ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




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  


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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Comenius University
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