Origametry: Mathematical Methods in Paper Folding

by Thomas Hull

Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.

Genres: Mathematics, Origami

340 pages, Hardcover

Published December 17, 2020

About the author

I finished my Ph.D. in mathematics at the University of Rhode Island in 1997. My dissertation was on list coloring bipartite graphs, but now I mostly study the mathematics of origami (paper folding).

I'm currently an associate professor in the Department of Mathematics at Western New England College in Springfield, MA.

Reviews

[Cynthia Frazer · Rating 4 out of 5]

I couldn't follow all the math....but I am interested enough to barrel through, lol.

[Carrie · Rating 5 out of 5]

This is not my typical book. I was attracted by the cover and my recent revival of interest in Origami. I now have a stack of books on the subject to read. Hull says in the intro that this book took him ages to write. By the same token, it took me ages to read, though I did read every page. Except for maybe the 30 page list of references at the end. OK, I said I read every page. I think that the verb read indicates a greater percentage of absorption of content. Let us say I LOOKED at every word and the multitude of mathematical symbols. For the avoidance of doubt I leave this message to potential readers who may have been attracted by the beautiful purple modular origami on the cover: This is essentially a textbook. If you do not have a good foundation in higher math, there will be a huge whoosh factor. Still, it was interesting and more seeped in than I expected. It was peppered with diversions which amounted to proving the theorems discussed in the book. Some people might find them fascinating. To me a diversion is something that takes you away from something. While I read this book I went off on countless diversions looking up things discussed along the way (you must check out Britany Gallivan's record breaking paper folding experiment) and Newton's historical dispute with Leibniz over priority in the development of calculus or why belcastro spells her name in lower case. Naming conventions are interesting. Do we go with the Tortilla-Tortilla, Taco-Tortilla or Taco-Taco Condition?

I did fold the two versions of the square twist in illustration 6.12 and the next time I attempt a tessellation I will have a better understanding of what's going on. I am giving this five stars because it kept me engaged through to the bitter end. Next book I pick up on math will have no formulae. Thanks, Mr Hull.

[Pasquale · Rating 4 out of 5]

It starts with a first part dedicated to the geometry of origami and what kind of constructions are admissible. It then follows with a review of flat-folding and then of rigid folding. The level of math required to understand some of the chapters may be quite high, well beyond high-school or most undergraduate courses, but even when the details are hard to grasp, the general picture is clear.

It is a fantastic non-introductory introduction on origami math, full of interesting problems (diversions) and lots of references to dig deeper in the subject.