### Abstract

We construct a set of n points (i) on the unit sphere S ^{d-1} (d≥4) so that they determine o(n) distinct distances and (ii) in the plane, in general position, so that they determine o(n ^{1 + ε{lunate}} ) distinct distances for any ε{lunate}>0. We also prove that if P is a set of n points in a disk of radius n such that the minimum distance between them is 1, and |P|/n→∞, then the set of angles determined by these points is everywhere dense in [0,2π].

Original language | English |
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Pages (from-to) | 189-196 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 111 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Feb 22 1993 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Erdős, P., Füredi, Z., Pach, J., & Ruzsa, I. Z. (1993). The grid revisted.

*Discrete Mathematics*,*111*(1-3), 189-196. https://doi.org/10.1016/0012-365X(93)90155-M