It is proved that, for any ε > 0 and n > n0(ε), every set of n points in the plane has at most n11e-3/5e-1+ε triples that induce isosceles triangles. (Here e denotes the base of the natural logarithm, so the exponent is roughly 2.136.) This easily implies the best currently known lower bound, n4e/5e-1-ε, for the smallest number of distinct distances determined by n points in the plane, due to Solymosi-Cs. Toth and Tardos.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics