par Demaine, Erik D. ;Demaine, Martin L.;Iacono, John ;Langerman, Stefan
Référence Computational geometry, 42, 8, page (748-757)
Publication Publié, 2009-10
Article révisé par les pairs
Résumé : We study wrappings of smooth (convex) surfaces by a flat piece of paper or foil. Such wrappings differ from standard mathematical origami because they require infinitely many infinitesimally small folds (″crumpling″) in order to transform the flat sheet into a surface of nonzero curvature. Our goal is to find shapes that wrap a given surface, have small area and small perimeter (for efficient material usage), and tile the plane (for efficient mass production). Our results focus on the case of wrapping a sphere. We characterize the smallest square that wraps the unit sphere, show that a 0.1% smaller equilateral triangle suffices, and find a 20% smaller shape contained in the equilateral triangle that still tiles the plane and has small perimeter. © 2009 Elsevier B.V. All rights reserved.