--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Boris foaf_name: Aronov, Boris foaf_surname: Aronov - foaf_Person: foaf_givenName: Bernard foaf_name: Chazelle, Bernard foaf_surname: Chazelle - foaf_Person: foaf_givenName: Herbert foaf_name: Edelsbrunner, Herbert foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Leonidas foaf_name: Guibas, Leonidas foaf_surname: Guibas - foaf_Person: foaf_givenName: Micha foaf_name: Sharir, Micha foaf_surname: Sharir - foaf_Person: foaf_givenName: Rephael foaf_name: Wenger, Rephael foaf_surname: Wenger bibo_doi: 10.1145/98524.98548 dct_date: 1990^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/978-0-89791-362-1 dct_language: eng dct_publisher: ACM@ dct_title: Points and triangles in the plane and halving planes in space@ ...