How to Fold It: The Mathematics of Linkages, Origami, and Polyhedra
Cambridge University Press
Edition: Reissue, 6/23/2011
EAN 9780521145473, ISBN10: 0521145473
Paperback, 190 pages, 22.9 x 15.2 x 1 cm
Language: English
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.