cp's OEIS Frontend

A197017 Decimal expansion of the radius of the circle tangent to the curve y=cos(2x) and to the positive x and y axes.

%I A197017 #9 Jul 01 2013 10:35:38
%S A197017 2,9,7,1,0,5,6,3,5,2,7,4,8,2,2,7,1,6,7,1,2,2,1,4,4,3,6,5,2,6,3,1,6,1,
%T A197017 9,9,4,0,7,2,9,6,0,7,1,0,8,5,6,7,0,4,0,0,5,6,7,6,8,6,4,5,5,2,4,8,5,8,
%U A197017 2,3,6,9,4,8,4,1,8,0,8,1,7,7,0,0,6,8,2,3,8,4,1,4,6,4,9,0,9,4,3
%N A197017 Decimal expansion of the radius of the circle tangent to the curve y=cos(2x) and to the positive x and y axes.
%C A197017 Let (x,y) denote the point of tangency.  Then
%C A197017 x=0.556627409764774263651183045638839616840052780212...
%C A197017 y=0.441743828977740325730277185387438343947805907493...
%C A197017 slope=-0.5283257380737094443139057566841614427843590...
%C A197017 (The Mathematica program includes a graph.)
%e A197017 radius=0.2971056352748227167122144365263161994072960710...
%t A197017 r = .297; c = 2;
%t A197017 Show[Plot[Cos[c*x], {x, 0, Pi}],
%t A197017 ContourPlot[(x - r)^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}],PlotRange -> All, AspectRatio -> Automatic]
%t A197017 f[x_] := (x - c*Sin[c*x] Cos[c*x])/(1 - c*Sin[c*x]);
%t A197017 t = x /. FindRoot[Cos[c*x] == f[x] + Sqrt[2*f[x]*x - x^2], {x, .5, 1}, WorkingPrecision -> 100]
%t A197017 x1 = Re[t]    (* x coordinate of tangency point *)
%t A197017 y = Cos[c*x1] (* y coordinate of tangency point *)
%t A197017 radius = f[x1]
%t A197017 RealDigits[radius] (* A197017 *)
%t A197017 slope = -Sin[x1] (* slope at tangency point *)
%Y A197017 Cf. A197016, A197018, A197019, A197020.
%K A197017 nonn,cons
%O A197017 0,1
%A A197017 _Clark Kimberling_, Oct 08 2011