Paper by Erik D. Demaine

Reference:

Alex Cole, Erik D. Demaine, and Eli Fox-Epstein, “On Wrapping Spheres and Cubes with Rectangular Paper”, in Revised Papers from the 12th Japan Conference on Discrete and Computational Geometry and Graphs (JCDCG^2 2013), Lecture Notes in Computer Science, Tokyo, Japan, September 17–19, 2013, to appear.

Abstract:

What is the largest cube or sphere that a given rectangular piece of paper can wrap? This natural problem, which has plagued gift-wrappers everywhere, remains very much unsolved. Here we introduce new upper and lower bounds and consolidate previous results. Though these bounds rarely match, our results significantly reduce the gap.

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CubeWrapping_JCDCGG2013 (On Wrapping Spheres and Cubes with Rectangular Paper)