On the polygon determined by the short diagonals of a convex polygon

2018/12/18 by Jacqueline Cho, Dan Ismailescu, Cho, Jacqueline +5
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Metric Geometry (math.MG) #graph theory and CDMA systems #math.HO #math.MG

paper · pdf · doi:10.48550/arxiv.1812.07682

arxiv created 2018/12/18 · openalex publication_date 2018/12/18 · arxiv updated 2018/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a convex pentagon in the plane and let K₁ be the pentagon bounded by the diagonals of K. It has been conjectured that the maximum of the ratio between the areas of K₁ and K is reached when K is an affine regular pentagon. In this paper we prove this conjecture. We also show that for polygons with at least six vertices the trivial answers are the best possible.

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