Discrete & Computational Geometry

, Volume 25, Issue 4, pp 629–634 | Cite as

Distinct Distances in the Plane

  • J. Solymosi
  • Cs. D. Tóth
Article

Abstract

It is shown that every set of n points in the plane has an element from which there are at least cn6/7 other elements at distinct distances, where c>0 is a constant. This improves earlier results of Erdős, Moser, Beck, Chung, Szemerédi, Trotter, and Székely.

Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • J. Solymosi
    • 1
  • Cs. D. Tóth
    • 1
  1. 1.Institut für Theoretische Informatik, ETH Zürich, CH-8092 Zürich, Switzerland \{solymosi,toth\}@inf.ethz.chSwitzerland

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