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Books on the Mathematics of Paperfolding

Hamilton Link , Origami-L, 8th May, asks about books on the mathematics of Origami, and in particular about a book Shuzo Fujimoto, of which he gives the title as "An Invitation to Creative Playing with Origami".

This book by Fujimoto is the one of which I have seen the title

transliterated into Roman letters as "Sozo Suri Origami Asobi".

Unfortunately it is in Japanese and has never been translated. It was

published in 1982, and, as you say, is out-of-print. It will be difficult to obtain a copy. How many copies were imported into Western countries., I do not know, but there cannot have been very many.

It is Fujimoto's most important book. It was preceded by "Twist Origami", of which two or three editions were issued in quite rough form by a duplicated process, and by "Solid Origami", which was a more professionally printed paper-back. Fujimoto has written one or two informal, smaller booklets since 1982.

Fujimoto is unquestionably one of the world's most important origami

geometers. Perhaps because of the limited publication of his books, his work has not been as widely recognised as it deserves. Would that someone would reissue his books in English, but the inevitable rejoinder from the publishers would be "They're not commercial".

Fujimoto is a most delightful person, very friendly and approachable, and one may say, very humble. He is a teacher by profession.

I obtained my copies of his books from him direct. He may be able to supply you with something, but I would not be optimistic about obtaining his main works. In any case they deal with complex folded structures and patterns and are somewhat beyond a simple analysis of the mathematics of the square.

Another important Japanese book about Origami geometry is "Origami no Kikagaku" ("Geometry of Origami") by Koji and Mitsue Husimi and published by Nippon Hyoron Sha in 1979. (" Husimi" is sometimes written as "Fusimi", because the initial sound is ambiguous to a Western ear). This was a pioneering work by a retired physicist and his wife. I understand that they hope to publish a revised and expanded edition. Our knowledge of the mathematics of paperfolding has certainly expanded greatly since 1979.

For the study of the mathematics of paperfolding at any advanced level, an essential work is "Proceedings of the First International Meeting of Origami Science and Technology" which was held at Ferrara in Italy in December 1989. The Proceedings were compiled by Humiaki Huzita (known as "Humi") and I understand copies can still be obtained from him by writing to him.

I regret that I do not know the present price. (Padova the same as Padua in English.)

Of equal interest will be the Proceedings of the Second International Meeting of Scientific Origami, held in Japan in December 1994. They are eagerly awaited, and publication has been promised soon. Many of the papers are readily accessible to people who are not advanced mathematicians. For instance, a paper by Kazuo Haga throws many interesting and surprising sidelights on the geometry of folding the square at an elementary level. At present summaries of the papers are available only in the Abstract issued befor the Meeting took place.

John Smith, who is a subscriber to Origami L has written many papers relevant to paperfolding geometry. Some remain unpublished, while others appear in the pages of the magazine of the British Origami Society.

One of the best general introductions to the mathematics of paperfolding is by the Frenchman, Jacques Justin. His articles originally appeared in French in the pages of "Le Pli", the magazine of the French society, MFPP. They were subsequently translated into English and somewhat revised and published in British Origami in 1985. It has been the hope of several of us in the BOS that these articles should be gathered together for publication as a separate booklet, but various difficulties continue to prevent this.

It will be apparent from this piecemeal survey that sources for the study of the geometry of paperfolding are not at all accessible. Sundara Row's "Geometric Exercises in Paper Folding has already been mentioned in Origami-L. Dover brought out a paper-backed reprint in1966. I do not know whether it is still in their list. There is , incidentally some mystery about this book. The original language in which it was written is uncertain. German has been suggested, but this seems unlikely. Perhaps it was some Indian language. And who was Sundara Row, (or Rau , as his name is sometimes spelt )?

Another elementary book, which may still be available is "Mathematics Through Paper Folding" by Alton T. Johnson, which was published by the National Council of Teachers of Mathematics (of the United States in 1975. It is a rewriting of an earlier book, "Paper Folding for the Mathematics Class" by Donovan A. Johnson, which was published in 1957. The address of the National Council of Teachers of Mathematics is: 1096, Association Drive, Reston, VA 22091. The have, however, revised their publication policy and Johnson's booklet may not now be available.

I give this information on the basis that some knowledge is better than none and I realise that it will not be easy to get copies of the books I refer to. I am very sorry that I do not have spare copies of the books and papers I mention. It may be possible to obtain photocopies of some of them, but others are to long for this to be reasonably practicable. The Fujimoto book, for instance, has 206 pages. Then the problems of copyright should not be forgotten. The Origami USA library may contain some of the books. But keep on trying: it is quite surprising how the rarest book can crop up when least expected.

David Lister.

   
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