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Averages for polygons formed by random lines in Euclidean and hyperbolic planes

Published online by Cambridge University Press:  14 July 2016

L. A. Santaló
Affiliation:
University of Buenos Aires
I. Yañez
Affiliation:
University of Madrid

Abstract

We consider a countable number of independent random uniform lines in the hyperbolic plane (in the sense of the theory of geometrical probability) which divide the plane into an infinite number of convex polygonal regions. The main purpose of the paper is to compute the mean number of sides, the mean perimeter, the mean area and the second order moments of these quantities of such polygonal regions. For the Euclidean plane the problem has been considered by several authors, mainly Miles [4]–[9] who has taken it as the starting point of a series of papers which are the basis of the so-called stochastic geometry.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1972 

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