Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 81, Issue 1, pp 93-100

First online:

On the volume product of polygons

  • Mathieu MeyerAffiliated withLaboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), Université Paris-Est Marne-la-Vallée
  • , Shlomo ReisnerAffiliated withDepartment of Mathematics, University of Haifa Email author 

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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.


Convex bodies Volume-product Polygons Affinely-regular

Mathematics Subject Classification (2010)