Kepler-Bouwkamp constant

From Wikipedia, the free encyclopedia

A sequence of inscribed polygons and circles.
A sequence of inscribed polygons and circles.

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.

[edit] Computing Kepler-Bouwkamp constant

The Kepler-Bouwkamp constant is equal to \prod_{k=3}^\infty \cos\left(\frac\pi k\right) = 0.1149420448\dots .

[edit] References

  • S. R. Finch, Mathematical Constants, Cambridge University Press, 2003
  • Adrian R. Kitson The prime analog of the Kepler-Bouwkamp constant math.HO/0608186