Covering families of triangles - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Periodica Mathematica Hungarica Year : 2023

Covering families of triangles

Abstract

A cover for a family F of sets in the plane is a set into which every set in F can be isometrically moved. We are interested in the convex cover of smallest area for a given family of triangles. Park and Cheong conjectured that any family of triangles of bounded diameter has a smallest convex cover that is itself a triangle. The conjecture is equivalent to the claim that for every convex set X there is a triangle Z whose area is not larger than the area of X , such that Z covers the family of triangles contained in X. We prove this claim for the case where a diameter of X lies on its boundary. We also give a complete characterization of the smallest convex cover for the family of triangles contained in a half-disk, and for the family of triangles contained in a square. In both cases, this cover is a triangle.
Fichier principal
Vignette du fichier
hal.pdf (1.09 Mo) Télécharger le fichier
Vignette du fichier
vignette.png (43.13 Ko) Télécharger le fichier
computations.mw.gz (76.78 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Format : Figure, Image

Dates and versions

hal-03662311 , version 1 (09-05-2022)

Licence

Attribution

Identifiers

Cite

Otfried Cheong, Olivier Devillers, Ji-Won Park, Marc Glisse. Covering families of triangles. Periodica Mathematica Hungarica, 2023, 87, pp.86--109. ⟨10.1007/s10998-022-00503-4⟩. ⟨hal-03662311⟩
138 View
80 Download

Altmetric

Share

Gmail Facebook X LinkedIn More