Paper by Martin L. Demaine
- Erik D. Demaine, Martin L. Demaine, John Iacono, and Stefan Langerman, “Wrapping Spheres with Flat Paper”, Computational Geometry: Theory and Applications, volume 42, number 8, 2009, pages 748–757. Special issue of selected papers from the 20th European Workshop on Computational Geometry, 2007.
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
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- The paper is 14 pages.
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- Related papers:
- SphereWrapping_EuroCG2007 (Wrapping the Mozartkugel)
See also other papers by Martin Demaine.
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