On the distinct distances determined by a planar point set
József Solymosi, Csaba D. Tóth · 2001
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 $c>0$ is a constant. This improves earlier results of Erd\H os, Moser, Beck, Chung, Szemer\'edi, Trotter, and Sz\'ekely.