{"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"year":"1991","abstract":[{"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.","lang":"eng"}],"publisher":"Springer","issue":"1","status":"public","article_type":"original","extern":"1","oa_version":"Published Version","type":"journal_article","citation":{"apa":"Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., &#38; Wenger, R. (1991). Points and triangles in the plane and halving planes in space. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02574700\">https://doi.org/10.1007/BF02574700</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.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1991. <a href=\"https://doi.org/10.1007/BF02574700\">https://doi.org/10.1007/BF02574700</a>.","mla":"Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes in Space.” <i>Discrete &#38; Computational Geometry</i>, vol. 6, no. 1, Springer, 1991, pp. 435–42, doi:<a href=\"https://doi.org/10.1007/BF02574700\">10.1007/BF02574700</a>.","short":"B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger, Discrete &#38; Computational Geometry 6 (1991) 435–442.","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 &#38; Computational Geometry. 6(1), 435–442.","ama":"Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. <i>Discrete &#38; Computational Geometry</i>. 1991;6(1):435-442. doi:<a href=\"https://doi.org/10.1007/BF02574700\">10.1007/BF02574700</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,” <i>Discrete &#38; Computational Geometry</i>, vol. 6, no. 1. Springer, pp. 435–442, 1991."},"date_created":"2018-12-11T12:06:43Z","scopus_import":"1","article_processing_charge":"No","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","title":"Points and triangles in the plane and halving planes in space","month":"12","date_updated":"2022-02-24T15:39:25Z","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/BF02574700"}],"oa":1,"quality_controlled":"1","language":[{"iso":"eng"}],"publist_id":"2063","intvolume":"         6","page":"435 - 442","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication":"Discrete & Computational Geometry","publication_status":"published","day":"01","date_published":"1991-12-01T00:00:00Z","volume":6,"_id":"4062","doi":"10.1007/BF02574700","author":[{"first_name":"Boris","last_name":"Aronov","full_name":"Aronov, Boris"},{"first_name":"Bernard","full_name":"Chazelle, Bernard","last_name":"Chazelle"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Guibas","full_name":"Guibas, Leonidas","first_name":"Leonidas"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"first_name":"Rephael","last_name":"Wenger","full_name":"Wenger, Rephael"}]}