# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a197019 Showing 1-1 of 1 %I A197019 #5 Mar 30 2012 18:57:52 %S A197019 1,7,1,9,9,4,5,1,7,3,4,8,1,0,1,6,9,0,7,3,9,0,2,4,8,6,5,4,4,8,7,1,4,9, %T A197019 5,4,3,9,4,8,8,2,2,2,6,6,4,9,3,9,8,1,5,8,8,7,3,3,3,6,3,7,9,7,1,0,0,0, %U A197019 0,9,9,8,4,8,7,9,6,2,8,7,0,9,0,3,8,6,7,0,8,8,4,8,6,8,9,7,3,6,6 %N A197019 Decimal expansion of the radius of the circle tangent to the curve y=cos(4x) and to the positive x and y axes. %C A197019 Let (x,y) denote the point of tangency. Then %C A197019 x=0.33861718723736417045737960551501765846156681578... %C A197019 y=0.21464425212782002883052365316387247038020190838... %C A197019 slope=-0.332183120530610097233795968342303024088179... %C A197019 (The Mathematica program includes a graph.) %e A197019 radius=0.171994517348101690739024865448714954394... %t A197019 r = .172; c = 4; %t A197019 Show[Plot[Cos[c*x], {x, 0, Pi}], %t A197019 ContourPlot[(x - r)^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic] %t A197019 f[x_] := (x - c*Sin[c*x] Cos[c*x])/(1 - c*Sin[c*x]); %t A197019 t = x /. FindRoot[Cos[c*x] == f[x] + Sqrt[2*f[x]*x - x^2], {x, .5, 1}, WorkingPrecision -> 100] %t A197019 x1 = Re[t] (* x coordinate of tangency point *) %t A197019 y = Cos[c*x1] (* y coordinate of tangency point *) %t A197019 radius = f[x1] %t A197019 RealDigits[radius] (* A197019 *) %t A197019 slope = -Sin[x1] (* slope at tangency point *) %Y A197019 Cf. A197016, A196017, A196018, A197020. %K A197019 nonn,cons %O A197019 0,2 %A A197019 _Clark Kimberling_, Oct 08 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE