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Japanese Conference on Discrete and Computational Geometry and Graphs

JCDCGG 2013: Discrete and Computational Geometry and Graphs pp 31–43Cite as

On Wrapping Spheres and Cubes with Rectangular Paper

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8845))

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.

Eli Fox-Epstein: Supported in part by NSF Grant CCF-0964037.

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References

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Acknowledgments

This research began in an open problem session and final project for MIT class 6.849: Geometric Folding Algorithms in Fall 2012. Thanks to Stephen Face for fruitful discussion and to Zachary Abel and Martin Demaine for their assistance with references.

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Authors and Affiliations

  1. MIT, Cambridge, MA, USA

    Alex Cole & Erik D. Demaine

  2. Brown University, Providence, RI, USA

    Eli Fox-Epstein

Authors
  1. Alex Cole
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  2. Erik D. Demaine
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  3. Eli Fox-Epstein
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Corresponding author

Correspondence to Alex Cole .

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Editors and Affiliations

  1. Tokyo University of Science, Tokyo, Japan

    Jin Akiyama

  2. The University of Electro-Communications, Tokyo, Japan

    Hiro Ito

  3. Tokai University, Tokyo, Japan

    Toshinori Sakai

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Cole, A., Demaine, E.D., Fox-Epstein, E. (2014). On Wrapping Spheres and Cubes with Rectangular Paper. In: Akiyama, J., Ito, H., Sakai, T. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science(), vol 8845. Springer, Cham. https://doi.org/10.1007/978-3-319-13287-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-13287-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13286-0

  • Online ISBN: 978-3-319-13287-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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