cp's OEIS Frontend

A197016 Decimal expansion of the radius of the circle tangent to the curve y=cos(x) and to the positive x and y axes.

%I A197016 #10 Jul 01 2013 10:35:49
%S A197016 4,2,8,7,7,8,5,3,6,0,3,0,6,1,2,8,6,3,6,1,3,6,9,1,7,4,1,0,4,8,9,9,9,7,
%T A197016 0,4,9,0,6,0,5,8,9,3,6,1,5,2,0,2,6,8,5,1,9,9,3,7,8,8,2,4,6,9,8,4,7,1,
%U A197016 3,9,3,2,2,8,8,8,9,7,9,4,8,6,0,3,5,1,0,1,5,5,4,3,3,2,3,1,2,3,6
%N A197016 Decimal expansion of the radius of the circle tangent to the curve y=cos(x) and to the positive x and y axes.
%C A197016 Let (x,y) denote the point of tangency.  Then
%C A197016 x=0.65099256993050253383380179140902527170294599...
%C A197016 y=0.79548271667012269646991174255794794798663548...
%C A197016 slope=-0.6059762763335882427824587356062000...
%C A197016 (The Mathematica program includes a graph.)
%e A197016 radius=0.428778536030612863613691741048999...
%t A197016 r = .428;
%t A197016 Show[Plot[Cos[x], {x, 0, Pi}],
%t A197016 ContourPlot[(x - r)^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%t A197016 f[x_] := (x - Sin[x] Cos[x])/(1 - Sin[x]);
%t A197016 t = x /.FindRoot[Cos[x] == f[x] + Sqrt[2*f[x]*x - x^2], {x, .5, 1}, WorkingPrecision -> 100]
%t A197016 x1 = Re[t]  (* x coordinate of tangency point *)
%t A197016 y = Cos[x1] (* y coordinate of tangency point *)
%t A197016 radius = f[x1]
%t A197016 RealDigits[radius] (* A197016 *)
%t A197016 slope = -Sin[x1]   (* slope at tangency point *)
%Y A197016 Cf. A197017, A197018, A197019, A197020.
%K A197016 nonn,cons
%O A197016 0,1
%A A197016 _Clark Kimberling_, Oct 08 2011