A Postscript on Distances in Convex n-Gons

@article{Erds1994APO,
  title={A Postscript on Distances in Convex n-Gons},
  author={Paul Erd{\"o}s and Peter C. Fishburn},
  journal={Discrete & Computational Geometry},
  year={1994},
  volume={11},
  pages={111-117}
}
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. 

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-3 of 3 references

On a problem of P

  • I E. Altman
  • ErdSs, Amer. Math. Monthly
  • 1963

On the different distances determined by n points

  • L. Moser
  • Amer. Math. Monthly
  • 1952

Oil sets of distances of n points

  • P. Erdos
  • Amer. Math. Monthly
  • 1946

Similar Papers

Loading similar papers…