Geometric Folding Algorithms

Introduction; Part I. Linkages: 1. Problem classification and examples; 2. Upper and lower bounds; 3. Planar linkage mechanisms; 4. Rigid frameworks; 5. Reconfiguration of chains; 6. Locked chains; 7. Interlocked chains; 8. Joint-constrained motion; 9. Protein folding; Part II. Paper: 10. Introduction; 11. One-dimensional paper; 12. Two-dimensional paper and continuous foldability; 13. Single-vertex foldability; 14. Multi-vertex flat foldability; 15. 2D Map folding; 16. Silhouettes and gift wrapping; 17. Tree method; 18. One complete straight cut; 19. Flattening polyhedra; 20. Geometric constructibility; 21. Curved and curved-fold origami; Part III. Polyhedra: 22. Introduction and overview; 23. Edge unfolding of polyhedra; 24. Reconstruction of polyhedra; 25. Shortest paths and geodesics; 26. Folding polygons to polyhedra; 27. Higher dimensions.

Erik D. Demaine is the Esther and Harold E. Edgerton Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, where he joined the faculty in 2001. He is the recipient of several awards, including the MacArthur Fellowship, the Harold E. Edgerton Faculty Achievement Award, the Ruth and Joel Spira Award for Distinguished Teaching, and the NSERC Doctoral Prize. His research interests range throughout algorithms from data structures for improving web searches to the geometry of understanding how proteins relate to the computational difficulty of playing games. He has published more than 150 papers with more than 150 collaborators and coedited the book Tribute to a Mathemagician in honor of the influential recreational mathematician Martin Gardner. Joseph O'Rourke is the Olin Professor of Computer Science at Smith College and the Chair of the Computer Science Department. He recently completed a one-year appointment as Interim Director of Engineering. He has received several grants and awards, including a Presidential Young Investigator Award, a Guggenheim Fellowship, and the NSF Director's Award for Distinguished Teaching Scholars. His research is in the field of computational geometry, where he has published a monograph and a textbook, and he coedited the 1500-page Handbook of Discrete and Computational Geometry. Thirty-one of his more than one hundred papers published in journals and conference proceedings are coauthored with undergraduates.

'Demaine and O'Rourke are among the best-qualified authors for a book on this subject; and the book that they have written is a delight ... it is exceptionally clear and readable. It could be read for pleasure by any mathematics undergraduate, and much of it (though not all) by amateurs with a high school mathematics background ... although there are sections that some amateurs will skip, the level is always kept as elementary as locally possible. This book should be in all university libraries, and many professional and amateur mathematicians will want to add it to their personal collections.' Robert Dawson (Halifax), Zentralblatt Math 'This book is one of those rare mathematics books that I had a hard time putting down. I wanted to keep reading to find the next insight. ... This is a serious mathematics book whose explorations have significant applications and real mathematical profundity, wonderfully mixed with some fun recreational mathematics. ... The book has a useful index and an extensive bibliography, so when you finish reading, it will remain a valuable resource far into the future. There is a lot of material in this book and it is really a lot of fun. I highly, highly recommend this book to anyone with even a passing interest in folding mathematics.' MAA Reviews 'The authors explain step-by-step interesting solutions of some folding problems. This splendidly illustrated book can be interesting for advanced undergraduate students in mathematics and computer science as well as for geometers and computer specialists who can find many new ideas and impulses ...' EMS Newsletter