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.

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."

Transforming Learning Through Tangible Instruction offers a transformative, student-centered approach to higher education pedagogy that integrates embodied cognition into classroom practice. Evidence across disciplines makes clear that people learn with their bodies as well as their brains, but no previous book has provided evidence-based guidance for adopting and refining its practice in colleges and universities. Collecting findings from cognitive science, educational neuroscience, learning theories, and beyond, this volume’s unique approach—radical yet practical, effective yet low-cost—will have profound implications for higher education faculty and administrators engaged in teaching and learning. Seven concise chapters explore how physical objects, hands-on making, active construction, and other elements of body and environment can enhance comprehension, memory, and individual and collaborative learning.

The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize–winning physicist Roger Penrose This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

This new book for mathematics and mathematics education majors helps students gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The first is devoted to a rigorous introduction of Euclidean geometry, the second covers various noneuclidean geometries, and the last part delves into symmetry and polyhedra. Historical contexts accompany each topic. Exercises and activities are interwoven with the text to enable the students to explore geometry. Some of the activities take advantage of geometric software so students - in particular, future teachers - gain a better understanding of its capabilities. Others explore the construction of simple models or use manipulatives allowing students to experience the hands-on, creative side of mathematics. While this text contains a rigorous mathematical presentation, key design features and activities allow it to be used successfully in mathematics for teachers courses as well.

Shortlisted for the 2023 PEN/E.O. Wilson Literary Science Writing Award An engaging and imaginative tour through the fundamental mathematical concepts—from arithmetic to infinity—that form the building blocks of our universe. Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing—no matter, no cosmos, not even empty space—could we create a universe using only math? Irreverent, richly illustrated, and boundlessly creative, The Big Bang of Numbers invites us to try. In this new mathematical origin story, mathematician and novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. He reveals the secret lives of real and imaginary numbers, teaches them to play abstract games with real-world applications, discovers unexpected patterns that connect humble lifeforms to enormous galaxies, and explores mathematical underpinnings for randomness and beauty. With evocative examples ranging from multidimensional crochet to the Mona Lisa’s asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence. Mathematics, Suri shows, might best be understood not as something we invent to explain Nature, but as the source of all creation, whose directives Nature tries to obey as best she can. Offering both striking new perspectives for math aficionados and an accessible introduction for anyone daunted by calculation, The Big Bang of Numbers proves that we can all fall in love with math.

Purl and stitch: Empowering, healing, and reconnecting us to each other and ourselves In a fractured world plagued by anxiety and loneliness, knitting is coming to the rescue of people from all walks of life. Economist and lifelong knitter Loretta Napoleoni unveils the hidden power of the purl and stitch mantra: an essential tool for the survival of our species, a means for women to influence history, a soothing activity to calm us, and a powerful metaphor of life. This book is a voyage through our history following the yarn of social, economic and political changes - from ancient Egypt and Peru to modern Mongolia, from the spinning bees of the American Revolution to the knitting spies of World War II, and from the hippies' rejection of consumerism to yarnbombing protests against climate change. For the author it is also a personal journey of discovery and salvation, drawing on the wisdom her grandmother passed along as they knit together. Revealing recent discoveries in neuroscience, The Power of Knitting offers proof of the healing powers of knitting on our bodies and minds. Breaking through societal barriers, even nursing broken hearts, and helping to advance cutting-edge science, knitting is still a valuable instrument for navigating our daily lives. As a bonus, the book includes patterns for ten simple yet iconic projects that reflect the creative, empowering spirit of knitting, with complete instructions.

The Routledge Companion to Biology in Art and Architecture collects thirty essays from a transdisciplinary array of experts on biology in art and architecture. The book presents a diversity of hybrid art-and-science thinking, revealing how science and culture are interwoven. The book situates bioart and bioarchitecture within an expanded field of biology in art, architecture, and design. It proposes an emergent field of biocreativity and outlines its historical and theoretical foundations from the perspective of artists, architects, designers, scientists, historians, and theoreticians. Includes over 150 black and white images.

Hyperbolic geometry is an essential part of theoretical astrophysics and cosmology. Besides specialists of these domains, many specialists of new domains start to show a growing interest both to hyperbolic geometry and to cellular automata. This is especially the case in biology and computer science. This book gives the reader a deep and efficient introduction to an algorithmic approach to hyperbolic geometry. It focuses the attention on the possibilities to obtain in this frame the power of computing everything a computer can compute, that is to say: universality. The minimal ways to get universality are investigated in a large family of tilings of the hyperbolic plane. In several cases the best results are obtained.In all cases, the results are close to the theoretical best values. This gives rise to fantastic illustrations: the results are jewels in all meanings of the word. ------------------------ Maurice MARGENSTERN is professor emeritus at the University of Lorraine, he is a member of LITA, the research unit of computer science in the campus of Metz of this university. Professor Margenstern is amongst top world experts in theory of computation, mathematical machines and geometry. He is a pioneer in cellular automata in hyperbolic spaces.