The intersection between the subjects of origami and mathematics is rich with interesting results and applications. It's also a field that's becoming more and more popular, especially the use of origami in math and science education.

Unfortunately, there are few general, all-around, "it's all here" references for the subject of origami-mathematics. The major sources in this subject are scattered throughout the mathematical and educational literature. I've tried to compile as complete a list of origami-math references as possible, but it's really impossible for me to catalog them all. Also, just because I list a reference here doesn't mean I have it! Many of the article and book references here were given to me by other people, and I haven't gotten around to finding them yet.

- Proceedings of the First
International Meeting of Origami Science and Technology

This conference took place in Ferrara, Italy in 1989. Its proceedings are a basic reference for origami-math, although they're now a bit out-dated, not to mention impossible to find. - Origami Science and Art:
Proceedings of the Second International Meeting of Origami Science
and Scientific Origami

This conference took place in Otsu, Japan in 1994. It is a very good collection of articles, although it too is almost impossible to find. - Proceedings of the First
International Conference on Origami in Education and Therapy
(COET91)

This conference took place in Birmingham, England in 1991. - Proceedings of the Second
International Conference on Origami in Education and Therapy
(COET95)

This conference took place in New York City in 1995. -
Symmetry: Culture and Science

This is the quarterly journal of the International Society for the Interdisciplinary Study of Symmetry (ISIS-Symmetry). In 1994 two issues of this journal were devoted to origami-math and science articles. - Origami3: Proceedings of the Third International Meeting of Origami Science, Mathematics, and Education

Finally, a proceedings book for this subject has been published by regular math and science textbook publisher, ensuring that this book will be easy to get copies of, as long as it stays in print! This conference took place in 2001 at the Asilomar Conference Grounds in Monterey, CA. It was sponsored by Origami USA. Click on the title to find out how to order a copy. (Or ask your local library to get one!)

- David Cox,
*Galois Theory*, John Wiley & Sons, Hoboken, 2004.

Chapter 10 of this book is devoted to geometric constructions, and Section 3 of this chapter is on origami. This is the best exposition of an algebraic, Galois Theory approach to origami geometric constructions that I've seen. - Erik Demaine and Joseph O'Rourke,
*Geometric Folding Algorithms: linkages, origami, polyhedra*, Cambridge University Press, Cambridge, 2007.

This book is the text for an introduction to all aspects of the field computational origami. From linkages (1D folding, which has applications to protein foldng) to origami to polyhedra. It includes Eric's solution to the famous "fold and cut" theorem, provides the proof that the flat foldability problem is NP-complete, and bunches of other stuff. It's good reading. - Thomas Hull,
*Project Origami: activities for exploring mathematics*, AK Peters, Wellesley, 2006.

OK, this is my book. But it's a good source for learning about many different aspects of origami-math. It is designed for teachers, including handouts and activities for using origami in various math classrooms. A lot can be learned from the book, though, just by reading it through. - K. Husimi [or Hushimi] and M. Husimi [or Hushimi],
*Origami no kikagaku*[Geometry of Origami, in Japanese], Nihon-hyoron-sha, Tokyo (1979, reprinted in 1984), currently out of print.

I finally obtained a copy of this. While it's very interesting, and contains a number of great puzzles, this book is a bit outdated in terms of current research in origami geometry. It doesn't discuss how to trisect angles using origami, for example. - Johnson, D.A.,
*Paper Folding for the Mathematics Class*, National Council of Teachers of Mathematics, Washington D.C., 32 pp. (1957). - Kunihiko Kasahara and Toshi Takahama,
*Origami for the Connoisseur*, Japan Publications, New York (1987), currently out of print.

This is an origami instruction book, but it contains many juicy nibblets of origami-mathness. - Robert J. Lang,
*Origami Design Secrets: mathematical methods for an ancient art*, AK Peters, Natick, 2003.

This is the book to read if you want to learn about the mathematics and algorithms behind origami design. Lang uses mostly an informal tone, but it's all there. It's the Bible for complex origami design. - George E. Martin,
*Geometric Constructions*, Springer, New York, 1998.

The last chapter (14 pages) of this book is devoted to geometric constructions via paper folding. Martin's approach is purely geometric, as opposed to Cox's algebraic analysis. Martin concentrates on only the most sophisticated of the single-fold origami operations (folding 2 points simultaneously to 2 lines). This is all one needs, however, to perform constructions such as angle trisections and cube doublings. Martin also compares this to other construction methods, for instance, using a marked ruler. - A. Olson,
*Mathematics Through Paper Folding*, National Council of Teachers of Mathematics, Reston, Virginia, 64 pp. (1975). - T. Sundra Row,
*Geometric Excercises in Paper Folding*, first published in 1893 and reprinted numerous times, most recently by Dover, New York, 148 pp. (1966).

This contains many origami versions of straight-edge and compass geometric constructions. It was a very influential book, since it was the first, it seems, to make a solid case for the use of paper folding to teach extensive topics in Euclidean geometry. Felix Klein mentions this book in several of his popular-math books in the late 1800s and early 1900s. - John Smith,
*Patterns in Paper*, British Origami Society Booklet No. 32, British Origami Society, 50 pp. (1990).

This presents a non-rigorous attempt at modeling origami via mathematics.

- Computational Origami
- Origami Geometry and Education
- Mathematical Models of Origami and Origami Design
- Modular Origami
- Physics of Origami and Applications
- Fractal Dragon Curves and Stuff Like That

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