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Fold-and-Cut Magic

By et al. Erik D. Demaine


Take a sheet of paper, fold it flat however you like, and make one complete straight cut. What are the possible shapes of the unfolded pieces? For example, Figure 1 shows how to produce a five-pointed star by folding and one straight cut. You could imagine cutting out the silhouette of your favorite animal, object, or geometric shape. Martin Gardner wrote about this fold-and-cut problem in a 1960 article in Scientific American called “Paper Cutting ” [7]. In addition to providing some of the historical references below, he was the first to pose the then-open problem: What are the limits of this fold-and-cut process? What polygonal shapes can be cut out

Year: 2009
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