Description
Book SynopsisThis is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal - although some remain more equal than others.
Trade Review[A] very ambitious and pleasantly succinct text . . . Highly recommended." -
CHOICETable of Contents
- Preface
- About Euclidean geometry
- Toy geometries and main definitions
- Abstract groups and group presentations
- Finite subgroups of 𝑆𝑂(3) and the platonic bodies
- Discrete subgroups of the isometry group of the plane and tilings
- Reflection groups and Coxeter geometries
- Spherical geometry
- The Poincaré disk model of hyperbolic geometry
- The Poincaré half-plane model
- The Cayley-Klein model
- Hyperbolic trigonometry and absolute constants
- History of non-Euclidean geometry
- Projective geometry
- “Projective geometry is all geometry”
- Finite geometries
- The hierarchy of geometries
- Morphisms of geometries
- Excerpts from Euclid’s “Elements”
- Hilbert’s axioms for plane geometry
- Answers & hints
- Bibliography
- Index
