On distinct distances from a vertex of a convex polygon
Given a set \(P\) of \(n\) points in convex position in the plane (i.e. the points are the vertices of a convex polygon), the author proves that there exists a point \(p \in P\) such that the number of distinct distances from \(p\) is at least \(\lceil(13n-6)/36\rceil\). The best previous bound, \(\lceil n/3\rceil\), from 1952, is due to Moser.
scientific article; zbMATH DE number 5077623