### Abstract

It is proved that, for any ε > 0 and n > n_{0}(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 language | English |
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Pages (from-to) | 769-779 |

Number of pages | 11 |

Journal | Graphs and Combinatorics |

Volume | 18 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 2002 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Pach, J., & Tardos, G. (2002). Isosceles triangles determined by a planar point set.

*Graphs and Combinatorics*,*18*(4), 769-779. https://doi.org/10.1007/s003730200063