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.

Finalist, 2022 PROSE Award for Mathematics

'This is a magnificent, comprehensive work. It gives a thorough overview of the underlying mathematics of flat-facet (polyhedral) origami, bringing together diverse contributions from many investigators (including the author’s own seminal work), along with historical notes and context that ties everything together. This will be the standard reference for the mathematics of origami for years to come, and with the plethora of open problems, will also undoubtedly be the inspiration for many master’s and Ph.D. theses in the future!'

Robert J. Lang - author of Origami Design Secrets and Twists, Tilings, and Tessellations

'Tom Hull has always been the authority and historian on origami mathematics. In this beautiful book, he ties together a wide range of classic and modern results, grounding them in their rich history.'

Erik Demaine - Massachusetts Institute of Technology

'Fans of classical geometry, geometry or topology of a combinatorial flavor, and even algebra and analysis will find much to appreciate in this book. Students and instructors alike will discover open problems, elegant theorems, and historical digressions, along with fascinating applications of concepts from standard courses. Origametry could easily function as a sourcebook for further explorations, capstone projects, or original research.'

D. P. Tumer Source: Notices of the American Mathematical Society

‘… a delightful and informative read for mathematicians curious about the mathematics behind origami, essential for researchers starting out in this area, and handy for educators searching for ideas in topics connecting mathematics, origami and its applications.’

Ana Rita Pires Source: European Mathematical Society Magazine

'This is not your typical origami book: it is a mathematics text, along with open problems, history, exercises and diversions. It is a good read for both the novice and the expert, and is sure to have something for anyone with even a small interest in the mathematics of origami.'

Alan S. McRae Source: MathSciNet