Product Description

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.

Product Details

• Amazon Sales Rank: #177778 in Books
• Published on: 2009-03-26
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 200 pages

Features

• ISBN13: 9781568814520
• Condition: NEW
• Notes: Brand New from Publisher. No Remainder Mark.
• Click here to view our Condition Guide and Shipping Prices

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

About the Author
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.

Customer Reviews

Stimulating Ideas, Beautiful Crochet
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.

Fun Creative Crochet to enhance your vision
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 http://www.theiff.org/exhibits/iff-e13.html. If you live in Arizona and are open to your natural creative bent visit the exhibit in Scottsdale http://www.theiff.org/exhibits/iff-e22.html etc in UK and NYC. The book points the reader to the physical representation crochet allows with the 3 dimensional representations.

An existence proof that mathematics is indeed everywhere
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.