### Abstract

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

Original language | English (US) |
---|---|

Pages (from-to) | 435-442 |

Number of pages | 8 |

Journal | Discrete and Computational Geometry |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1991 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Discrete and Computational Geometry*,

*6*(1), 435-442. https://doi.org/10.1007/BF02574700

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

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 6, no. 1, pp. 435-442. https://doi.org/10.1007/BF02574700

}

TY - JOUR

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

AU - Aronov, Boris

AU - Chazelle, Bernard

AU - Edelsbrunner, Herbert

AU - Guibas, Leonidas J.

AU - Sharir, Micha

AU - Wenger, Rephael

PY - 1991/12

Y1 - 1991/12

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

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

UR - http://www.scopus.com/inward/record.url?scp=51249171292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249171292&partnerID=8YFLogxK

U2 - 10.1007/BF02574700

DO - 10.1007/BF02574700

M3 - Article

VL - 6

SP - 435

EP - 442

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -