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Distinct Distances from Three Points

Part of: Discrete geometry Graph theory

Published online by Cambridge University Press:  30 September 2015

MICHA SHARIR  and
JÓZSEF SOLYMOSI
MICHA SHARIR
Affiliation:
School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: michas@tau.ac.il)
JÓZSEF SOLYMOSI
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver BC, V6T 1Z4, Canada (e-mail: solymosi@math.ubc.ca)
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Abstract

Let p 1, p 2, p 3 be three noncollinear points in the plane, and let P be a set of n other points in the plane. We show that the number of distinct distances between p 1, p 2, p 3 and the points of P is Ω(n 6/11), improving the lower bound Ω(n 0.502) of Elekes and Szabó [4] (and considerably simplifying the analysis).

MSC classification

Primary: 52C10: Erdős problems and related topics of discrete geometry
Secondary: 52C45: Combinatorial complexity of geometric structures 05C35: Extremal problems

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 4 , July 2016 , pp. 623 - 632
Copyright
Copyright © Cambridge University Press 2015 

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References

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