Geometry with an introduction to cosmic topology /
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| Author / Creator: | Hitchman, Michael P. |
|---|---|
| Imprint: | Sudbury, Mass. : Jones and Bartlett Publishers, c2009. |
| Description: | xiii, 238 p. : ill. (some col.) ; 24 cm. |
| Language: | English |
| Series: | The Jones and Bartlett Publishers series in mathematics. Geometry Jones and Bartlett Publishers series in mathematics. Geometry. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7629649 |
Table of Contents:
- 1. An Invitation to Geometry
- 1.1. Introduction
- 1.2. A Brief History of Geometry
- 1.3. Geometry on Surfaces: A First Look
- 2. The Plane and Complex Numbers
- 2.1. Basic Notions
- 2.2. Polar Form of a Complex Number
- 2.3. Division of Complex Numbers
- 2.4. Complex Expressions
- 3. Transformations
- 3.1. Basic Transformations of C
- 3.2. Inversion
- 3.3. The Extended Plane
- 3.4. Mobius Transformations
- 3.5. Mobius Transformations: A Closer Look
- 4. Geometry
- 4.1. The Basics
- 4.2. Möbius Geometry
- 5. Hyperbolic Geometry
- 5.1. The Hyperbolic Transformation Group
- 5.2. Figures of Hyperbolic Geometry
- 5.3. Measurement in Hyperbolic Geometry
- 5.4. Area and Triangle Trigonometry
- 5.5. The Upper Half-Plane Model (optional)
- 6. Elliptic Geometry
- 6.1. Antipodal Points
- 6.2. Elliptic Geometry
- 6.3. Measurement in Elliptic Geometry
- 6.4. Revisiting Euclid's Postulates
- 7. Geometry on Surfaces
- 7.1. Curvature
- 7.2. Elliptic Geometry with Curvature k > 0
- 7.3. Hyperbolic Geometry with Curvature k
- 7.4. Observing Curvature in a Universe (optional)
- 7.5. Surfaces
- 7.6. Geometry of Surfaces
- 7.7. Quotient Spaces
- 8. Cosmic Topology
- 8.1. Three-Dimensional Geometry and 3-manifolds
- 8.2. Cosmic Crystallography
- 8.3. Circles in the Sky
- 8.4. Final Remarks
- Bibliography
- Index
