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When you see a paper crane, what do you think of? A symbol of hope, a delicate craft, The Karate Kid? What you might not see, but is ever present, is the fascinating mathematics underlying it. Origami is increasingly applied to engineering problems, including origami-based stents, deployment of solar arrays in space, architecture, and even furniture design. The topic is actively developing, with recent discoveries at the frontier (e.g., in rigid origami and in curved-crease origami) and an infusion of techniques and algorithms from theoretical computer science. The mathematics is often advanced, but this book instead relies on geometric intuition, making it accessible to readers with only a high school geometry and trigonometry background. Through careful exposition, more than 150 color figures, and 49 exercises all completely solved in an Appendix, the beautiful mathematics leading to stunning origami designs can be appreciated by students, teachers, engineers, and artists alike.
List of contents
Preface; 1. Introduction; 2. Stamp folding; 3. Flat vertex folds; 4. Flat folding is hard; 5. Rigid origami and degree-4 vertices; 6. Origami design; 7. Fold & 1-cut; 8. Curved crease origami; 9. Self-folding origami; 10. Origamizer; 11. Beyond: topics not covered; 12. Solutions to exercises; References; Index.
About the author
Joseph O'Rourke is Olin Professor Emeritus of Computer Science at Smith College where he has a joint appointment in Mathematics. He has written or coauthored eight books, including two textbooks and two books written for high school students: 'How to Fold It' (2011) and 'Pop-Up Geometry' (2022). His research is in computational geometry, developing algorithms for geometric computations, and he has published 175 papers in journals and conference proceedings in this area. He has won several awards, including a Guggenheim Fellowship in 1987 and the NSF Director's Award for Distinguished Teaching Scholars in 2001. He was named an ACM Fellow in 2012.
