cp's OEIS Frontend

A197019 Decimal expansion of the radius of the circle tangent to the curve y=cos(4x) and to the positive x and y axes.

%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