Paper by Erik D. Demaine

Reference:

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.

Abstract:

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.

Length:

The abstract is 4 pages.

Availability:

The abstract is available in PostScript (1380k), gzipped PostScript (669k), and PDF (151k).

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SphereWrapping_CGTA (Wrapping Spheres with Flat Paper)