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Crocheting Adventures with Hyperbolic Planes

Daina Taimina
CRC Press
Publication Date: 
Number of Pages: 
[Reviewed by
Rachelle Bouchat
, on
This is the second edition of the book Crocheting Adventures with Hyperbolic Planes, which won the 2012 Euler Book Prize.  (See the prize committee’s remarks.)  The Euler Book Prize is awarded each year to an outstanding book in mathematics that is likely to improve the public view of the field of mathematics, and this book doesn’t disappoint.  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.  It presents a very tactile approach to the theoretical ideas of non-Euclidean geometries.  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 ( is an Associate Professor of Mathematics at Indiana University of Pennsylvania.  Her area of specialization is combinatorial commutative algebra.  In her spare time, she is an avid knitter and crocheter.