A197019 - OEIS

%I #5 Mar 30 2012 18:57:52

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

%C Let (x,y) denote the point of tangency.  Then

%C x=0.33861718723736417045737960551501765846156681578...

%C y=0.21464425212782002883052365316387247038020190838...

%C slope=-0.332183120530610097233795968342303024088179...

%C (The Mathematica program includes a graph.)

%e radius=0.171994517348101690739024865448714954394...

%t r = .172; c = 4;

%t Show[Plot[Cos[c*x], {x, 0, Pi}],

%t  ContourPlot[(x - r)^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic]

%t f[x_] := (x - c*Sin[c*x] Cos[c*x])/(1 - c*Sin[c*x]);

%t t = x /. FindRoot[Cos[c*x] == f[x] + Sqrt[2*f[x]*x - x^2], {x, .5, 1}, WorkingPrecision -> 100]

%t x1 = Re[t]    (* x coordinate of tangency point *)

%t y = Cos[c*x1] (* y coordinate of tangency point *)

%t radius = f[x1]

%t RealDigits[radius] (* A197019 *)

%t slope = -Sin[x1]   (* slope at tangency point *)

%Y Cf. A197016, A196017, A196018, A197020.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Oct 08 2011