Cutting Corners

a page from Wakoku Chiyekurabe            Erik Demaine

Knowing mathematicians (as we think we do), it should come as no great surprise that there is a theorem about the cutting and folding of paper. Nor should it come as a surprise that the first known reference to this activity comes to us from Japan ~ in the book Wakoku Chiyekurabe (Mathematical Contests), published in 1721. Among the "contests" it describes is one that challenges the reader to fold a piece of paper in such a way that, with one straight cut, it will become a Japanese crest called a sangaibisi. Skip forward a couple of centuries, and you have yourself a theorem, the fold-and-cut theorem, that states that any shape consisting of straight lines can be made from just one straight cut. The key is figuring out how to fold the paper right. Hard to believe, but it was actually proved. In the video accompanying this story, mathematician Katie Steckles creates every letter of the alphabet with only one cut each (story, video): http://mentalfloss.com/article/69222/mathematician-shows-how-make-any-shape-single-cut