From the Publisher 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. Editorial Reviews - Shape of Space From the Publisher 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. Features - Shape of Space Table of Contents Table of Contents Preface to the Second EditionPreface to the First EditionAcknowledgmentsPt. ISurfaces and Three-Manifolds11Flatland32Gluing133Vocabulary254Orientability455Connected Sums656Products837Flat Manifolds998Orientability vs. Two-Sidedness125Pt. IIGeometries on Surfaces1339The Sphere13510The Hyperbolic Plane14911Geometries on Surfaces15712The Gauss - Bonnet Formula and the Euler Number165Pt. IIIGeometries on Three-Manifolds18513Four-Dimensional Space18714The Hyper