Accéder directement au contenu Accéder directement à la navigation
Article dans une revue

Maximal perimeter, diameter and area of equilateral unit-width convex polygons

Charles Audet Jordan Ninin 1
1 Lab-STICC_ENSTAB_CID_IHSEV ; OSM
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : The paper answers the three distinct questions of maximizing the perimeter, diameter and area of equilateral unit-width convex polygons. The solution to each of these problems is trivially unbounded when the number of sides is even. We show that when this number is odd, the optimal solution to these three problems is identical, and arbitrarily close to a trapezoid. The paper also considers the maximization of the sum of distances between all pairs of vertices of equilateral unit-width convex polygons. Based on numerical experiments on the three first open cases, it is conjectured that the optimal solution to this fourth problem is the same trapezoid as for the three other problems.
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00847259
Contributeur : Annick Billon-Coat <>
Soumis le : mardi 23 juillet 2013 - 11:07:43
Dernière modification le : vendredi 27 novembre 2020 - 09:34:05

Lien texte intégral

Identifiants

Citation

Charles Audet, Jordan Ninin. Maximal perimeter, diameter and area of equilateral unit-width convex polygons. Journal of Global Optimization, Springer Verlag, 2013, 56 (3), pp.1007-1016. ⟨10.1007/s10898-011-9780-4⟩. ⟨hal-00847259⟩

Partager

Métriques

Consultations de la notice

431