewLine]", "}"}]}], "]"}], ",", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], "&"}], "/@", RowBox[{"{", RowBox[{ RowBox[{"X", "[", "853", "]"}], ",", RowBox[{"X", "[", "854", "]"}], ",", RowBox[{"X", "[", "855", "]"}], ",", RowBox[{"X", "[", "856", "]"}], ",", RowBox[{"X", "[", "857", "]"}], ",", RowBox[{"X", "[", "859", "]"}], ",", RowBox[{"X", "[", "860", "]"}], ",", RowBox[{"X", "[", "861", "]"}], ",", RowBox[{"X", "[", "862", "]"}], ",", RowBox[{"X", "[", "864", "]"}], ",", RowBox[{"X", "[", "865", "]"}], ",", RowBox[{"X", "[", "866", "]"}], ",", RowBox[{"X", "[", "867", "]"}], ",", RowBox[{"X", "[", "868", "]"}]}], "}"}]}]], "Input",ExpressionUUID->\ "d72f3894-cf97-4f03-be71-2aabc7473ec6"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}]], "Output",ExpressionUUID->"138a198f-eac0-4bc6-b22a-f54f29f588ce"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Distances", "Section",ExpressionUUID->"558abbf7-717f-4af5-815f-61b107a67b52"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"h", ",", "g", ",", "o", ",", "n"}], "}"}], "=", RowBox[{"{", RowBox[{ "Orthocenter", ",", "Centroid", ",", "Circumcenter", ",", "NinePointCenter"}], "}"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{ RowBox[{"Distance", "[", RowBox[{"#1", ",", "#2"}], "]"}], "/", RowBox[{"Distance", "[", RowBox[{"#3", ",", "#4"}], "]"}]}], "]"}]}], ")"}], "&"}], "@@@", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"h", ",", "g", ",", "g", ",", "o"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"h", ",", "o", ",", "g", ",", "o"}], "}"}]}], "\[IndentingNewLine]", "}"}]}]}], "Input",ExpressionUUID->"fc1cc2e3-d5b5-\ 4a76-9146-f572a7408fc5"], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}]], "Output",ExpressionUUID->"f4abbcaa-33be-42eb-b287-48abdc8e0250"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Simplify", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"Together", "//@", RowBox[{"DistanceTrilinears", "[", RowBox[{ RowBox[{ RowBox[{"Distance", "[", RowBox[{"#1", ",", "#2"}], "]"}], "/", RowBox[{"Distance", "[", RowBox[{"#3", ",", "#4"}], "]"}]}], "/.", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "x_", "]"}], "\[RuleDelayed]", RowBox[{"TrigExpand", "[", RowBox[{"Cos", "[", "x", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Sin", "[", "x_", "]"}], "\[RuleDelayed]", RowBox[{"TrigExpand", "[", RowBox[{"Sin", "[", "x", "]"}], "]"}]}]}], "\[IndentingNewLine]", "}"}]}], "\[IndentingNewLine]", "]"}]}], ")"}], "&"}], "@@@", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"h", ",", "o", ",", "n", ",", "o"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"h", ",", "o", ",", "g", ",", "n"}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"TriangleQ", "[", "]"}]}], "]"}], "//", "Timing"}]], "Input",Expre\ ssionUUID->"8bc29815-bf6c-44d0-a4d2-849ec3f1e9a4"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"157.1800000000003`", " ", "Second"}], ",", RowBox[{"{", RowBox[{"2", ",", "6"}], "}"}]}], "}"}]], "Output",ExpressionUUID->\ "7458ec93-85da-424c-81e5-6cb0024a106c"] }, Open ]] }, Closed]] }, Open ]] }, WindowSize->{703, 709}, WindowMargins->{{Automatic, 370}, {Automatic, 116}}, DockedCells->(FrontEndExecute[{ FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, Placeholder]}]& ), 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, 82, 0, 92, "Title", "ExpressionUUID" -> \ "1908b17e-9c90-45b2-91e6-766f2b0badf8"], Cell[CellGroupData[{ Cell[687, 26, 83, 0, 44, "Subsection", "ExpressionUUID" -> \ "5e0a3ccc-a8f7-4a2a-a990-4f3dcc06f469"], Cell[773, 28, 111, 3, 49, "Text", "ExpressionUUID" -> \ "4174208d-520e-4352-9cc4-08b19d2e47f7"], Cell[887, 33, 335, 8, 49, "Text", "ExpressionUUID" -> \ "3884f925-f756-45b1-b9aa-51fa8d00853d"], Cell[1225, 43, 348, 10, 49, "Text", "ExpressionUUID" -> \ "5310b6f5-0ba7-45c9-874a-2a2be97d259f"], Cell[1576, 55, 154, 2, 30, "Text", "ExpressionUUID" -> \ "06697f88-1730-4761-972f-451cae7ed1bb"] }, Open ]], Cell[CellGroupData[{ Cell[1767, 62, 87, 0, 64, "Section", "ExpressionUUID" -> \ "7201e03b-5bc3-43e2-8f86-548c7d5d85e9"], Cell[CellGroupData[{ Cell[1879, 66, 128, 1, 32, "Input", "ExpressionUUID" -> \ "359228d3-7d3d-4e1e-a621-4bcdf17173ad"], Cell[2010, 69, 865, 27, 58, "Output", "ExpressionUUID" -> \ "313c1a33-0ba2-4f55-b533-206944fcf54d"] }, Open ]], Cell[CellGroupData[{ Cell[2912, 101, 244, 5, 32, "Input", "ExpressionUUID" -> \ "e3ce8ce3-58c0-45bc-9bea-24ec17898b27"], Cell[3159, 108, 1153, 33, 54, "Output", "ExpressionUUID" -> \ "7b045710-42e7-4799-b4ee-10626137a4f9"] }, Open ]], Cell[CellGroupData[{ Cell[4349, 146, 331, 9, 32, "Input", "ExpressionUUID" -> \ "56d5cfeb-2ee1-40fb-8ba3-aef2e073c396"], Cell[4683, 157, 1053, 35, 58, "Output", "ExpressionUUID" -> \ "e9638785-752b-4d51-8a70-d1084d25a9ee"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[5785, 198, 103, 0, 64, "Section", "ExpressionUUID" -> \ "d9d8c96a-7c26-4b10-9cc8-8f87a827e259"], Cell[CellGroupData[{ Cell[5913, 202, 281, 7, 32, "Input", "ExpressionUUID" -> \ "aed2a39d-590a-438c-8c57-0ae6571efda9"], Cell[6197, 211, 374, 12, 35, "Output", "ExpressionUUID" -> \ "64bfc9bc-e27a-48e8-b5d9-bcc6b40f60b8"] }, Open ]], Cell[CellGroupData[{ Cell[6608, 228, 296, 7, 32, "Input", "ExpressionUUID" -> \ "92a50f4f-5837-4c31-a41f-3a5c90e60284"], Cell[6907, 237, 356, 11, 70, "Output", "ExpressionUUID" -> \ "3131b535-0ce3-4f4f-9740-dc3a1bae1326"] }, Open ]], Cell[CellGroupData[{ Cell[7300, 253, 291, 7, 70, "Input", "ExpressionUUID" -> \ "a3da9feb-c2d4-42a7-a33d-f70369b2114d"], Cell[7594, 262, 356, 11, 70, "Output", "ExpressionUUID" -> \ "284dc485-a1d6-4e2d-9734-cbb0a7222227"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[7999, 279, 80, 0, 70, "Section", "ExpressionUUID" -> \ "b0714851-0c8e-48db-b76d-7f3d6b756a03"], Cell[8082, 281, 1358, 42, 70, "Input", "ExpressionUUID" -> \ "1292f6fb-e599-4e82-b358-fe7eeaae5f6f"], Cell[9443, 325, 865, 20, 70, "Input", "ExpressionUUID" -> \ "8b4165e2-4b6c-42d0-9e4f-f436ce5025bf"], Cell[10311, 347, 33628, 668, 70, "Input", "ExpressionUUID" -> \ "2887c6ba-db78-4e33-b6aa-06c81e7c0153"] }, Open ]], Cell[CellGroupData[{ Cell[43976, 1020, 92, 0, 70, "Section", "ExpressionUUID" -> \ "419ad808-d06c-4e2b-b68c-34570cca0693"], Cell[CellGroupData[{ Cell[44093, 1024, 523, 13, 70, "Input", "ExpressionUUID" -> \ "68e261f6-f01d-4d4c-bdbf-0a46518cca04"], Cell[44619, 1039, 2115, 55, 70, "Output", "ExpressionUUID" -> \ "0713ae50-badd-4bae-a733-d98e887b4c86"] }, Open ]], Cell[46749, 1097, 1527, 39, 70, "Input", "ExpressionUUID" -> \ "2f75df4e-4908-4c35-861a-7ae3e36442b4"], Cell[CellGroupData[{ Cell[48301, 1140, 171, 3, 70, "Input", "ExpressionUUID" -> \ "55122cb2-fe0c-48d0-a6f2-37169fc82758"], Cell[48475, 1145, 768, 19, 70, "Output", "ExpressionUUID" -> \ "dd55f720-f5a6-4cd4-a42d-c2246c31eeae"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[49292, 1170, 92, 0, 70, "Section", "ExpressionUUID" -> \ "5c227374-5726-4a36-b9a1-7de1e2925e5f"], Cell[CellGroupData[{ Cell[49409, 1174, 523, 13, 70, "Input", "ExpressionUUID" -> \ "05488949-05e1-4664-b22a-9689ed7af365"], Cell[49935, 1189, 2188, 58, 70, "Output", "ExpressionUUID" -> \ "ae3bb75d-df5a-4a38-b2f2-51ec819bb113"] }, Open ]], Cell[52138, 1250, 1479, 38, 70, "Input", "ExpressionUUID" -> \ "dfba3c9c-34ca-45dc-a5e6-b22dfa3d32b1"], Cell[CellGroupData[{ Cell[53642, 1292, 363, 9, 70, "Input", "ExpressionUUID" -> \ "de930920-a4b1-48d1-8aec-5c5a2a27dc9a"], Cell[54008, 1303, 2136, 57, 70, "Output", "ExpressionUUID" -> \ "d976c86c-6379-45f3-8dea-629471f8a172"] }, Open ]], Cell[CellGroupData[{ Cell[56181, 1365, 171, 3, 70, "Input", "ExpressionUUID" -> \ "c302268d-1ebe-4cc4-bf5b-d88b5c6a4053"], Cell[56355, 1370, 1793, 44, 70, "Output", "ExpressionUUID" -> \ "0f832a8d-849d-431c-997c-503f36c8abae"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[58197, 1420, 90, 0, 70, "Section", "ExpressionUUID" -> \ "182e7303-2435-42d9-bc5a-8ee8cd81443a"], Cell[58290, 1422, 118, 0, 70, "Print", "ExpressionUUID" -> \ "eec3ca60-909d-41b2-aa4c-1bcce010fa68"], Cell[CellGroupData[{ Cell[58433, 1426, 257, 6, 70, "Input", "ExpressionUUID" -> \ "2919102e-8a2e-4b20-b1b9-3c69fccf0a1c"], Cell[58693, 1434, 10705, 248, 70, "Output", "ExpressionUUID" -> \ "f9319699-2eec-4bcd-9faa-abae0dd1b312"] }, Open ]], Cell[CellGroupData[{ Cell[69435, 1687, 112, 1, 70, "Input", "ExpressionUUID" -> \ "ccbf56d7-41b7-4412-bced-2d3ae717625d"], Cell[69550, 1690, 3274, 45, 70, "Output", "ExpressionUUID" -> \ "1a7efc0b-2805-4a34-ace8-bb9e4cd78791"] }, Open ]], Cell[CellGroupData[{ Cell[72861, 1740, 117, 1, 70, "Input", "ExpressionUUID" -> \ "8375da95-1b8b-4603-9f92-bea96d2d1874"], Cell[72981, 1743, 85, 0, 70, "Output", "ExpressionUUID" -> \ "3de5ff5d-b959-4524-a2d1-97fbe4ea5c2d"] }, Open ]], Cell[CellGroupData[{ Cell[73103, 1748, 256, 8, 70, "Input", "ExpressionUUID" -> \ "337a2f66-1770-4d44-bea4-3ef02776efd3"], Cell[73362, 1758, 23369, 721, 70, "Output", "ExpressionUUID" -> \ "4cf606dd-587f-44be-9831-27b498913884"] }, Open ]], Cell[CellGroupData[{ Cell[96768, 2484, 82, 0, 70, "Subsection", "ExpressionUUID" -> \ "c3099dc0-948e-4217-914f-47d6634a2bec"], Cell[CellGroupData[{ Cell[96875, 2488, 1379, 34, 70, "Input", "ExpressionUUID" -> \ "2d307a8b-ad07-40e0-83f2-1dce1cfd0138"], Cell[CellGroupData[{ Cell[98279, 2526, 268, 7, 70, "Print", "ExpressionUUID" -> \ "48fe9ade-ea21-4027-a1ad-9dc870b21e9f"], Cell[98550, 2535, 268, 7, 70, "Print", "ExpressionUUID" -> \ "f651c55c-c3f2-4c99-be75-ce5cece30276"], Cell[98821, 2544, 268, 7, 70, "Print", "ExpressionUUID" -> \ "b5851ae4-d3ca-4b5c-9f46-2c985a26f935"], Cell[99092, 2553, 266, 7, 70, "Print", "ExpressionUUID" -> \ "33070451-953e-4342-861c-b3a925f5f891"], Cell[99361, 2562, 269, 7, 70, "Print", "ExpressionUUID" -> \ "43bb3d6a-4dfc-4926-8a7f-73d9e2e8b8c6"], Cell[99633, 2571, 269, 7, 70, "Print", "ExpressionUUID" -> \ "40248b57-d54c-40ad-a4a4-84574b9d1a9f"], Cell[99905, 2580, 267, 7, 70, "Print", "ExpressionUUID" -> \ "b4e98f5a-1f59-49dc-a7f5-c0a2bf65b97e"], Cell[100175, 2589, 269, 7, 70, "Print", "ExpressionUUID" -> \ "dbc4212f-d8df-415e-9fa4-e84812c07647"], Cell[100447, 2598, 269, 7, 70, "Print", "ExpressionUUID" -> \ "1d61ee37-60e9-462d-9c10-521e898f810c"], Cell[100719, 2607, 271, 7, 70, "Print", "ExpressionUUID" -> \ "ea5f2649-df88-4ef2-bfd5-62aea5775beb"], Cell[100993, 2616, 270, 7, 70, "Print", "ExpressionUUID" -> \ "2b33b26a-1f69-4eda-8e18-d1004ebb2e44"], Cell[101266, 2625, 270, 7, 70, "Print", "ExpressionUUID" -> \ "7d324b89-56cb-4afd-9759-574d5dbe7ee9"], Cell[101539, 2634, 269, 7, 70, "Print", "ExpressionUUID" -> \ "62c49b0c-b164-4eff-bd55-969f89c03676"], Cell[101811, 2643, 269, 7, 70, "Print", "ExpressionUUID" -> \ "f46adf42-59a1-4c4f-8960-c612f6f2c162"], Cell[102083, 2652, 270, 7, 70, "Print", "ExpressionUUID" -> \ "972943f9-75ee-41ab-867c-5db2c88422bd"], Cell[102356, 2661, 271, 7, 70, "Print", "ExpressionUUID" -> \ "f61affda-72bf-4445-bf4b-a32f7c6cf90a"], Cell[102630, 2670, 271, 7, 70, "Print", "ExpressionUUID" -> \ "99aed333-dc86-479b-8eda-72c2377a8154"], Cell[102904, 2679, 270, 7, 70, "Print", "ExpressionUUID" -> \ "4bf73b09-2407-4b06-9e65-08ffbdebe779"], Cell[103177, 2688, 269, 7, 70, "Print", "ExpressionUUID" -> \ "aa767476-b40a-4eb8-ba61-a683f00363ee"], Cell[103449, 2697, 269, 7, 70, "Print", "ExpressionUUID" -> \ "519f78d4-09c9-470e-bc62-619d4bb1a963"], Cell[103721, 2706, 270, 7, 70, "Print", "ExpressionUUID" -> \ "3b2589dc-3081-4219-8714-fea7581778b1"], Cell[103994, 2715, 270, 7, 70, "Print", "ExpressionUUID" -> \ "8a704008-4494-4111-a4a2-20bb6b9bf477"], Cell[104267, 2724, 271, 7, 70, "Print", "ExpressionUUID" -> \ "212f3736-c6c7-4fd5-ad8c-07b4c33226f1"], Cell[104541, 2733, 270, 7, 70, "Print", "ExpressionUUID" -> \ "4f1e9b9b-be9b-42d4-bfcd-a3dd9a901924"], Cell[104814, 2742, 271, 7, 70, "Print", "ExpressionUUID" -> \ "0d6c19b5-e5b6-40ed-96f9-c4c7ea979aea"], Cell[105088, 2751, 270, 7, 70, "Print", "ExpressionUUID" -> \ "e43b93c4-8d31-428a-861c-47d78fcf4873"], Cell[105361, 2760, 271, 7, 70, "Print", "ExpressionUUID" -> \ "2bd3f4f2-08c1-4855-a003-8abd66288e6b"], Cell[105635, 2769, 270, 7, 70, "Print", "ExpressionUUID" -> \ "78605ebc-fad4-4cb7-b3c2-61e6a4a76fb4"], Cell[105908, 2778, 271, 7, 70, "Print", "ExpressionUUID" -> \ "c41aacd4-5398-4d64-9316-d290ca877b2e"], Cell[106182, 2787, 255, 7, 70, "Print", "ExpressionUUID" -> \ "147ffdec-4ad8-4ed6-8c7e-d5d5d3d10b6d"], Cell[106440, 2796, 271, 7, 70, "Print", "ExpressionUUID" -> \ "65d6820d-d1c1-4b5f-ba84-9d6e9abce493"], Cell[106714, 2805, 271, 7, 70, "Print", "ExpressionUUID" -> \ "410cc8d6-bcbb-486f-95d5-8207b50bf77c"], Cell[106988, 2814, 271, 7, 70, "Print", "ExpressionUUID" -> \ "a5ea103d-5ad9-413e-8b65-fffd88bb4615"], Cell[107262, 2823, 271, 7, 70, "Print", "ExpressionUUID" -> \ "f4f3b2d9-be39-4f04-8cd3-c7c4800fd115"], Cell[107536, 2832, 271, 7, 70, "Print", "ExpressionUUID" -> \ "92d7173f-d8a0-4f00-b67a-d726c9fcafdb"], Cell[107810, 2841, 269, 7, 70, "Print", "ExpressionUUID" -> \ "e77afdf9-3900-4600-8fb7-ab4eb4fcebf7"], Cell[108082, 2850, 271, 7, 70, "Print", "ExpressionUUID" -> \ "f3f71a73-f8be-407b-972e-733b98ffc99d"], Cell[108356, 2859, 270, 7, 70, "Print", "ExpressionUUID" -> \ "10852e87-80d5-4659-b058-c6d1d31d21dd"], Cell[108629, 2868, 269, 7, 70, "Print", "ExpressionUUID" -> \ "65e4dd4e-d6c9-4bb1-b3fc-f38f340e7bc4"], Cell[108901, 2877, 270, 7, 70, "Print", "ExpressionUUID" -> \ "774a9057-b975-4049-b31d-73b51f954cc6"], Cell[109174, 2886, 270, 7, 70, "Print", "ExpressionUUID" -> \ "fd610d50-eb93-4e65-8bca-1b4fffb6b11b"], Cell[109447, 2895, 271, 7, 70, "Print", "ExpressionUUID" -> \ "04bb7906-e6eb-4c8a-82e4-c6385ef76ca6"], Cell[109721, 2904, 271, 7, 70, "Print", "ExpressionUUID" -> \ "c1128e86-940b-48ae-b057-30e484075448"], Cell[109995, 2913, 271, 7, 70, "Print", "ExpressionUUID" -> \ "62e93ae5-f10a-4a29-ae5f-0f113a9fe23e"], Cell[110269, 2922, 269, 7, 70, "Print", "ExpressionUUID" -> \ "e94215ff-c17d-4d48-a623-f2ef4cff0d26"], Cell[110541, 2931, 269, 7, 70, "Print", "ExpressionUUID" -> \ "02767b3b-1ebd-4af7-9074-b4c315005ece"], Cell[110813, 2940, 271, 7, 70, "Print", "ExpressionUUID" -> \ "33cfc7c6-48a1-4c41-baef-3e5cdf7b933c"], Cell[111087, 2949, 271, 7, 70, "Print", "ExpressionUUID" -> \ "16772ceb-6afa-4914-9810-18d218d18ed3"], Cell[111361, 2958, 271, 7, 70, "Print", "ExpressionUUID" -> \ "b0f2b90a-65be-4ae0-96e4-b02ab524d0cf"], Cell[111635, 2967, 271, 7, 70, "Print", "ExpressionUUID" -> \ "ec21db35-64ad-4da9-a8de-c8a0651acd6c"], Cell[111909, 2976, 269, 7, 70, "Print", "ExpressionUUID" -> \ "0379f5b1-14e4-4849-be27-8eb58347ea46"], Cell[112181, 2985, 269, 7, 70, "Print", "ExpressionUUID" -> \ "7de4e347-fbbf-410f-b8a7-b4b2e727d997"], Cell[112453, 2994, 280, 8, 70, "Print", "ExpressionUUID" -> \ "0181dcf4-8129-4018-929a-7f122ff260f5"], Cell[112736, 3004, 280, 8, 70, "Print", "ExpressionUUID" -> \ "4fd4f25d-c723-4a51-9a37-c7beb25e107c"], Cell[113019, 3014, 264, 7, 70, "Print", "ExpressionUUID" -> \ "b2dc57be-ab4d-455c-83e8-05dbd784eb8d"], Cell[113286, 3023, 280, 8, 70, "Print", "ExpressionUUID" -> \ "634c0438-b304-44c8-a727-c613bc1ba107"], Cell[113569, 3033, 281, 8, 70, "Print", "ExpressionUUID" -> \ "25b3dbf3-0eab-4d0c-b496-283a84e102e9"], Cell[113853, 3043, 270, 7, 70, "Print", "ExpressionUUID" -> \ "978e5aee-c2b4-4a46-88f5-d18eabf052c9"], Cell[114126, 3052, 280, 8, 70, "Print", "ExpressionUUID" -> \ "095477af-fb87-44ce-a4fc-b560ae4f7251"], Cell[114409, 3062, 275, 7, 70, "Print", "ExpressionUUID" -> \ "0fd6374b-0c9b-486c-a067-466f2f0f31d5"], Cell[114687, 3071, 281, 8, 70, "Print", "ExpressionUUID" -> \ "a8d4e028-746d-4f4b-98b5-20ef0caaa855"], Cell[114971, 3081, 280, 8, 70, "Print", "ExpressionUUID" -> \ "b952bd01-5e57-4393-9e0d-8245fdee203e"], Cell[115254, 3091, 269, 7, 70, "Print", "ExpressionUUID" -> \ "d8dfce08-f363-4266-b21e-c6d98e87a979"], Cell[115526, 3100, 280, 8, 70, "Print", "ExpressionUUID" -> \ "4b5ae0a4-a5c5-49ed-8ea6-4b9d1a111276"], Cell[115809, 3110, 280, 8, 70, "Print", "ExpressionUUID" -> \ "0796971c-737d-4874-999f-b21af6d1ff2c"], Cell[116092, 3120, 280, 8, 70, "Print", "ExpressionUUID" -> \ "138318e6-e3ad-4498-9d7f-b1c653777720"], Cell[116375, 3130, 264, 7, 70, "Print", "ExpressionUUID" -> \ "3624523f-5061-40ae-ac64-8ad098d6c357"], Cell[116642, 3139, 280, 8, 70, "Print", "ExpressionUUID" -> \ "ebb003a2-6c09-404c-ba29-cb9b88b98fa6"], Cell[116925, 3149, 271, 7, 70, "Print", "ExpressionUUID" -> \ "264c6b1e-cfdd-46d6-930b-6a853c2b1daa"], Cell[117199, 3158, 272, 7, 70, "Print", "ExpressionUUID" -> \ "67acb04e-bd6b-42a9-acf1-11a0ea96c66f"], Cell[117474, 3167, 272, 7, 70, "Print", "ExpressionUUID" -> \ "ae34169a-29f0-4818-b04b-fe9cf407ed9d"], Cell[117749, 3176, 271, 7, 70, "Print", "ExpressionUUID" -> \ "fef8e6c0-ac75-43df-a258-e8105381cc7e"], Cell[118023, 3185, 256, 7, 70, "Print", "ExpressionUUID" -> \ "8ab3e4a3-9dd8-4186-9a12-9ec6bf43d590"], Cell[118282, 3194, 271, 7, 70, "Print", "ExpressionUUID" -> \ "8411acd9-fc1c-40f6-b186-bffd86c1b2bf"], Cell[118556, 3203, 271, 7, 70, "Print", "ExpressionUUID" -> \ "fa9d2135-c0da-4d8c-bf87-b58d751bfa56"], Cell[118830, 3212, 272, 7, 70, "Print", "ExpressionUUID" -> \ "a9f5f51b-3480-4548-8177-608a2730bc6d"], Cell[119105, 3221, 272, 7, 70, "Print", "ExpressionUUID" -> \ "66c33157-efff-4766-adf1-2f8f12e5c3b0"], Cell[119380, 3230, 271, 7, 70, "Print", "ExpressionUUID" -> \ "ad0b61a4-ab7a-4e31-940a-1b98f5c4ac5a"], Cell[119654, 3239, 272, 7, 70, "Print", "ExpressionUUID" -> \ "7110059c-9cc2-47da-a3ea-6e9b13cd8f75"], Cell[119929, 3248, 271, 7, 70, "Print", "ExpressionUUID" -> \ "15a405fa-37a6-407a-9688-b325dcd951dc"], Cell[120203, 3257, 272, 7, 70, "Print", "ExpressionUUID" -> \ "de10e7e6-1a34-4b85-b1cc-90210ef29de9"], Cell[120478, 3266, 272, 7, 70, "Print", "ExpressionUUID" -> \ "aded7e2b-d549-4b92-b37f-2837381767cd"], Cell[120753, 3275, 272, 7, 70, "Print", "ExpressionUUID" -> \ "acd6c5e7-8b55-45ae-96a2-7d30bbb75862"], Cell[121028, 3284, 255, 7, 70, "Print", "ExpressionUUID" -> \ "40232e4f-24e5-4309-97b6-0ee02297b008"], Cell[121286, 3293, 272, 7, 70, "Print", "ExpressionUUID" -> \ "82403384-4c4d-40b8-ae6b-30f57391906a"], Cell[121561, 3302, 271, 7, 70, "Print", "ExpressionUUID" -> \ "fd7e48cf-f31b-4801-bff1-f8eaaaacbf05"], Cell[121835, 3311, 272, 7, 70, "Print", "ExpressionUUID" -> \ "01592913-ef19-4bcf-ad2b-358afd607160"], Cell[122110, 3320, 272, 7, 70, "Print", "ExpressionUUID" -> \ "ac3d5863-aa1a-48cd-b218-43d43bac31a7"], Cell[122385, 3329, 272, 7, 70, "Print", "ExpressionUUID" -> \ "9d4e5106-15ff-41b3-973e-15d1b16c13b1"], Cell[122660, 3338, 271, 7, 70, "Print", "ExpressionUUID" -> \ "11aff9e3-3a9e-4c77-9d17-7b56ccb918ec"], Cell[122934, 3347, 271, 7, 70, "Print", "ExpressionUUID" -> \ "805389a9-3577-42fb-880d-f5881d33cec2"], Cell[123208, 3356, 271, 7, 70, "Print", "ExpressionUUID" -> \ "05d2a480-55cb-451d-8bec-96e0b52e1da1"], Cell[123482, 3365, 270, 7, 70, "Print", "ExpressionUUID" -> \ "42396cdf-df24-41c6-96ef-a8a77dbe4626"], Cell[123755, 3374, 272, 7, 70, "Print", "ExpressionUUID" -> \ "d3358b2a-328c-40ad-8432-5cc86e2d7476"], Cell[124030, 3383, 272, 7, 70, "Print", "ExpressionUUID" -> \ "889bd10a-8b87-450f-865e-041875b68f9f"], Cell[124305, 3392, 272, 7, 70, "Print", "ExpressionUUID" -> \ "16d70c6d-748e-425c-b5c7-0ef7017e1c1b"], Cell[124580, 3401, 272, 7, 70, "Print", "ExpressionUUID" -> \ "a4e3ce2c-b42d-4640-aba8-41572e1bc8f9"], Cell[124855, 3410, 272, 7, 70, "Print", "ExpressionUUID" -> \ "4e015284-c5c6-466f-8fcc-6bf5845af4eb"], Cell[125130, 3419, 272, 7, 70, "Print", "ExpressionUUID" -> \ "8610fe28-7b44-4f57-b8a6-9835fcb600f5"], Cell[125405, 3428, 273, 7, 70, "Print", "ExpressionUUID" -> \ "e1a27fcd-e2e4-41a4-b0db-8b3a5af2f036"], Cell[125681, 3437, 273, 7, 70, "Print", "ExpressionUUID" -> \ "18a3d478-38e9-49f7-98c8-bc1df8ef91e7"], Cell[125957, 3446, 273, 7, 70, "Print", "ExpressionUUID" -> \ "1554335e-4aef-44a0-83a5-68f0e861373f"], Cell[126233, 3455, 273, 7, 70, "Print", "ExpressionUUID" -> \ "a94039ce-e8cf-42a5-9141-fd4a23f03090"], Cell[126509, 3464, 272, 7, 70, "Print", "ExpressionUUID" -> \ "85a0fa1b-0729-4efc-9140-466bf5ba45c9"], Cell[126784, 3473, 273, 7, 70, "Print", "ExpressionUUID" -> \ "1af62b27-b29b-4473-bd77-6ca75149d088"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[127106, 3486, 2063, 54, 70, "Input", "ExpressionUUID" -> \ "d72f3894-cf97-4f03-be71-2aabc7473ec6"], Cell[129172, 3542, 258, 5, 70, "Output", "ExpressionUUID" -> \ "138a198f-eac0-4bc6-b22a-f54f29f588ce"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[129491, 3554, 83, 0, 70, "Section", "ExpressionUUID" -> \ "558abbf7-717f-4af5-815f-61b107a67b52"], Cell[CellGroupData[{ Cell[129599, 3558, 912, 27, 70, "Input", "ExpressionUUID" -> \ "fc1cc2e3-d5b5-4a76-9146-f572a7408fc5"], Cell[130514, 3587, 128, 2, 70, "Output", "ExpressionUUID" -> \ "f4abbcaa-33be-42eb-b287-48abdc8e0250"] }, Open ]], Cell[CellGroupData[{ Cell[130679, 3594, 1491, 37, 70, "Input", "ExpressionUUID" -> \ "8bc29815-bf6c-44d0-a4d2-849ec3f1e9a4"], Cell[132173, 3633, 225, 6, 70, "Output", "ExpressionUUID" -> \ "7458ec93-85da-424c-81e5-6cb0024a106c"] }, Open ]] }, Closed]] }, Open ]] } ] *) (* End of internal cache information *)