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Discrete & Computational Geometry

, Volume 7, Issue 1, pp 1–11 | Cite as

The number of different distances determined by a set of points in the Euclidean plane

  • Fan R. K. Chung
  • E. Szemerédi
  • W. T. Trotter
Article

Abstract

In 1946 P. Erdös posed the problem of determining the minimum numberd(n) of different distances determined by a set ofn points in the Euclidean plane. Erdös provedd(n) ≥cn1/2 and conjectured thatd(n)≥cn/ √logn. If true, this inequality is best possible as is shown by the lattice points in the plane. We showd(n)≥n4/5/(logn) c .

Keywords

Discrete Comput Geom Euclidean Plane Vertical Side Perpendicular Bisector Standard Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Fan R. K. Chung
    • 1
  • E. Szemerédi
    • 2
    • 3
  • W. T. Trotter
    • 1
    • 4
  1. 1.Bell Communications ResearchMorristownUSA
  2. 2.Mathematics Institute of the Hungarian Academy of SciencesBudapestHungary
  3. 3.Department of Computer ScienceRutgers UniversityNew BrunswickUSA
  4. 4.Department of MathematicsArizona State UniversityTempeUSA

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