The Fold-and-Cut Problem:

Kan Chu Sen's Wakoku Chiyekurabe

The first published reference to folding and cutting of which we are aware is a Japanese book, Wakoku Chiyekurabe (Mathematical Contests), by Kan Chu Sen, published in 1721. This book contains a variety of problems for testing mathematical intelligence. One of the problems asks to fold a rectangular piece of paper flat and make one complete straight cut, so as to make a typical Japanese crest called sangaibisi, which translates to ``three folded rhombics.'' The author gives a solution that consists of a sequence of simple folds, each of which folds along a line.

Many thanks are due to Gisaku Nakamura for providing us with the reference, a copy of the book, and translation of the title and relevant contents. Here are scanned images of the relevant pages in the book:

Title page Problem statement
Solution (page 1) Solution (page 2)

Last updated November 28, 2010 by Erik Demaine.