Crocheting Adventures With Hyperbolic Planes - Couverture rigide

Taimina, Daina

Couverture rigide

ISBN 10 : 1568814526 ISBN 13 : 9781568814520

Editeur : A K Peters, 2009

Synopsis

Rare book

A propos du livre

Revue de presse :

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. It is refreshing different from coffee-table books about mathematics where the actual mathematics is all too often hidden under a layer of high-quality photographs. Using crocheted hyperbolic planes, Taimina explains hyperbolic geometry in a visual and explorative way. In fact, her crocheted pieces have been photographed in natural settings, reminding us that hyperbolic shapes are familiar shapes that appear all around us. I found that Taimina has done a wonderful job providing a history of hyperbolic geometry, explaining hyperbolic geometry to a broad audience, and presenting the crocheted hyperbolic planes for tactile explorations, while keeping the book s length down at the same time. The first chapter discusses the notions of positive and negative curvature and is representative for the rest of the book: several mathematical concepts are explained both visually and in words, without becoming too technical. Moreover, the reader is introduced to the crochet instructions for making his/her own hyperbolic planes. These crocheted models are used to explain the concepts of perpendicular and parallel straight lines, which is then used to visualize that the sum of the angles of a triangle in hyperbolic geometry actually depends on the lengths of its sides. The educational benefit from the tactile experience is very powerful and should be a standard part of geometry lectures! I thoroughly enjoyed this chapter. In fact, the essence of using crochet to explore otherwise hard to visualize objects is well maintained throughout the entire book. The real power of the book, however, lies in Taimina s skill to bring hyperbolic geometry in the realm of applied mathematics. She discusses how human experiences in areas as different as art/patterns, buildings/structures, navigation/stargazing and motion/machines influenced the development of geometry. People are still interested in and use hyperbolic geometry and the breadth of applications listed in this book is enlightening; not only do they come from all branches of science, there are also wonderful applications in music and art. For example, Daina Taimina s crocheted hyperbolic planes inspired industrial designer Radu Comsa to design the Rasta Stool (www.raducomsa.ro/furniture/full_rs.html), which is apparently very comfortable. 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 LMS Newsletter January 2010

Présentation de l'éditeur :

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."

À propos de cette édition

• Éditeur: A K Peters
• Date d'édition: 2009
• ISBN 10: 1568814526
• ISBN 13: 9781568814520
• Reliure: Relié
• Nombre de pages: 160