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Crocheting Adventures with Hyperbolic Planes

4.1 out of 5 stars 22 customer reviews
ISBN-13: 978-1568814520
ISBN-10: 1568814526
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  • Crocheting Adventures with Hyperbolic Planes
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Editorial Reviews

Review

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

2012 Euler Book Prize Winner
By bringing crochet technology to the subject, she makes it easy and fun to construct hyperbolic surfaces that vividly illustrate essential features of non-Euclidean geometry. The book is elegant, from both a visual and mathematical point of view. … a novel approach to geometry that has brought a whole new audience to mathematics. In this respect it has greater outreach potential than any book we have previously considered. But it is much more than that; it 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

Non-Euclidean or hyperbolic geometry is a topic of great mystery (for a lot of people) and very important in mathematics. Now, 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. These crochet models have a fascination far beyond their visual appearance (a lot of beautiful pictures are in this book!) ... Following the simple instructions and crocheting the reader will develop a new understanding of the hyperbolic geometry which is all around us. 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

Daina Taimina's hyperbolic-manifold crochet is a durable and easy-to-contruct model useful for demonstrating the features of hyperbolic geometry. ... The book... [has] a greater grounding in historical and scientific context, and in a style more accessible to a lay audience. It lays out the fundamental knowledge for appreciation of tactile hyperbolic manifolds cautiously and accessibly. ... One of the benefits of the crocheted hyperbolic manifold as a manipulable is its ease of creation. Even for readers who have no familiarity with crochet, the instructions for producing a simple manifold are lucid, concise, and easily followed. ... it remains an enjoyable read for a general audience.
David Jacob Wildstrom, Mathematical Reviews, December 2009

Taimina's book is not only a coffee-table book of the highest quality, but it is also, first and foremost, a book about mathematics. ... I highly recommend this book because of its unique combination of a historical account of hyperbolic geometry with the use of crochet as a tool for its understanding. Finally, we have a beautiful coffee-table book that uses visual delight to emphasise rather than hide serious mathematics. Readers with little knowledge of geometry or mathematics in general may find it hard to understand everything, but as Bill Thurston writes in his foreword: I hope this book gives you pause for thought and changes your way of thinking about mathematics. 
Hinke Osinga, The London Mathematical Society, December 2009

This book takes the simple but highly imaginative step of trying to show Einstein's fourth dimension by writing it into a knitting pattern. The results are extraordinarily beautiful, closely resembling coral reefs. It's a great coffee table book and conversation starter ...  
Geoff Robbins, Cool Science Books Blog, February 2010

Daina Taimina's crocheted pieces are works of art that have been photographed in settings that emphasize their artistic beauty and remind us that hyperbolic shapes are familiar and occur naturally around us. ... I highly recommend this book....
―Journal of Mathematics and the Arts, March 2010

I must say that the title of Daina Taimina's book is a bit misleading, since it's far from being only about hyperbolic planes and crocheting. It does indeed contain simple and beautifully illustrated explanations of those two subjects, along with scholarly histories of both of them. However, it does the same for many other parts of art and science and mathematics, and all this in a beautifully simple and simply beautiful book. 
John Conway, Princeton University, February 2009

Crocheting Adventures with Hyperbolic Planes is a work of gargantuan proportions whose influence will be measured for decades to come. Delightfully brilliant yet down to earth, Daina Taimina brings together the best aspects of "right brain" imagination and risk-taking with "left brain" facts, practicality, and pattern perception, creating a win-win that everyone will enjoy. Lavish with photos throughout the book, the art is creatively placed in nature and the math schematics are crisp and clear. Daina's compendium of crochet history is the best I have seen, and this book is a must for the bookshelves of crochet and math students alike. 
Gwen Blakley Kinsler, Crochet Guild of America, February 2009

Taimina's beautiful crochet works hooked me into unraveling her all of a piece book in one sitting. I realized that when my father's mother introduced me to crochet (I was five or so) she really taught me intrinsic algorithms for generating spherical, plane, and hyperbolic geometries. Daina Taimina has wrapt my earliest memories in glorious colors, intricate histories, and marvelous theorems. 
Helaman Ferguson, February 2009

The women of Latvia are making a coral reef, with help from Daina Taimina, inventor of hyperbolic crochet. The Latvian Reef Project was initiated by Tija Viksna, a fiber artist and owner of Gallery Consentio, a small craft store and gallery in the Latvian capital, Riga. On January 12, 2009, the Latvian Reef got under way seriously with a Hyperbolic Crochet Day held at the Musturs (Latvian for "pattern") Knitting Club. With help from Dr Taimina, Tija had prepared a short introduction to the Reef Project and a helpful handout flier for participants. It was the first in a series of workshops that will be held throughout the year, leading up to the debut of the Latvian Reef in Gallery Consentio in August. . . . Daina Taimina specially made a hyperbolic crochet homage to the Baltic Sea, entitled "Land and Sea," as a contribution to the Latvian Reef, to which Dr Taimina is acting as an advisor, supporter, and inspirer. 
―The Latvian Reef, May 2009

It all amounts to an eye- and brain-opening journey connecting the history of ideas to their natural sources and practical applications. Lots to ponder. It takes a mind like Daina's to bring material like this together, and to convey it in scupltures that sit tranquilly in the natural landscape. 
Dora Ohrenstein, Crochet Insider, June 2009

Winner of the 2009 Diagram Prize, having received the majority of the public vote for the oddest titled book of the year at thebookseller.com
The Bookseller.com, March 2010

This artfully created book belongs on a mathematics classroom coffee table. ... Those interested in crocheting or hyperbolic geometry will certainly find something interesting here. If you know someone who likes both, you have just found the perfect gift!
Keith R. Leatham, Brigham Young University

From the Author

Writing this book I kept in mind that "a picture is worth 1000 words" - therefore 300 pictures in the book with expanded captures. So it is possible to read this book as a picture book. This is what children like to do. Then next level in this book is the text - if some of the pictures have caught the interest of a reader, then it is possible to get more explanation by reading the text close to the picture. For those who really want to know more and deeper - look in endnotes where I put a lot of references for further reading.
The idea to write this book grew out of many questions I was asked after my talks. Hope I have answered many of these questions. And I keep waiting for new ones!
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Product Details

  • Hardcover: 148 pages
  • Publisher: A K Peters/CRC Press (February 23, 2009)
  • Language: English
  • ISBN-10: 1568814526
  • ISBN-13: 978-1568814520
  • Product Dimensions: 10 x 0.4 x 8 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (22 customer reviews)
  • Amazon Best Sellers Rank: #361,791 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover
This is a marvelous book linking forms from the natural world to the human mind, to symbol-making, to art and to abstract mathematical concepts. It's an entertaining and enlightening read. It starts with an overview of geometry, then proceeds to the more specialized subject of hyperbolic geometry -- a mathematical concept mathematicians did not believe could exist in concrete form. Taimina's stunning crochet models prove them wrong. She has a wonderful chapter on geometric patterns in ancient and folk arts, showing examples from the Maori, Incas, and Pacific Islanders. She discusses how geometric symbols were used in human societies to convey cosmological knowledge, and how these symbols circulated via art. She continues with a grand tour through the development of geometrical concepts from building and construction, navigation and stargazing, and motion and machines. There are beautiful photos of many ancient objects - over 300 photos in the book altogether. It all amounts to an eye-opening journey connecting the history of ideas to their natural sources and their practical applications in life. It's no wonder her beautiful scupltures sit so tranquilly in the natural landscape.
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Format: Hardcover
Of course there's no patterns.

You do not have to be a math genius to use and appreciate this book (I certainly am not). However, you do need to realize this is a book as much about math as crochet, so an understanding of geometry and experience with shaping crochet without a pattern are a requirement - not advanced skills, but a bit beyond basic math and technical crochet skills.

The reason there are no patterns is because patterns do the math for you, and this book's main point IS the math so patterns defeat the purpose.
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Format: Hardcover Verified Purchase
Gives vision to the ART of Crochet. Why the rythmic crocheted spaces take shape to remind you of nature. No, no patterns, not one more double crochet - you are invited to use your creativity. Add this crochet insight into your current skill set and develop the 3 dimensional view in your work. On the other hand, a site you may wish to visit before purchasing to better understand the use of the book to you, if at all, is [...] If you live in Arizona and are open to your natural creative bent visit the exhibit in Scottsdale [...] etc in UK and NYC. The book points the reader to the physical representation crochet allows with the 3 dimensional representations.
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Format: Hardcover Verified Purchase
I first heard about this book while I was crocheting pieces for the Hyperbolic Crochet Coral Reef currently on display in the Smithsonian's Museum of Natural History. I have been learning to become a docent for this particular exhibit and learned, through the training, that this book would probably be discussed.

I recently received it and have been reading through it. I'm a crocheter, not a mathematician, (SMILE), so some of the geometry concepts are a challenge to understand but this book makes it fun to learn!
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Format: Hardcover Verified Purchase
I like crochet and mathematics. The book looked promising, but (of course, there is always a 'but'):
The math was sometimes explained as if the readers were 8 year old kids who never heard of Pythagoras, and suddenly it goes off with not much explanation about more complicated issues. #That's why I call it 'uneven'#
There wasn't enough crochet, or al least it's too short on crocheting ideas.

Still, it was an interesting addition to some not too often discussed areas.
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Format: Hardcover Verified Purchase
I really enjoyed this book. I am an astrophysicist and a crocheter. There aren't actually any crochet patterns, but this book tells you how to crochet a representation of a hyperbolic plane, and then shows you how to use it to visualize the properties of hyperbolic planes. I now have more intuition about negatively curved space. Great fun, and beautiful pictures. So far I've only made a demo, but I hope to make some flowers for my desk.
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Format: Hardcover
You don't have to know how to crochet or understand geometry to appreciate the beauty of the mathematical and natural worlds. Taimina, a professor of mathematics at Cornell University, uses simple crochet forms to explain difficult concepts such as negative curvature. She places geometry in the history of art, discussing patterns and symbols used in many native cultures. She then brings those patterns and symbols into the complex math that helps in construction, navigation, and machine building - as well as the organizational structures that make up much of nature. With vivid photographs and text written for easy understanding, you'll learn how a simple fiber technique can connect kelp, Venice, soccer balls, and modern art.
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Format: Hardcover Verified Purchase
Exciting, creative and scientific - what more could one want? Superlatives abound. I'm hooked and this is not a nerdy book, it's fascinating and exquisite. All stars.
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