Intersections of Random Chords of a Circle
Abstract
Where are the intersection points of diagonals of a regular n-gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate these and related new questions in geometric probability, extend a largely forgotten result of Karamata, and elucidate its connection to the Bertrand paradox.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Random Matrices and Applications
Publication details
- Journal / source
- American Mathematical Monthly
- Publisher
- Informa UK Limited
- Volume
- 133
- Issue
- 7
- Pages
- 661–680
- Publication date
- 20 May 2026
- Language
- EN