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The chord length distribution function for regular polygons

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

H. S. Harutyunyan  and
V. K. Ohanyan
H. S. Harutyunyan*
Affiliation:
Yerevan State University
V. K. Ohanyan*
Affiliation:
Yerevan State University
*
∗ Postal address: Department of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian Street, Yerevan 0025, Armenia.
∗ Postal address: Department of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian Street, Yerevan 0025, Armenia.
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Abstract

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In this paper we obtain an elementary expression for the chord length distribution function of a regular polygon. The formula is derived using δ-formalism in Pleijel identity. In the particular cases of a regular triangle, a square, a regular pentagon, and a regular hexagon, our formula coincides with the results of Sulanke (1961), Gille (1988), Aharonyan and Ohanyan (2005), and Harutyunyan (2007), respectively.

Keywords

Chord length distribution functionPleijel identityregular polygons

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 52A22: Random convex sets and integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 41 , Issue 2 , June 2009 , pp. 358 - 366
Copyright
Copyright © Applied Probability Trust 2009 

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