A197016 - OEIS

A197016

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

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, 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, 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

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

OFFSET

0,1

COMMENTS

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

x=0.65099256993050253383380179140902527170294599...

y=0.79548271667012269646991174255794794798663548...

slope=-0.6059762763335882427824587356062000...

(The Mathematica program includes a graph.)

LINKS

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

EXAMPLE

radius=0.428778536030612863613691741048999...

MATHEMATICA

r = .428;

Show[Plot[Cos[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 - Sin[x] Cos[x])/(1 - Sin[x]);

t = x /.FindRoot[Cos[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[x1] (* y coordinate of tangency point *)

radius = f[x1]

RealDigits[radius] (* A197016 *)

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

CROSSREFS

Cf. A197017, A197018, A197019, A197020.

Sequence in context: A094312 A182848 A228834 * A198145 A143942 A265291

Adjacent sequences: A197013 A197014 A197015 * A197017 A197018 A197019

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 08 2011

STATUS

approved