--- _id: '4062' abstract: - lang: eng text: We prove that for any set S of n points in the plane and n3-α triangles spanned by the points in S there exists a point (not necessarily in S) contained in at least n3-3α/(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. acknowledgement: "Work on this paper by Boris Aronov and Rephael Wenger has been supported by DIMACS under NSF Grant STC-88-09648. Work on this paper by Bernard Chazelle has been supported by NSF Grant CCR-87-00917. Work by Herbert Edelsbrunner has been supported by NSF Grant CCR-87-14565. Micha Sharir has been supported by ONR Grant N00014-87-K-0129, by NSF Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the Israeli National Council for Research and Development, and the Fund for Basic Research administered by the Israeli\r\nAcademy of Sciences" article_processing_charge: No article_type: original author: - first_name: Boris full_name: Aronov, Boris last_name: Aronov - first_name: Bernard full_name: Chazelle, Bernard last_name: Chazelle - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Leonidas full_name: Guibas, Leonidas last_name: Guibas - first_name: Micha full_name: Sharir, Micha last_name: Sharir - first_name: Rephael full_name: Wenger, Rephael last_name: Wenger citation: ama: Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. Discrete & Computational Geometry. 1991;6(1):435-442. doi:10.1007/BF02574700 apa: Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., & Wenger, R. (1991). Points and triangles in the plane and halving planes in space. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02574700 chicago: Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving Planes in Space.” Discrete & Computational Geometry. Springer, 1991. https://doi.org/10.1007/BF02574700. ieee: B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger, “Points and triangles in the plane and halving planes in space,” Discrete & Computational Geometry, vol. 6, no. 1. Springer, pp. 435–442, 1991. ista: Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1991. Points and triangles in the plane and halving planes in space. Discrete & Computational Geometry. 6(1), 435–442. mla: Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes in Space.” Discrete & Computational Geometry, vol. 6, no. 1, Springer, 1991, pp. 435–42, doi:10.1007/BF02574700. short: B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger, Discrete & Computational Geometry 6 (1991) 435–442. date_created: 2018-12-11T12:06:43Z date_published: 1991-12-01T00:00:00Z date_updated: 2022-02-24T15:39:25Z day: '01' doi: 10.1007/BF02574700 extern: '1' intvolume: ' 6' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/article/10.1007/BF02574700 month: '12' oa: 1 oa_version: Published Version page: 435 - 442 publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer publist_id: '2063' quality_controlled: '1' scopus_import: '1' status: public title: Points and triangles in the plane and halving planes in space type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 6 year: '1991' ...