Kepler-Bouwkamp constant

In plane geometry, Kepler-Bouwkamp constantis obtained as a limit of the following sequence.Take a circle of radius 1. Inscribe a regular triangle in this circle. Inscribea circle in this triangle. Inscribe a square init. Inscribe a circle, regular pentagon, circle,
regular hexagon and so forth. Radius of the limiting circle is called the Kepler-Bouwkamp constant.

Computing Kepler-Bouwkamp constant

The Kepler-Bouwkamp constant is equal to $prod\_\{k=3\}^infty\; cosleft(fracpi\; k\; ight)\; =\; 0.1149420448dots\; .$

References

* S. R. Finch, "Mathematical Constants", Cambridge University Press, 2003

* Adrian R. Kitson "The prime analog of the Kepler-Bouwkamp constant" [http://arxiv.org/abs/math/0608186 math.HO/0608186]