The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

What Shape is Space? is a question with surprisingly far-reaching implications for our understanding of the very nature of reality and our place within it. The concepts involved may be sophisticated, but Giles Sparrows effortless prose style easily renders them understandable, allowing readers to get to grips with the overarching debates at the cutting edge of cosmology today. Infographics, diagrams and astronomical visualizations illustrate and clarify the various astonishing implications of a universe of infinite space.

This book will appeal to at least three groups of readers: prospective high school teachers, liberal arts students, and parents whose children are studying high school or college math. It is modern in its selection of topics, and in the learning models used by the authors. The book covers some exciting but non-traditional topics from the subject area of geometry. It is also intended for undergraduates and tries to engage their interest in mathematics. Many innovative pedagogical modes are used throughout.

An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

An international exploration of how our physical environments shape and define us

Do you know things without being able to explain how or why? Do you solve problems in unusual ways? Do you think in pictures rather than in words? If so, you are not alone. One-third of the population thinks in images. You may be one or you may live with one. If you teach, it is absolutely certain that some of your students.

There is a space within you where you are already perfect, whole, and complete. It is pure consciousness - the space inside of which all thoughts come and go. When you rest in the feeling of this space, the warmth of it heals your mind and body. When you operate from the infinite creative potential of this space, you produce high levels of performance and creative flow. When you sit in the openness of this space with others, you experience a level of connection and intimacy that is breathtakingly enjoyable and filled with love. And when you explore this space more deeply, you will find yourself growing closer and closer to the divine, even if you're not sure there is such a thing and wouldn't know how to talk about it if there was. Every problem we have in life is the result of losing our bearings and getting caught up in the content of our own thinking; the solution to every one of those problems is to find our way back home.This is both the invitation and the promise of this book. One problem. One solution. Infinite possibilities. Are you ready to begin?