cp's OEIS Frontend

A197018 Decimal expansion of the radius of the circle tangent to the curve y=cos(3x) and to the positive x and y axes.

%I A197018 #9 Jul 01 2013 10:35:30
%S A197018 2,1,8,7,2,9,4,8,8,8,0,3,6,4,4,0,6,5,8,9,7,2,8,5,2,2,3,2,6,8,1,2,1,0,
%T A197018 4,9,3,0,3,6,3,6,1,9,9,7,3,1,4,1,4,9,9,5,8,2,2,1,6,6,9,4,6,6,9,0,3,1,
%U A197018 8,5,8,6,5,0,7,6,2,9,6,0,6,3,4,5,6,6,6,1,3,7,9,4,2,8,4,3,0,0,7
%N A197018 Decimal expansion of the radius of the circle tangent to the curve y=cos(3x) and to the positive x and y axes.
%C A197018 Let (x,y) denote the point of tangency.  Then
%C A197018 x=0.4252834568497833490618545391964703664552948...
%C A197018 y=0.2906881405190418936802785128662388404186594...
%C A197018 slope=-0.41257900534470955829852211550705870735...
%C A197018 (The Mathematica program includes a graph.)
%e A197018 radius=0.218729488803644065897285223268121049303636199...
%t A197018 r = .219; c = 3;
%t A197018 Show[Plot[Cos[c*x], {x, 0, Pi}],
%t A197018 ContourPlot[(x - r)^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%t A197018 f[x_] := (x - c*Sin[c*x] Cos[c*x])/(1 - c*Sin[c*x]);
%t A197018 t = x /. FindRoot[Cos[c*x] == f[x] + Sqrt[2*f[x]*x - x^2], {x, .5, 1}, WorkingPrecision -> 100]
%t A197018 x1 = Re[t]      (* x coordinate of tangency point *)
%t A197018 y = Cos[c*x1]   (* y coordinate of tangency point *)
%t A197018 radius = f[x1]
%t A197018 RealDigits[radius] (* A197018 *)
%t A197018 slope = -Sin[x1] (* slope at tangency point *)
%Y A197018 Cf. A197016, A197017, A197019, A197020.
%K A197018 nonn,cons
%O A197018 0,1
%A A197018 _Clark Kimberling_, Oct 08 2011