Shape of Space

Part I Surfaces and Three-Manifolds

Flatland

Gluing

Vocabulary

Orientability

Classification of Surfaces

Products

Flat Manifolds

Orientability vs. Two-Sidedness

Part II Geometries on Surfaces

The Sphere

The Hyperbolic Plane

Geometries on Surfaces

Gauss-Bonnet Formula and Euler Number

Part III Geometries on Three-Manifolds

Four-Dimensional Space

The Hypersphere

Hyperbolic Space

Geometries on Three-Manifolds I

Bundles

Geometries on Three-Manifolds II

Part IV The Universe

The Universe

The History of Space

Appendix A: Answers

Appendix B: Bibliography

Appendix C: Conway's ZIP Proof

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• Fundamentos da Matemática
• Topologia
• Geometria

Colored Lunes;Geometry;Cosmic Microwave Background Radiation;Dimensions;COBE Satellite;Geometry of surfaces;Solvable Lie Groups;Topology;Klein Bottle;handle approach;Hyperbolic Geometry;cosomology;Earth's Spherical Surface;crosscap approach;Playing Tic Tac Toe;two-dimensional space;Doughnut Surface;three-dimensional space;Cosmic Microwave Background;Hyperbolic Plane;Flat Tori;Spherical Triangle;Ordinary Euclidean Space;Global Topology;Homogeneous Geometry;Geometry Geometry;Hyperbolic Space;Vice Versa;Cone Point;Flat Geometry;Spherical Geometry;Euclidean Plane;Euler Number;Clockwise Turn