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Polygons formed by random lines in a plane: some further results

Published online by Cambridge University Press:  14 July 2016

J. C. Tanner
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Abstract

Expressions are derived for the third and fourth moments of the distribution of the numbers of sides of the polygons formed by random lines in a plane. These are evaluated numerically; it seems unlikely that they can be expressed simply in terms of elementary functions or constants. Using these results, the third and fourth moments of the distribution of the perimeters of the polygons are derived.

Keywords

GEOMETRICAL PROBABILITYRANDOM POLYGONSPOISSON LINE PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 778 - 787
Copyright
Copyright © Applied Probability Trust 1983 

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References

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. USA 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
Tanner, J. C. (1983) The proportion of quadrilaterals formed by random lines in a plane. J. Appl. Prob. 20, 400–404.CrossRefGoogle Scholar