p. 1 - 18 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
PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |