Averages for polygons formed by random lines in Euclidean and hyperbolic planes
- 1 March 1972
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 9 (1) , 140-157
- https://doi.org/10.2307/3212643
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.Keywords
This publication has 8 references indexed in Scilit:
- Poisson flats in Euclidean spaces Part II: Homogeneous Poisson flats and the complementary theoremAdvances in Applied Probability, 1971
- On the homogeneous planar Poisson point processMathematical Biosciences, 1970
- Poisson flats in Euclidean spaces Part I: A finite number of random uniform flatsAdvances in Applied Probability, 1969
- Horocycles and convex sets in hyperbolic planeArchiv der Mathematik, 1967
- RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANE, IIProceedings of the National Academy of Sciences, 1964
- AVERAGES FOR POLYGONS FORMED BY RANDOM LINESProceedings of the National Academy of Sciences, 1964
- RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANEProceedings of the National Academy of Sciences, 1964
- Random Distribution of Lines in a PlaneReviews of Modern Physics, 1945