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.
About this article
Cite this article
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