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 journalArticle

    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 languageEnglish (US)
    Pages (from-to)435-442
    Number of pages8
    JournalDiscrete and Computational Geometry
    Volume6
    Issue number1
    DOIs
    StatePublished - Dec 1991

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    ASJC Scopus subject areas

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

    Cite this

    Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L. J., Sharir, M., & Wenger, R. (1991). Points and triangles in the plane and halving planes in space. 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.

    In: Discrete and Computational Geometry, Vol. 6, No. 1, 12.1991, p. 435-442.

    Research output: Contribution to journalArticle

    Aronov, B, Chazelle, B, Edelsbrunner, H, Guibas, LJ, Sharir, M & Wenger, R 1991, 'Points and triangles in the plane and halving planes in space', Discrete and Computational Geometry, vol. 6, no. 1, pp. 435-442. https://doi.org/10.1007/BF02574700
    Aronov B, Chazelle B, Edelsbrunner H, Guibas LJ, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. Discrete and Computational Geometry. 1991 Dec;6(1):435-442. https://doi.org/10.1007/BF02574700
    Aronov, Boris ; Chazelle, Bernard ; Edelsbrunner, Herbert ; Guibas, Leonidas J. ; Sharir, Micha ; Wenger, Rephael. / Points and triangles in the plane and halving planes in space. In: Discrete and Computational Geometry. 1991 ; Vol. 6, No. 1. pp. 435-442.
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