Kepler–Bouwkamp constant

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 a 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 (sequence A085365 in OEIS)

If the product is taken only over the odd primes, another constant

is defined (A131671).

References

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

* Kitson, Adrian R. (2006). "The prime analog of the Kepler–Bouwkamp constant". arΧiv:math/0608186.

* Kitson, Adrian R. (2008). "The prime analogue of the Kepler-Bouwkamp constant". The Mathematical Gazette 92: 293.