Random secants of a convex body

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.