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

Autor Joseph O’Rourke
en Limba Engleză Hardback – 24 apr 2011
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.
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Specificații

ISBN-13: 9780521767354
ISBN-10: 0521767350
Pagini: 192
Ilustrații: 171 b/w illus. 1 table 48 exercises
Dimensiuni: 157 x 236 x 15 mm
Greutate: 0.48 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States

Cuprins

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.

Recenzii

'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

Notă biografică


Descriere

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