Distinct Distances in the Plane |
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| Authors: | J. Solymosi Cs. D. Tóth |
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| Affiliation: | (1) Institut für Theoretische Informatik, ETH Zürich, CH-8092 Zürich, Switzerland {solymosi,toth}@inf.ethz.ch, CH |
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| Abstract: | It is shown that every set of n points in the plane has an element from which there are at least cn 6/7 other elements at distinct distances, where c>0 is a constant. This improves earlier results of Erdős, Moser, Beck, Chung, Szemerédi, Trotter, and Székely. Received November 15, 2000, and in revised form December 13, 2000. Online publication April 6, 2001. |
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