## On distinct distances from a vertex of a convex polygon

- Adrian Dumitrescu
- Symposium on Computational Geometry
- 2004

@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} }

- Published 1994 in Discrete & Computational Geometry
DOI:10.1007/BF02573998

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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