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On the mean length of the chords of a closed curve

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Abstract

Let us consider theN-gons with unit length of sides in the plane. What is the maximum of the arithmetical mean of the length of diagonals? We give an elementary solution for this problem and some more general ones. We deal with continuous analogons too.

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Authors and Affiliations

  1. József Attila University of Szeged, Hungary

    Lükő Gábor

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  1. Lükő Gábor
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Gábor, L. On the mean length of the chords of a closed curve. Israel J. Math. 4, 23–32 (1966). https://doi.org/10.1007/BF02760067

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  • DOI: https://doi.org/10.1007/BF02760067

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