On triple intersections of three families of unit circles

Orit E. Raz, Micha Sharir, József Solymosi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Let p1, p2, p3 be three distinct points in the plane, and, for i = 1, 2, 3, let Ci be a family of n unit circles that pass through pi. We address a conjecture made by Székely, and show that the number of points incident to a circle of each family is O(n11/6), improving an earlier bound for this problem due to Elekes, Simonovits, and Szabó [4]. The problem is a special instance of a more general problem studied by Elekes and Szabó [5] (and by Elekes and Rónyai [3]).

Original languageAmerican English
Title of host publicationProceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
PublisherAssociation for Computing Machinery
Pages198-205
Number of pages8
ISBN (Print)9781450325943
DOIs
StatePublished - 2014
Externally publishedYes
Event30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan
Duration: 8 Jun 201411 Jun 2014

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference30th Annual Symposium on Computational Geometry, SoCG 2014
Country/TerritoryJapan
CityKyoto
Period8/06/1411/06/14

Keywords

  • Combinatorial geometry
  • Incidences
  • Polynomials
  • Unit circles

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