Editing Concyclic points (section)

===Polygon circumscribing constant===
[[File:Kepler constant inverse.svg|thumb|right|upright=0.8|A sequence of circumscribed polygons and circles.]]

Any [[regular polygon]] is cyclic. Consider a unit circle, then circumscribe a regular triangle such that each side touches the circle. Circumscribe a circle, then circumscribe a square. Again circumscribe a circle, then circumscribe a regular [[pentagon]], and so on. The radii of the circumscribed circles converge to the so-called ''polygon circumscribing constant''

:<math>\prod_{n=3}^\infty \frac 1 {\cos\left( \frac\pi n \right)} = 8.7000366\ldots.</math>

{{OEIS|A051762}}. The reciprocal of this constant is the [[Kepler–Bouwkamp constant]].