### 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 |

State | Published - 1990 |

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

### Other

Other | Proceedings of the Sixth Annual Symposium on Computational Geometry |
---|---|

City | Berkeley, CA, USA |

Period | 6/6/90 → 6/8/90 |

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proc Sixth Annu Symp Comput Geom*(pp. 112-115). Publ by ACM.

**Points and triangles in the plane and halving planes in space.** / Aronov, Boris; Guibas, Leonidas J.; Chazelle, Bernard; Sharir, Micha; Edelsbrunner, Herbert; Wenger, Rephael.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proc Sixth Annu Symp Comput Geom.*Publ by ACM, pp. 112-115, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/6/90.

}

TY - GEN

T1 - Points and triangles in the plane and halving planes in space

AU - Aronov, Boris

AU - Guibas, Leonidas J.

AU - Chazelle, Bernard

AU - Sharir, Micha

AU - Edelsbrunner, Herbert

AU - Wenger, Rephael

PY - 1990

Y1 - 1990

N2 - We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.

AB - We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.

UR - http://www.scopus.com/inward/record.url?scp=0025028278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025028278&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0897913620

SP - 112

EP - 115

BT - Proc Sixth Annu Symp Comput Geom

PB - Publ by ACM

ER -