A Disk-Packing Algorithm for an Origami Magic Trick
Marshall W. Bern · 2007
We present an algorithm for a magic trick. Given a polygon with holes P , our algorithm determines a folding of a rectangular sheet of paper such that a single straight cut suffices to cut out P . Keywords: Computational Geometry, Paperfolding, Polygon. 1 Introduction The great Harry Houdini was one of the first to perform the following magic trick: fold a sheet of paper so that a single straight cut produces a cut-out of a rabbit, a dog, or whatever else one likes. Whereas Houdini only published a method for a five-pointed star [11] (a method probably known to Betsy Ross [10]), Martin Gardner [9] posed the question of cutting out more complex shapes. Demaine and Demaine [5] stated this question more formally: given a polygon with holes P (possibly with more than one connected component) and a rectangle R large enough to contain P , find a "flat folding" of R such that the cross-section of the folding with a perpendicular plane is the boundary of P . More intuitively, a single str...