In plane geometry, the Kepler–Bouwkamp constant (or polygon inscribing 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. The radius of the limiting circle is called the Kepler–Bouwkamp constant (Finch, 2003), it is the inverse of the polygon circumscribing constant.
- The natural logarithm of the Kepler-Bouwkamp constant is given by
where is the Riemann zeta function.
If the product is taken over the odd primes, the constant
- Kitson, Adrian R. (2006). "The prime analog of the Kepler–Bouwkamp constant". arXiv:math/0608186
- Kitson, Adrian R. (2008). "The prime analogue of the Kepler-Bouwkamp constant". The Mathematical Gazette. 92: 293.
- Mathar, Richard J. "Tightly circumscribed regular polygons". arXiv:1301.6293.
- Doslic, Tomislav (2014). "Kepler-Bouwkamp radius of combinatorial sequences". J. Int. Seq. 17 (14.11.3).