The Shape Of Space How To Visualize Surfaces And Three Dimensional Manifolds

The Shape of Space

The Shape of Space

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 Shape of Space

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.