### Abstract

We prove that for any set S of n points in the plane and n^{3-α} triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n^{3-3α}/(512 log^{25} n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n^{8/3} log^{5/3} n halving planes.

Original language | English (US) |
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Title of host publication | Proc Sixth Annu Symp Comput Geom |

Publisher | Publ by ACM |

Pages | 112-115 |

Number of pages | 4 |

ISBN (Print) | 0897913620, 9780897913621 |

DOIs | |

State | Published - 1990 |

Event | Proceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA Duration: Jun 6 1990 → Jun 8 1990 |

### Publication series

Name | Proc Sixth Annu Symp Comput Geom |
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### Conference

Conference | Proceedings of the Sixth Annual Symposium on Computational Geometry |
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City | Berkeley, CA, USA |

Period | 6/6/90 → 6/8/90 |

### ASJC Scopus subject areas

- Engineering(all)

## Cite this

Aronov, B., Guibas, L. J., Chazelle, B., Sharir, M., Edelsbrunner, H., & Wenger, R. (1990). Points and triangles in the plane and halving planes in space. In

*Proc Sixth Annu Symp Comput Geom*(pp. 112-115). (Proc Sixth Annu Symp Comput Geom). Publ by ACM. https://doi.org/10.1145/98524.98548