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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.
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.
While piloting his spaceship through the skies, Captain Invincible encounters three-dimensional shapes, including cubes, cylinders, and pyramids.
Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.
The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
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.
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.
A complete introduction to the history, evolution, and future of the modern city, this book covers a wide range of theory, including the significance of space and place, to provide a balanced account of why cities are an essential part of the global human experience. Covers a wide range of theoretical approaches to the city, from the historical to the cutting edge Emphasizes the important themes of space and place Offers a balanced account of cities and offers extensive coverage including urban inequality, environment and sustainability, and methods for studying the city Takes a global approach, with examples from Berlin and Chicago to Shanghai and Mumbai Includes a range of pedagogical features such as a substantial glossary of key terms, critical thinking questions, suggestions for further reading and a range of innovative textboxes which follow the themes of Exploring Further, Studying the City and Making the City Better Extensively illustrated with maps, charts, tables, and over 80 photographs Accompanied by a comprehensive student companion site featuring a list of relevant journals, a guide to useful web resources, and an annotated documentary film guide, alongside a useful instructor companion site with further examples, case studies, and discussion and essay questions; instructors will find a link to the instructor website on the student website at www.wiley.com/go/cities