{"month":"01","date_published":"1990-01-01T00:00:00Z","title":"Points and triangles in the plane and halving planes in space","year":"1990","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 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."}],"_id":"4077","status":"public","publication":"Proceedings of the 6th annual symposium on Computational geometry","type":"conference","quality_controlled":"1","conference":{"end_date":"1990-06-09","location":"Berkley, CA, United States","start_date":"1990-06-07","name":"SCG: Symposium on Computational Geometry"},"oa_version":"None","author":[{"first_name":"Boris","full_name":"Aronov, Boris","last_name":"Aronov"},{"last_name":"Chazelle","full_name":"Chazelle, Bernard","first_name":"Bernard"},{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","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"},{"last_name":"Wenger","first_name":"Rephael","full_name":"Wenger, Rephael"}],"date_created":"2018-12-11T12:06:48Z","date_updated":"2022-02-17T09:42:27Z","publication_identifier":{"isbn":["978-0-89791-362-1"]},"doi":"10.1145/98524.98548","language":[{"iso":"eng"}],"day":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"112 - 115","publisher":"ACM","publication_status":"published","publist_id":"2045","scopus_import":"1","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. In: <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>. ACM; 1990:112-115. doi:<a href=\"https://doi.org/10.1145/98524.98548\">10.1145/98524.98548</a>","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.” In <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, 112–15. ACM, 1990. <a href=\"https://doi.org/10.1145/98524.98548\">https://doi.org/10.1145/98524.98548</a>.","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,” in <i>Proceedings of the 6th annual symposium on Computational geometry</i>, Berkley, CA, United States, 1990, pp. 112–115.","ista":"Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990. Points and triangles in the plane and halving planes in space. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 112–115.","apa":"Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., &#38; Wenger, R. (1990). Points and triangles in the plane and halving planes in space. In <i>Proceedings of the 6th annual symposium on Computational geometry</i> (pp. 112–115). Berkley, CA, United States: ACM. <a href=\"https://doi.org/10.1145/98524.98548\">https://doi.org/10.1145/98524.98548</a>","mla":"Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes in Space.” <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, ACM, 1990, pp. 112–15, doi:<a href=\"https://doi.org/10.1145/98524.98548\">10.1145/98524.98548</a>.","short":"B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 112–115."},"extern":"1","article_processing_charge":"No","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98548"}]}