On the distinct distances determined by a planar point set

Authors:
J. Solymosi;Csaba D. Toth
Affiliations:
Institute for Theoretical Computer Science, ETH Zürich, CH-8092 Zürich, Switzerland;Institute for Theoretical Computer Science, ETH Zürich, CH-8092 Zürich, Switzerland
Venue:
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Year:
2001

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Abstract

It is shown that every set of $n$ points in the plane has an element f rom which there are at least $cn^{6/7}$ other elements at distinct distances, where $c0$ is a constant. This improves earlier results of Erd\H os, Moser, Beck, Chung, Szemer\'edi, Trotter, and Sz\'ekely.