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Notes on Geometry

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Author(s): Elmer G. Rees
Publisher: Springer
Year: 1983

Language: English

Cover
Title page
Introduction
Part I: Euclidean Geometry
The Linear Groups
The Relationship Between O(n) and GL(n,R)
Affine Subspaces and Affine Independence
Isometries of R^n
Isometries of R²
Isometries of R³
Some Subsets of R³
Finite Groups of Isometries
The Platonic Solids
Duality
The Symmetry Groups of the Platonic Solids
Finite Groups of Rotations of R³
Crystals
Rotations and Quaternions
Problems
Part II: Projective Geometry
Homogeneous Co-ordinates
The Topology of P¹ and P²
Duality
Projective Groups
The Cross-Ratio
Fixed Points of Projectivities
The Elliptic Plane
Conics
Diagonalization of Quadratic Forms
Polarity
Problems
Part III: Hyperbolic Geometry
The Parallel Axiom
The Beltrami (or projective) Model
Stereographie Projection
The Poincaré Model
The Local Metric
Areas
Trigonometry
Hyperbolic Trigonometry
Lines and Polarity
Isometries
Elliptic Trigonometry
Problems
Further Reading
List of Symbols
Index