On distinct distances from a vertex of a convex polygon

Given a set P of n points in convex position in the plane, we prove that there exists a point p ∈ P such that the number of distinct distances from p is at least (13n−6)/36 . The best previous bound, n/3 , from 1952, is due to Leo Moser. Categories and Subject Descriptors G.2.1 [Discrete Mathematics]: Combinatorics—Counting problems General Terms Theory Keywords Distinct distances, convex polygons

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Adrian Dumitrescu
• Keywords: COMPGEOM 2004, Convex Position, Distinct Distances, Keywords Distinct Distances