Winner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.
Table of Contents
Foreword by William Thurston
1. What Is the Hyperbolic Plane? Can We Crochet It?
2. What Can You Learn from Your Model?
3. Four Strands in the History of Geometry
4. Tidbits from the History of Crochet
5. What is Non-Euclidean Geometry?
7. Metamorphoses of the Hyperbolic Plane
8. Other Surfaces with Negative Curvature
9. Looking for Applications of Hyperbolic Geometry
10. Hyperbolic Crochet goes Viral
Appendix. How to Make Models
Daina Taimina was born in Riga, Latvia in 1954--the same year as an International Congress of Mathematicians pivotal to non-Euclidean geometry (as she describes in the Introduction), so her influence on the hyperbolic plane almost seems fated. Now a professor of mathematics at Cornell University, Taimina regularly participates in art exhibitions and educational workshops related to her crocheted models. She was nominated as one of the "Most Innovative People and Organizations in the Science and Technology World in 2006."
"This beautifully and profusely illustrated second edition of "Crocheting Adventures with Hyperbolic Planes" is a unique and extraordinary instructional manual and guide that is unreservedly recommended for personal, professional, community, and academic library"
—James A. Cox, Editor-in-Chief, Midwest Book Review
"This book shows just how fun deep mathematics can be and reveals the importance of thinking of mathematics with your hands, eyes and body — not just the brain. More importantly, it shows how good mathematics needs input from all sorts of people and cultures, in particular here the geometry essential to fibre arts."
—Professor Edmund Harris, University of Arkansas, co-author of Patterns/Visions of the Universe with Alex Bellos
"This is a lovely introduction to hyperbolic geometry and how to represent it in a tactile, playful way. The book takes you through a wonderful history of both the maths and the art, exploring how we have perceived the world around us over the centuries and how this applies today. You get to explore the concepts with your own hands and really see how it all works. As both a mathematician and a crocheter I’m itching to make my own hyperbolic planes and use them in all sorts of places!"
—Samantha Durbin, The Royal Institution of Great Britain
This is the second edition of the book Crocheting Adventures with Hyperbolic Planes, which won the 2012 Euler Book Prize[. . . . ]This book presents an amazing hybrid approach to two seemingly different audiences: mathematicians and fiber artists.
For the mathematician, the book presents a tactile approach to the very theoretical concepts in hyperbolic geometry, providing clear directions on how to construct objects in hyperbolic geometry. This book is a great introduction to hyperbolic geometry for anyone wanting to know about the subject and would be a great asset to any undergraduate math student studying non-Euclidean geometries.
For the fiber artist interested in crochet, the book does a great job of explaining very advanced mathematics in an inviting and understanding way, encouraging artists to pursue more mathematics to incorporate into their creative works. It also provides insight into the creative process of developing mathematics, showing that mathematicians and artists both use very creative processes.
This book is extremely well-written and organized. [. . . .] The book also weaves together the history and development of non-Euclidean geometries and their connections to many different areas such as art, biology and nature, physics, computer science, music, chemistry, and architecture. Each chapter has a clear purpose, and the imagery really complements the writing.
At the end of the book, there is a section on how to make models. For the artist interested in crochet, the directions are a little bit more mathematical, but they are presented clearly. It will definitely be quite different than any pattern you have read before! For the mathematician who would like to have some tactile hyperbolic models, there are directions for making models out of paper as well.
This book is more than just a great introduction to hyperbolic geometry, it is a great book to showcase the work of mathematicians and the process of discovering mathematics. As mathematicians, we often only present our finished and most-polished versions of our work, and we don’t let many people see the process by which this polished mathematics was developed.This book gives the reader insight into that process and illuminates the creativity involved in the development of mathematics.
—Rachelle Bouchat, MAA Reviews October 2019
Praise for previous edition
"2012 Euler Book Prize Winner ...elegant, novel approach... that is perfectly capable of standing on its mathematical feet as a clear, rigorous, and beautifully illustrated introduction to hyperbolic geometry. It is truly a book where art, craft, science, and mathematics come together in perfect harmony."
—MAA, December 2011
"This book is richly illustrated with photographs and colored illustrations and it has been produced on high-quality paper. It would be a useful addition to the library of a school or university."
—Gazette-Australia, May 2011
"Daina's crochet models break through the austere, formal stereotype of mathematics and present a path to a whole-brain understanding of a beautiful cluster of simple and significant ideas. The book helps to change the way of thinking about mathematics - an art of human understanding!"
—Corina Mohorianu, Zentralblatt MATH, September 2009
"The models illustrated in this book are prime examples of art influencing mathematics. Daina provides the necessary instructions for even novices to crochet and create hyperbolic models of their own."
—Swami Swaminathan, Canadian Mathematical Society Notes, October 2009
"It lays out the fundamental knowledge for appreciation of tactile hyperbolic manifolds cautiously and accessibly. ... an enjoyable read for a general audience."
—David Jacob Wildstrom, Mathematical Reviews, December 2009