Kepler–Bouwkamp constant

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In plane geometry, Kepler-Bouwkamp constant is obtained as a limit of the following sequence. Take a circle of radius 1. Inscribe a regular triangle in this circle. Inscribe s circle in this triangle. Inscribe a square in it. 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 $\prod _{k=3}^{\infty }\cos \left({\frac {\pi }{k}}\right)$

Reference

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

Adrian R. Kitson The prime analog of the Kepler-Bouwkamp constant math.HO/0608186