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Zusammenfassung 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. Klappentext 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. Inhaltsverzeichnis SURFACES AND THREE-MANIFOLDSFlatlandGluingVocabularyOrientabilityConnected SumsProductsFlat ManifoldsOrientability vs. Two-SidednessGEOMETRIES ON SURFACESThe SphereThe Hyperbolic PlaneGeometries on SurfacesThe Gauss-Bonnet Formula and the Euler NumberGEOMETRIES ON THREE-MANIFOLDSFour-Dimensional SpaceThe HypersphereHyperbolic SpaceGeometries on Three-Manifolds IBundlesGeometries on Three-Manifolds IITHE UNIVERSE The UniverseThe History of SpaceCosmic CrystallographyCircles in the SkyAppendix A AnswersAppendix B BibliographyAppendix C Conway's ZIP ProofIndex ...
