Periodica Mathematica Hungarica

, Volume 38, Issue 3, pp 173–177 | Cite as

A Note on the Number of Distinct Distances

  • G. Elekes


We refine a method introduced in [1] and [2] for studying the number of distinct values taken by certain polynomials of two real variables on Cartesian products. We apply it to prove a "gap theorem", improving a recent lower bound on the number of distinct distances between two collinear point sets in the Euclidean space.


Euclidean Space Real Variable Collinear Point Distinct Distance 
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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • G. Elekes
    • 1
  1. 1.Eötvös Loránd UniversityBudapestHungary

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