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The proportion of quadrilaterals formed by random lines in a plane

Published online by Cambridge University Press:  14 July 2016

J. C. Tanner
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Abstract

An expression is derived for the proportion of quadrilaterals among the polygons formed by random lines in the plane. Its value is 0.381 466….

Keywords

GEOMETRICAL PROBABILITYRANDOM POLYGONSPOISSON LINE PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 400 - 404
Copyright
Copyright © Applied Probability Trust 1983 

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References

Crain, I. K. and Miles, R. E. (1976) Monte Carlo estimates of the distributions of the random polygons determined by random lines in a plane. J. Statist. Comput. Simul. 4, 293–325.CrossRefGoogle Scholar
George, E. I. (1981) Sequential Stochastic Construction of Random Polygons. Ph.D. Dissertation, Stanford University.Google Scholar
Goudsmit, S. (1945) Random distribution of lines in a plane. Rev. Mod. Phys. 17, 321–322.CrossRefGoogle Scholar
Miles, R. E. (1964) Random polygons determined by random lines in a plane. Proc. Nat. Acad. Sci. US.A. 52, 901–907; 1157–1160.CrossRefGoogle ScholarPubMed
Miles, R. E. (1973) The various aggregates of random polygons determined by random lines in a plane. Adv. Math. 10, 256–290.CrossRefGoogle Scholar
Solomon, H. (1978) Geometric Probability. Society for Industrial and Applied Mathematics, Philadelphia.CrossRefGoogle Scholar