Crocheting Adventures with Hyperbolic Planes [Hardcover]

Daina Taimina (Author)

Book Description

Publication Date: March 26, 2009 | ISBN-10: 1568814526 | ISBN-13: 978-1568814520

This richly illustrated book discusses non-Euclidean geometry and the hyperbolic plane in an accessible way. The author provides instructions for how to crochet models of the hyperbolic plane, pseudosphere, and catenoid/helicoids. With this knowledge, the reader has a hands-on tool for learning the properties of the hyperbolic plane and negative curvature. The author also explores geometry and its historical connections with art, architecture, navigation, and motion, as well as the history of crochet, which provides a context for the significance of a physical model of a mathematical concept that has plagued mathematicians for centuries.

Editorial Reviews

Review

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 situation 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, Founder and proud Lifetime Member of the Crochet Guild of America

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. --London Mathematical Society Newsletter

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. --Crochet Insider

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: 200 pages
• Publisher: AK Peters (March 26, 2009)
• Language: English
• ISBN-10: 1568814526
• ISBN-13: 978-1568814520
• Product Dimensions: 10.1 x 8.1 x 0.6 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #200,240 in Books (See Top 100 in Books)
  • #72 in Books > Humor & Entertainment > Puzzles & Games > Math Games

More About the Author

here is a recent video interview
http://www.youtube.com/watch?v=uFl8GftHpTk

and here one from earlier:
http://www.sciencentral.com/articles/view.php3?type=article&article_id=218392811

also please visit my blog
http://hyperbolic-crochet.blogspot.com/

Customer Reviews

Most Helpful Customer Reviews

35 of 35 people found the following review helpful:

5.0 out of 5 stars Stimulating Ideas, Beautiful Crochet, May 5, 2009

By 

Dora Ohrenstein "crochet insider" (NYC, US) - See all my reviews
(REAL NAME)   

This review is from: Crocheting Adventures with Hyperbolic Planes (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.

26 of 26 people found the following review helpful:

5.0 out of 5 stars An existence proof that mathematics is indeed everywhere, June 2, 2009

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Crocheting Adventures with Hyperbolic Planes (Hardcover)

My mother has been crocheting since I was an infant and at one point, I was able to crochet simple things like potholders. It is a simple process as long as you are going straight across to make a rectangle, the hard part is when you have to turn corners and make rounded structures. I never mastered that aspect of crocheting, it requires a degree of three-dimensional foresight that was beyond my mechanical talents.

With this as my background, I was even more impressed by the talents of the author as she uses crocheted fabrics to represent the negative curvature of hyperbolic surfaces. The book opens with a search for hyperbolic surfaces down through history as well as in nature. Although the mathematics of the non-Euclidean hyperbolic surface is of relatively recent origin, such surfaces are found in nature. The photos on page 18 demonstrate their appearance in coral, holly leaves, flower blossoms and nudibranchs.

I must confess that I have seen crocheted items similar to the hyperbolic, catenoid and helicoid surfaces demonstrated in this book at craft shows and flea markets but never made the connection that they were in fact such surfaces. It was a real eye-opener to see them illustrated and Taimina explains the algorithmic ratios behind their creation.

Along with many others, I have been a proponent of the statement, "Mathematics is everywhere." While I firmly believe it, until I read this book I had no idea how all encompassing that statement really is. This is a fun book to read and even people that have never crocheted can appreciate the tactics and results. Some of them are truly works of art.

24 of 24 people found the following review helpful:

5.0 out of 5 stars Not a math genius, July 18, 2009

By 

Colleen K. Ziemer - See all my reviews
(REAL NAME)   

This review is from: Crocheting Adventures with Hyperbolic Planes (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.