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