Intersections of random chords of a circle
Metric Geometry
2025-04-18 v1 Probability
Abstract
Where are the intersection points of diagonals of a regular -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.
Cite
@article{arxiv.2504.12866,
title = {Intersections of random chords of a circle},
author = {Cynthia Bortolotto and Victor Souza},
journal= {arXiv preprint arXiv:2504.12866},
year = {2025}
}
Comments
Unrefereed draft, final version to appear in The American Mathematical Monthly