The expected number and angle of intersections between random curves in a plane
- 1 December 1966
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 3 (2) , 559-562
- https://doi.org/10.2307/3212140
Abstract
Consider a plane containing a set of curves. Suppose a separate set of curves is constrained to lie at random on a particular region of this plane. In this note an expression is obtained for the expected number of intersections between the two sets of curves, and it is shown that the angles between the two sets at their points of intersection are distributed as ½ sin θ.Keywords
This publication has 2 references indexed in Scilit:
- RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANEProceedings of the National Academy of Sciences, 1964
- The distribution of plane angles of contactQuarterly of Applied Mathematics, 1949