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Discrete & Computational Geometry

, Volume 11, Issue 1, pp 111–117 | Cite as

A postscript on distances in convexn-gons

  • Paul Erdos
  • Peter Fishburn
Article

Abstract

Letg(n) be the largest integerk such that every convex polygon withn vertices and sides has a vertexx such that the nextk vertices clockwise fromx, or the nextk vertices counterclockwise fromx, are successively farther fromx. We prove thatg(n)=[n/3]+1 forn≥4. An example givesg(n)≤[n/3]+1, and an extension of a 1952 construction of Leo Moser for a related planar problem shows thatg(n)≥[n/3]+1.

Keywords

Discrete Comput Geom Convex Polygon Adjacent Vertex Regular Polygon Interior Angle 
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.

References

  1. 1.
    E. Altman, On a problem of P. Erdös,Amer. Math. Monthly 70 (1963), 148–157.zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    P. Erdős, On sets of distances ofn points,Amer. Math. Monthly 53 (1946), 248–250.MathSciNetCrossRefGoogle Scholar
  3. 3.
    P. Erdős and P. C. Fishburn, Multiplicities of interpoint distances in finite planar sets,Discrete Appl. Math., in press.Google Scholar
  4. 4.
    L. Moser, On the different distances determined byn points.Amer. Math. Monthly 59 (1952), 85–91.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • Paul Erdos
    • 1
  • Peter Fishburn
    • 2
  1. 1.Mathematical InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.AT&T Bell LaboratoriesMurray HillUSA

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