Points and triangles in the plane and halving planes in space

Boris Aronov; Bernard Chazelle; Herbert Edelsbrunner; Leonidas J. Guibas; Micha Sharir; Rephael Wenger

doi:10.1007/BF02574700

Points and triangles in the plane and halving planes in space

Boris Aronov, Bernard Chazelle, Herbert Edelsbrunner, Leonidas J. Guibas, Micha Sharir, Rephael Wenger

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

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 log⁵ 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 & Computational Geometry
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/BF02574700
State	Published - Dec 1991
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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10.1007/BF02574700

Cite this

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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 log5 n) of the triangles. This implies that any set of n points in three-dimensional space defines at most {Mathematical expression} halving planes.",

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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.

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Points and triangles in the plane and halving planes in space

Abstract

All Science Journal Classification (ASJC) codes

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