Origami-Math Bibliography

(Note: last updated 6/5/08)
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.

Tom's Picks

As this bibliography has grown, it occurred to me that I should make an effort to draw people's attention to articles that are of special significance. Go to this page to see my suggestions.

Proceedings and Special Journal Issues

A number of proceedings books resulting from origami conferences have been published, as well as a few special journal issues devoted to origami-math. Most of these are hard to find, except the last one! Still, you can click on the title to see the table of contents and see whatever other information I have.

Books

There are a few books devoted to origami mathematics and a few other books that devote a chapter to the subject.
• 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.

Articles

There are an amazing number of articles dealing with the mathematics of origami that have been published over the years. I've tried to break them down into six subcategories.
Back to Origami Math page