How to Fold It
The Mathematics of Linkages, Origami, and Polyhedra

Discover and understand mathematical theorems through paper folding, starting with high school algebra and geometry through to more advanced concepts.

Joseph O’Rourke (Author)

9780521145473, Cambridge University Press

Paperback, published 25 April 2011

190 pages, 171 b/w illus. 1 table 48 exercises
22.6 x 15.2 x 1.3 cm, 0.33 kg

'… a great book for someone who wants to learn about the mathematics behind origami without being overwhelmed by the mathematics itself. This is a great book for a high school or undergraduate student to get introduced to the open problems in computational origami.' Brittany Terese Fasy and David L. Millman, SIGACT News

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.

Part I. Linkages: 1. Robot arms
2. Straight-line linkages and the pantograph
3. Protein folding and pop-up cards
Part II. Origami: 4. Flat vertex folds
5. Fold and one-cut
6. The shopping bag theorem
Part III. Polyhedra: 7. Durer's problem: edge unfolding
8. Unfolding orthogonal polyhedra
9. Folding polygons to convex polyhedra
10. Further reading
11. Glossary
12. Answers to exercises
13. Permissions and acknowledgments.

Subject Areas: Geometry [PBM], Algebra [PBF]