Random chords and point distances in regular polygons
U. Bäsel Received: July 9, 2012;
Revised: September 27, 2013;
Accepted: September 30, 2013
Abstract.
In this paper we obtain the chord length distribution function for any regular polygon.
From this function we conclude the density function and the distribution function of the
distance between two uniformly and independently distributed random points in the regular
polygon. The method to calculate the chord length distribution function is quite different
from those of Harutyunyan and Ohanyan, uses only elementary methods and provides the result
with only a few natural case distinctions.
Keywords:
Geometric probability; random sets; integral geometry; chord length distribution function;
random distances; distance distribution function; regular polygons; Piefke formula
AMS Subject classification:
Primary: 60D05, 52A22
Version to read:
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