The Shape of Space brings topology to the general reader by showing how to visualize manifolds directly...complements existing textbooks, which often deal only in abstractions, by offering a wealth of concrete examples...includes the first elementary exposition of William P. Thurston's revolutionary discoveries...applies topology to cosmology...gives the first simple pictorial exposition of the Gauss-Bonnet formula...builds intuition with more than 140 hands-on exercises, all with complete solutions...and offers over 170 illustrations. An annotated bibliography lists useful references for further study on specific topics.
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.
Ambitious, controversial and absorbing, God and the Universe tackles the highly-charged issue of God's relevance in the light of new scientific thinking on cosmology. Engaging with poststructuralism, ethics, mathematics, and philosophy through the ages, this persuasively argued book reinvigorates religious debate for the new millennium.
Author: Albert Marden
Publisher: Cambridge University Press
Release Date: 2016-02-01
Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.
In the present time, objects generated by computers are replacing models made from wood, wire, and plaster. It is interesting to see how computer graphics can help us to understand the geometry of surfaces and illustrate some recent results on representations of the real projective plane.