 
Summary: The unit distance problem for centrally symmetric convex
polygons
Bernardo M. Ábrego
Department of Mathematics
California State University, Northridge
Silvia FernándezMerchant
Department of Mathematics
California State University, Northridge
January 2002
Abstract
Let f(n) be the maximum number of unit distances determined by the vertices of a convex
ngon. Erdos and Moser conjectured that this function is linear. Supporting this conjecture
we prove that fsym
(n) 2n where fsym
(n) is the restriction of f (n) to centrally symmetric
convex ngons. We also present two applications of this result. Given a strictly convex domain
K with smooth boundary, if fK (n) denotes the maximum number of unit segments spanned by
n points in the boundary of K, then fK (n) = O (n) whenever K is centrally symmetric or has
width > 1.
1 Introduction
