Folding a Better Checkerboard

Abstract. 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 n2 . Indeed, within a restricted class of foldings that match all previous origami models of this flavor, one can prove a lower bound of n2 (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 2 n2 + O(n). In particular, our construction strictly beats semiperimeter n2 for (even) n > 16, and for n = 8, we improve on the best seamless folding.

• Type: Conference
• Year: 2009
• Where: ISAAC
• Authors: Erik D. Demaine, Martin L. Demaine, Goran Konjevod, Robert J. Lang
• Keywords: Algorithms, Checkerboard Pattern, ISAAC 2009, Paper Square, Semiperimeter N2