On the volume product of polygons

Mathieu Meyer; Shlomo Reisner

doi:10.1007/s12188-011-0054-3

On the volume product of polygons

Mathieu Meyer, Shlomo Reisner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	93-100
Number of pages	8
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	81
Issue number	1
DOIs	https://doi.org/10.1007/s12188-011-0054-3
State	Published - Apr 2011

Keywords

Affinely-regular
Convex bodies
Polygons
Volume-product

ASJC Scopus subject areas

General Mathematics

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10.1007/s12188-011-0054-3

Cite this

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On the volume product of polygons

Abstract

Keywords

ASJC Scopus subject areas

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