Isosceles triangles determined by a planar point set

Janos Pach, Gabor Tardos

Research output: Contribution to journalArticle

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)769-779
Number of pages11
JournalGraphs and Combinatorics
Issue number4
Publication statusPublished - Jan 1 2002

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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