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 .

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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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