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Geometry with an Introduction to Cosmic Topology
Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits.
- Author
- Michael P. Hitchman
- Publisher
- Linfield College
- Source
- LibreTexts
- License
- CC BY-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 42 sections
- 01: An Invitation to Geometry
- 1.01: Introduction
- 1.02: A Brief History of Geometry
- 1.03: Geometry on Surfaces- A First Look
- 02: The Complex Plane
- 2.01: Basic Notions
- 2.02: Polar Form of a Complex Number
- 2.03: Division and Angle Measure
- 2.04: Complex Expressions
- 03: Transformations
- 3.01: Basic Transformations of Complex Numbers
- 3.02: Inversion
- 3.03: The Extended Plane
- 3.04: Mobius Transformations
- 3.05: Mobius Transformations: A Closer Look
- 04: Geometry
- 4.01: The Basics
- 4.02: Mobius Geometry
- 05: Hyperbolic Geometry
- 5.01: The Poincare Disk Model
- 5.02: Figures of Hyperbolic Geometry
- 5.03: Measurement in Hyperbolic Geometry
- 5.04: Area and Triangle Trigonometry
- 5.05: The Upper Half-Plane Model
- 06: Elliptic Geometry
- 6.01: Antipodal Points
- 6.02: Elliptic Geometry
- 6.03: Measurement in Elliptic Geometry
- 6.04: Revisiting Euclid's Postulates
- 07: Geometry on Surfaces
- 7.01: Curvature
- 7.02: Elliptic Geometry with Curvature k 0
- 7.03: Hyperbolic Geometry with Curvature k 0
- 7.04: The Family of Geometries ( X k G k )
- 7.05: Surfaces
- 7.06: Geometry of Surfaces
- 7.07: Quotient Spaces
- 08: Cosmic Topology
- 8.01: Section 1-
- 8.02: Section 2-
- 8.03: Section 3-
- 8.04: Section 4-