Kepler–Bouwkamp constant
In plane geometry, the 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.
The radius of the limiting circle is called the Kepler–Bouwkamp constant. It is named after Johannes Kepler and, and is the inverse of the polygon circumscribing constant.The decimal expansion of the Kepler–Bouwkamp constant is
where is the Riemann zeta function.
If the product is taken over the odd primes, the constant
is obtained.
