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Distinct Distances in the Plane

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.

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Received November 15, 2000, and in revised form December 13, 2000. Online publication April 6, 2001.

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Solymosi, J., Tóth, C. Distinct Distances in the Plane. Discrete Comput Geom 25, 629–634 (2001). https://doi.org/10.1007/s00454-001-0009-z

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