OFFSET
0,1
COMMENTS
Let (x,y) denote the point of tangency. Then
x=0.346818914654599529577486037538498433565584415464...
y=0.505826306518745297430716717373078359704411629139...
slope=-2.5879060509806840663013781941932136174746999...
(The Mathematica program includes a graph.)
EXAMPLE
radius=0.3718110417361721840195647351588579028970626...
MATHEMATICA
r = .371; c = 3;
Show[Plot[Cos[c*x], {x, -0.5, 0.5}],
ContourPlot[x^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic]
t = x /. FindRoot[c*Sin[c*x] Cos[c*x] - x == x*Sqrt[1 + (c*Sin[c*x])^2], {x, .25, .55}, WorkingPrecision -> 100]
RealDigits[t] (* x coordinate of tangency point *)
y = Cos[c*t] (* y coordinate of tangency point *)
radius = Cos[c*t] - t/(c*Sin[c*t])
RealDigits[radius] (* A197021 *)
slope = -c*Sin[c*t] (* slope at tangency point *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 08 2011
STATUS
approved