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On the volume product of polygons

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Abstract

We present a method that allows us to prove that the volume product of polygons in ℝ2 with at most n vertices is bounded from above by the volume product of regular polygons with n vertices. The same method shows that the volume product of polygons is bounded from below by the volume product of triangles (or parallelograms in the centrally symmetric case). These last results give a new proof of theorems of K. Mahler. The cases of equality are completely described.

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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), Université Paris-Est Marne-la-Vallée, Cité Descartes, 5 Bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée cedex 2, France

    Mathieu Meyer

  2. Department of Mathematics, University of Haifa, Haifa, 31905, Israel

    Shlomo Reisner

Authors
  1. Mathieu Meyer
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  2. Shlomo Reisner
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Correspondence to Shlomo Reisner.

Additional information

Communicated by V. Cortés.

Both authors were supported in part by the France-Israel Research Network Program in Mathematics.

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Meyer, M., Reisner, S. On the volume product of polygons. Abh. Math. Semin. Univ. Hambg. 81, 93–100 (2011). https://doi.org/10.1007/s12188-011-0054-3

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  • DOI: https://doi.org/10.1007/s12188-011-0054-3

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