Crocheting Adventures with Hyperbolic Planes

by Daina Taimina

With more than 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.

From the Foreword by William Thurston:

"These models have a fascination far beyond their visual appearance. As illustrated in the book, there is actually negative curvature and hyperbolic geometry all around us, but people generally see it without seeing it. You will develop an entirely new understanding by actually following the simple instructions and crocheting! The models are deceptively interesting. Perhaps you will come up with your own variations and ideas. In any case, I hope this book gives you pause for thought and changes your way of thinking about mathematics."

Genres: Crochet, Nonfiction, Mathematics, Crafts, Science, Geometry, Adult

148 pages, Hardcover

First published February 23, 2009

Reviews

[notgettingenough · Rating 4 out of 5]

I personally am not able to review this book. If you want a full understanding of why, do go here:

http://www.youtube.com/watch?v=JZcUjY...

which explains the great knitting/crochet divide. It is quite funny.

It will simply never bother me that I can’t knit hyperbolas. I’m sorry if this offends any crocheters. On second thoughts, no I’m not.

Still, this book has interest for a few reasons. One is that it won this year’s Oddest Booktitle of the Year award ahead of:

Afterthoughts of a Worm Hunter by David Crompton.

Governing Lethal Behavior in Autonomous Robots, by Ronald C. Arkin.

The Changing World of Inflammatory Bowel Disease, by Ellen Scherl and Marla Dubinsky.

Third place: Collectible Spoons of the Third Reich, by James A. Yannes, receiving 11% of the vote.

Second place: What Kind of Bean is this Chihuahua? by Tara Jansen-Meyer, 30% of the vote.

First place: Crocheting Adventures with Hyperbolic Planes, by Dr. Daina Taimina, 42% of the vote.

Another is the unlikeliness of seeing a book of crochet patterns being brought out by a science and technology publisher and reviewed by science and maths journals.

You can see a few pictures from the book here: http://scitech.blogs.cnn.com/2010/04/...


Being a knitter, I can’t say anything positive about this book, but in the interests of fairness, I will quote the eminent mathematician William Thurston, who said of it:

“These models have a fascination far beyond their visual appearance. As illustrated in the book, there is actually negative curvature and hyperbolic geometry all around us, but people generally see it without seeing it. You will develop an entirely new understanding by actually following the simple instructions and crocheting! The models are deceptively interesting. Perhaps you will come up with your own variations and ideas. In any case, I hope this book gives you pause for thought and changes your way of thinking about mathematics.”

I’m sure it should, William, I’m sure it should, but.

[Jessica · Rating 3 out of 5]

I want to crochet a hyperbolic plane! So, I ordered this book in the hopes it would help in that quest, as well as give some background and an increased understanding of the relevant mathematics. Mission sort-of accomplished. Yes, there are instructions for crocheting your own example, and yes there's a fair amount of history, but still this book was not quite what I was expecting. The instructions are not written for the basic-knowlege crocheter and are not set out as clearly as I am used to seeing in "project" books. Turns out, this is not a project book...more a ramble of thoughts by the author, a mathematician who came into fiber arts fame through the back door, in a way. It shows. I think this book would have benefited greatly by having a co-author, someone who came out of the fiber art instruction world and could have helped to include more novice - friendly patterning and discussion.

I'm still going to try to make my own hyperbolic plane example, though. I'll let you know how it turns out.

[Valerie · Rating 5 out of 5]

Sadly, no patterns...but I got to see one of her hyperbolic planes at the Exploratorium, and it was very cool. Finally, a craft I can get behind....

This book gave me so many ideas for class...hyperbolic plane hats for every student and a little known Lewis Carroll play, and some easy ways to introduce topology. I can't wait to do projects.

[Ellen · Rating 4 out of 5]

Another book of maths and crochet. This one is beautifully illustrated, but information about how to create the shapes is not provided.

[Morgan · Rating 4 out of 5]

This book is really something special. It's a neat introduction to non-euclidean geometry, a splash of history of both mathematics and crochet, and a welcome reminder that math and art are forever and always interconnected. With beautiful photos of the author's own hyperbolic crochet, as well as other mathematicians' and artists hyperbolic models.

I won't pretend I understood the bits of differential geometry, since I haven't taken any math courses in nearly 15 years, but what I did glean was really exciting. I wasn't able to crochet everything in the book, as some of the projects involved actual formulas (that felt advanced to me) to calculate where to place certain stitches. But the ones I did make (basic model of a hyperbolic plane, Gabriel's Horn/Torricelli's Trumpet, and Klein Quartic), I loved making and learning about.

And as an unexpected bonus, I was able to achieve a major life goal. When I was in high school, I was assigned to the computer lab for study hall, and with internet access and little supervision, I found some white paper explaining the fourth dimension to us three dimensional beings, and I decided that at some point in my life, I really wanted to make a 3 dimensional representation of a 4 dimensional object. This book includes such a pattern, made from hyperbolic granny squares, and I have now crocheted an approximation of a four dimensional surface!

[Wing · Rating 3 out of 5]

I find this beautifully illustrated book both frustrating and lacking. The easier aspects of the mathematics are explained well, but the more difficult parts are not. They are discussed in a very rushed way, with—at least in my view—some unwarranted assumptions that the reader can follow without the details being spelled out. There are whole sections on history and interdisciplinary topics. While interesting, they are treated in an overly simplistic and superficial manner. I don’t feel I’ve learned much from the book. Prerequisite knowledge of geometry and topology is helpful, if not essential. As alluded to, the book contains many beautiful photographs—some of which are truly mesmerising. Three stars.

[Christine · Rating 4 out of 5]

My husband bought this book for me at the MOMath in NYC, I've dipped into it all year at my bedside table.

There are plenty of photos, but since they are strange and rare, they are not always sharp and clear. The crochet sections themselves would have benefited from a glance from Lindsay Stevens or the Stitchstud, both wonderful technical editors for crochet patterns; it's so much easier to read about crochet when it's written conventionally, even if British and American publishing do use different conventions.

However, the fun and wonder of this book is the way it smashes different disciplines together and shows how they benefit each other - perhaps have always benefited each other. Any math book that makes me reach for a crochet hook and some sketching yarn is a fun book in my opinion.

[Valerie Sherman · Rating 3 out of 5]

I would have rated it higher if she gave specific pattern instructions to make some of the crazy awesome corals and hyperbolic planes in the book!

[Felix · Rating 5 out of 5]

I cannot recommend this book highly enough. The sheer amount of excitement and happiness it's brought me is immeasurable. I absolutely adore topology, and I'd already dabbled in some hyperbolic crochet before putting this book on my christmas list, but I found all of the various chapters (ranging from the history of geometric art, to the basics of topology) really interesting. This book also introduced me the the concept of Seifert Surfaces, and I was able to figure out how to make one for Borromean rings (highly recommend).

Having said that, if you are not the target audience (ie- both a maths nerd, and a crochet nerd)- it probably won't be so fun. I loved the book because I already adored the topics it covered, and if I am completely honest I would have a wonderful time reading anything tangentially related. But as an introduction, for somebody only interested in one (or neither) out of crochet and topology, I don't think this would be as exciting.

[Sarah · Rating 2 out of 5]

I really wanted to like this book. I love the crocheted examples. However the writing is awful. The author seems to have no idea who her audience is - crocheters or mathematicians. So chapter 1 starts with a nice clear description of curvature. Chapter 8 on the other hand has sentences like - Scherk’s minimal surfaces are complete embedded minimal surfaces but they have infinite topological type. There is some explanation of most terms but too fast and too briefly. I studied Maths at Uni and I was lost early on. There is also a lot that seems unnecessary about the history of the subject for example. Space that could have been used for longer explanations of the actual subject. If you wish to crochet a plane the instructions are minimal. I understand this is because people’s tension and materials differ but longer, clearer instructions could have been given.

[MD · Rating 4 out of 5]

I could have done with less history and more information about crocheting hyperbolic planes. Why are they always single crochet? Why not slip stitch or double crochet? If you make continuous increases using a different stitch, what would that be? How would it be different? I would have liked a more beginner-friendly level of detail in the math too.

I didn't really understand why a lot of the information about patterns in other art forms was included since it didn't seem related to hyperbolic planes. I would have welcomed more information about the mathematics behind them. I liked the inclusion of mathematical formulas. There is a lot of mathematics in crochet! I wish someone would write a more general book about the mathematics of crochet.

[Colin Chick · Rating 4 out of 5]

A great dip-into source for the non-euclidiens amongst us, who insist in working with wool. If you can get your hands on the hardback, its binding is far more robust.

[Tathagata Sengupta · Rating 3 out of 5]

A bit over my head.

[Calcédoine · Rating 5 out of 5]

Very good and accessible introduction to college-level geometry, with some nice practical work.

[Emily · Rating 5 out of 5]

🤠😵‍💫🧶⚽️🪸

[Kathleen · Rating 4 out of 5]

Math for crafters, and crafts for math lovers!

[Jasmine · Rating 4 out of 5]

It was smaller than I was expecting- think a large hardcover picture book. Except for math geeks. And probably not for very little kids. Maybe a sixth grader (or precocious fourth grader), rereading over the years and getting more and more understanding from it.
Still, it's a fun book. Title may be a little misleading, as it's more mathy than crochet-y, but I'm enough of a math geek that it was just as satisfying.

[Stacy · Rating 4 out of 5]

This book is really cool, but I would not recommend it unless you have some sort of an interest in math. She delves a lot into mathematical history; there's actually a lot more of that than there is crochet. But it's still an interesting read. Lots of fun theories to think about and she does a pretty good job helping you to visualize them.

[Pat · Rating 4 out of 5]

It has been a few decades since my college math classes, but Daina Taimina managed to keep my interest. I may have to read parts of the book a few times to understand the concepts, but I'm already crocheting a hyperbolic plane to help me visualize. The profuse illustrations in the book will assist also.

[Anne · Rating 3 out of 5]

Non-Euclidean geometry explained with crochet. Math, not craft. As nearly as I can tell, it would be a good way to learn the math involved. Unfortunately, it's not a great crochet bookm though some of the projects are inspiring,

[Christina · Rating 3 out of 5]

Very interesting, but I didn't quite have the math skills to follow all of it.