A197019 - OEIS

A197019

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

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, 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, 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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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

x=0.33861718723736417045737960551501765846156681578...

y=0.21464425212782002883052365316387247038020190838...

slope=-0.332183120530610097233795968342303024088179...

(The Mathematica program includes a graph.)

LINKS

Table of n, a(n) for n=0..98.

EXAMPLE

radius=0.171994517348101690739024865448714954394...

MATHEMATICA

r = .172; c = 4;

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

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

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

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

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

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

radius = f[x1]

RealDigits[radius] (* A197019 *)

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

CROSSREFS

Cf. A197016, A196017, A196018, A197020.

Sequence in context: A200500 A199669 A349580 * A048835 A124970 A251768

Adjacent sequences: A197016 A197017 A197018 * A197020 A197021 A197022

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 08 2011

STATUS

approved