The moments of the distance between two random points in a regular polygon

Abstract

In this paper, we derive formulas for the analytical calculation of the moments of the distance between two uniformly and independently distributed random points in an $n$-sided regular polygon. A number of closed form expressions is provided, e.g. the expected distances for $n=3,4,5,6,8,10,12$, where the results for $n=5,8,10,12$ are new to the best of the author's knowledge. Applying results of Voss, remarkably short formulas for the second and the fourth moments are derived.

22 pages,6 figures

References in corpus (1)

• Sharp inequalities for the mean distance of random points in convex bodies

Cited by in corpus (1)

• Sharp inequalities for the mean distance of random points in convex bodies