Points and lines configurations for perpendicular bisectors of convex cyclic polygons

Paul Melotti (1) , Sanjay Ramassamy (2) , Paul Thévenin (3)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 Department of Mathematics [Uppsala]

We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and asymptotic formulas describing a random realizable configuration, obtained either by sampling the points uniformly at random on the circle or by sampling a realizable configuration uniformly at random.

Domaines: Combinatoire [math.CO]; Géométrie métrique [math.MG]; Probabilités [math.PR]

Paul Melotti, Sanjay Ramassamy, Paul Thévenin. Points and lines configurations for perpendicular bisectors of convex cyclic polygons. The Electronic Journal of Combinatorics, 2022, 29 (1), pp.1-46. ⟨10.37236/9957⟩. ⟨hal-02518173v2⟩