Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T06:53:57.746Z Has data issue: false hasContentIssue false
  • English
  • Français

The proportion of quadrilaterals formed by random lines in a plane

Published online by Cambridge University Press:  14 July 2016

J. C. Tanner
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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