Fold-and-Cut Magic

Figure 2: Japanese crest from [12]. The first published reference we know of is a Japanese puzzle book [12] by Kan Chu Sen in 1721. As one of many problems testing mathematical intelligence, this book asks the reader whether it is possible to fold a rectangular piece of paper flat and make one complete straight cut so as to produce a typical Japanese crest called sangaibisi (Figure 2), which translates to “three folded rhombics”. Towards the end, the book shows a solution. Another early reference to folding and cutting is an 1873 article in Harper’s New Monthly Magazine [1]. This article may be the first written account of a