Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

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

This fascinating entry in the “Big Idea” series is a well-informed, comprehensive and accessibly written look at the very nature of the universe. What Shape Is Space? is a question with 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 Sparrow’s effortless prose style renders them understandable, allowing readers to come to grips with the overarching debates at the cutting edge of cosmology today. Illustrations, diagrams, and astronomical visualizations demonstrate and clarify the various astonishing implications of a universe of infinite space. This entry in the “Big Idea” series explores four key topics: “Mapping Space,” featuring the evidence that favors the expanding and infinite universe theory; “The Expanding Universe,” which examines the rate at which the cosmos is expanding; “The Omega Factor,” which explores the possibilities for different types of hypothetically infinite universes; and “The Shape of the Multiverse,” which analyzes the effect of each possible shape on the likely future of the universe. Well-informed and lucid, What Shape Is Space? is an in-depth and approachable exploration of the ideas and possibilities born from this seemingly simple question.

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.

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

This is a revised and updated edition of Graham Nerlich's classic book (1976). It develops a metaphysical account of space that treats it as a real and concrete entity, showing that shape plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument and investigates how different spaces would affect perception differently. Along the way Professor Nerlich criticizes and rejects conventionalism as a non-realist metaphysics of space, concluding that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, while offering an extensive discussion of the relativity of motion.