Folding a Better Checkerboard

  • Erik D. Demaine
  • Martin L. Demaine
  • Goran Konjevod
  • Robert J. Lang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)


Folding an n ×n checkerboard pattern from a square of paper that is white on one side and black on the other has been thought for several years to require a paper square of semiperimeter n 2. Indeed, within a restricted class of foldings that match all previous origami models of this flavor, one can prove a lower bound of n 2 (though a matching upper bound was not known). We show how to break through this barrier and fold an n ×n checkerboard from a paper square of semiperimeter \({1 \over 2} n^2 + O(n)\). In particular, our construction strictly beats semiperimeter n 2 for (even) n > 16, and for n = 8, we improve on the best seamless folding.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Goran Konjevod
    • 2
  • Robert J. Lang
    • 3
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Department of Computer Science and EngineeringArizona State UniversityTempeUSA
  3. 3.No Affiliations 

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