Discrete & Computational Geometry

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

A postscript on distances in convexn-gons

  • Paul Erdos
  • Peter Fishburn


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.


Discrete Comput Geom Convex Polygon Adjacent Vertex Regular Polygon Interior Angle 
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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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