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. It is named after Johannes Kepler and , and is the inverse of the polygon circumscribing constant.
Numerical value
The decimal expansion of the Kepler–Bouwkamp constant is
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
is obtained .
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Further reading
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