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.
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."
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