Kepler–Bouwkamp constant
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.[1] It is named after Johannes Kepler and Christoffel Bouwkamp, and is the inverse of the polygon circumscribing constant.
![](../I/Kepler-constant.gif)
A sequence of inscribed polygons and circles
Numerical value
The decimal expansion of the Kepler–Bouwkamp constant is (sequence A085365 in the OEIS)
- 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
References
- Finch, S. R. (2003). Mathematical Constants. Cambridge University Press. MR 2003519.
Further reading
- 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. doi:10.1017/S0025557200183214.
- Doslic, Tomislav (2014). "Kepler-Bouwkamp radius of combinatorial sequences". Journal of Integer Sequence. 17: 14.11.3.
External links
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