TY - GEN
T1 - On triple intersections of three families of unit circles
AU - Raz, Orit E.
AU - Sharir, Micha
AU - Solymosi, József
PY - 2014
Y1 - 2014
N2 - 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]).
AB - 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]).
KW - Combinatorial geometry
KW - Incidences
KW - Polynomials
KW - Unit circles
UR - http://www.scopus.com/inward/record.url?scp=84904409212&partnerID=8YFLogxK
U2 - https://doi.org/10.1145/2582112.2582149
DO - https://doi.org/10.1145/2582112.2582149
M3 - Conference contribution
SN - 9781450325943
T3 - Proceedings of the Annual Symposium on Computational Geometry
SP - 198
EP - 205
BT - Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
T2 - 30th Annual Symposium on Computational Geometry, SoCG 2014
Y2 - 8 June 2014 through 11 June 2014
ER -