Kawasaki's Theorem - History

History

In the late 1970s, Yasuji Husimi and David A. Huffman independently discovered the special case of Kawasaki's theorem for crease patterns with four creases; Huffman called it the "critical π condition". The theorem for crease patterns with arbitrarily many creases was discovered by Kawasaki, by Stuart Robertson, and by Jacques Justin (again, independently of each other) in the late 1970s and early 1980s. Because of Justin's contribution to the problem, it has also been called the Kawasaki–Justin theorem.

Kawasaki himself has called the result Husimi's theorem, after Yasuji Husimi, and some other authors have followed this terminology as well. The name "Kawasaki's theorem" was first given to this result in Origami for the Connoisseur by Kunihiko Kasahara and Toshie Takahama (Japan Publications, 1987).

Hull (2003) credits the lower bound of 2n on the number of different flat-foldings of a crease pattern meeting the conditions of the theorem to independent work in the early 1990s by Azuma, Justin, and Ewins and Hull.