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

2021/01/11 by Bäsel, Uwe
#52A22 #53C65 #60D05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2101.03815

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.

Related

• Mean distance in polyhedra
• Random Distances Associated With Equilateral Triangles
• Random Distances Associated with Arbitrary Triangles: A Systematic Approach between Two Random Points
• The Mean Distance to the n-th Neighbour in a Uniform Distribution of Random Points: An Application of Probability Theory
• Degree of Convexity and Expected Distances in Polygons