Skip to content
Register Sign in Wishlist

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

  • Date Published: April 2011
  • availability: Available
  • format: Hardback
  • isbn: 9780521767354


Add to wishlist

Other available formats:
Paperback, eBook

Looking for an inspection copy?

This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • 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,, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.

    • Nearly 200 color figures and 50 exercises, with complete solutions
    • Written in accessible language and discusses tangible topics which render abstract mathematics concrete
    • Presumes only high-school algebra and geometry
    Read more

    Reviews & endorsements

    'The major theorems presented are remarkable - results that may surprise the reader include the fact that, with the right folds, any shape or collection of shapes (even ones with holes in) … composed of straight lines may be cut out from a sheet of paper with just a single cut.' London Mathematical Society Newsletter

    'In this beautiful and inspiring book with many colour figures the reader can find a fascinating mathematical approach to linkages, foldings and unfoldings. Many exercises with detailed solutions give the reader the chance to control the acquired skills.' Hansueli Hosli, Zentralblatt MATH

    '… 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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: April 2011
    • format: Hardback
    • isbn: 9780521767354
    • length: 192 pages
    • dimensions: 236 x 157 x 15 mm
    • weight: 0.48kg
    • contains: 171 b/w illus. 1 table 48 exercises
    • availability: Available
  • Table of Contents

    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.

  • Instructors have used or reviewed this title for the following courses

    • Advanced Topics in Mathematics
    • Design of Materials: Mechanisms and Structures
    • Special Topic: Mathematical Methods in Origami
  • Author

    Joseph O’Rourke, Smith College, Massachusetts
    Joseph O'Rourke is Professor and Chair of the Computer Science Department, a Professor of Mathematics, and Director of Arts and Technology at Smith College. His research is in computational geometry, developing algorithms for geometric computations. He has won several awards, including a Guggenheim Fellowship in 1987 and the NSF Director's Award for Distinguished Teaching Scholars in 2001. He has published more than 145 papers in journals and conference proceedings, more than 30 of which were coauthored with undergraduates. He has taught folding and unfolding to students in grade school, middle school, high school, college and graduate school, and to teachers - of grade school, middle school, and high school - professors, and researchers. This is his sixth book.

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.