Crocheting Adventures with Hyperbolic Planes

Winner of the Euler Book Prize -- Awarded by the Mathematical Association of America 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."

ISBN 1568814526   Pages 160 ISBN13 9781568814520 (What's this?)   Volumes 000 Publisher Taylor & Francis Inc   Weight (grammes) 612 Imprint A K Peters   Published in Natick Format Hardback   Height (mm) 204 Publication date 31 Jan 2009   Width (mm) 254 Library of Congress QA685   Spine width (mm) 10 DEWEY 746.434   Academic level General DEWEY edition DC22

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 occ

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