Crocheting Adventures with Hyperbolic Planes: Tactile Mathematics, Art and Craft for all to Explore, Second Edition, 2nd Edition (e-Book) book cover

Crocheting Adventures with Hyperbolic Planes

Tactile Mathematics, Art and Craft for all to Explore, Second Edition, 2nd Edition

By Daina Taimina

CRC Press

200 pages | 372 Color Illus.

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pub: 2018-03-29
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Description

Winner, Euler Book Prize, awarded by the Mathematical Association of America. With over 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. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.

Reviews

Praise for previous edition

"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

Table of Contents

Foreword by William Thurston

Introduction

1. What Is the Hyperbolic Plane? Can We Crochet It?

2. What Can You Learn from Your Model?

3. Four Strands in the History of Geometry

4. Tidbits from the History of Crochet

5. What is Non-Euclidean Geometry?

6. Pseudosphere

7. Metamorphoses of the Hyperbolic Plane

8. Other Surfaces with Negative Curvature

9. Looking for Applications of Hyperbolic Geometry

10. Hyperbolic Crochet goes Viral

Appendix. How to Make Models

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."

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT012000
MATHEMATICS / Geometry / General
MAT025000
MATHEMATICS / Recreations & Games