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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? You can answer these questions and more through the mathematics of folding and unfolding. From this book, you will discover new and old mathematical theorems by folding paper and find out how to reason toward proofs. With the help of 200 color 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 Web site, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.Read more
- 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
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) that is composed of straight lines may be cut out from a sheet of paper with just a single cut."
Martin Smith, London Mathematical Society NewsletterSee more reviews
"Readers learn firsthand how the right way of looking at the right question potentially launches new fields of mathematics."
D.V. Feldman, Choice Magazine
"... 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
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- Date Published: December 2011
- format: Adobe eBook Reader
- isbn: 9781139119382
- contains: 171 b/w illus. 1 table 48 exercises
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
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
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