Paper by Martin L. Demaine
- Erik D. Demaine, Martin L. Demaine, John Iacono, and Stefan Langerman, “Wrapping the Mozartkugel”, in Abstracts from the 24th European Workshop on Computational Geometry (EuroCG 2007), Graz, Austria, March 19–21, 2007, pages 14–17.
We study wrappings of the unit sphere by a piece of paper
(or, perhaps more accurately, a piece of foil).
Such wrappings differ from standard origami because they require
infinitely many infinitesimally small “folds” in order to transform
the flat sheet into a positive-curvature sphere.
Our goal is to find shapes that have small area even when expanded to
shapes that tile the plane.
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 that still tiles the plane.
- The abstract is 4 pages.
- The abstract is available in PostScript (1380k), gzipped PostScript (669k), and PDF (151k).
- See information on file formats.
- [Google Scholar search]
- Related papers:
- SphereWrapping_CGTA (Wrapping Spheres with Flat Paper)
See also other papers by Martin Demaine.
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Last updated May 13, 2021 by