Random secants of a convex body
- 1 April 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 6 (03) , 660-672
- https://doi.org/10.1017/s0021900200026693
Abstract
Summary: Let two points be taken at random in an n-dimensional convex body K, and let σ be the line joining them. The distribution of σ is found and compared with other distributions for random secants of K. More generally, if r + 1 ≦ npoints are taken in K, the distribution of the r-dimensional affine subspace containing them is computed. The results find application to the n-dimensional case of a problem of Sylvester.Keywords
This publication has 4 references indexed in Scilit:
- Random paths through convex bodiesJournal of Applied Probability, 1969
- What is the Expected Volume of a Simplex Whose Vertices are Chosen at Random from a Given Convex Body?The American Mathematical Monthly, 1969
- A note on recent research in geometrical probabilityJournal of Applied Probability, 1966
- Mean free paths in a convex reflecting regionJournal of Applied Probability, 1965