A Postscript on Distances in Convex n-Gons

  title={A Postscript on Distances in Convex n-Gons},
  author={Paul Erd{\"o}s and Peter C. Fishburn},
  journal={Discrete & Computational Geometry},
Let g(n) be the largest integer k such that every convex polygon with n vertices and sides has a vertex x such that the next k vertices clockwise from x, or the next k vertices counterclockwise from x, are successively farther from x. We prove that g(n) = Ln/3J + 1 for n _>_ 4. An example gives y(n) < Ln/3J + 1, and an extension of a 1952 construction of Leo Moser for a related planar problem shows that #(n) _> Ln/3j + 1. 

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