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Introduction to Classical Geometries

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ISBN-10: 3764375175

ISBN-13: 9783764375171

Edition: 2007

Authors: Ana Irene Ramirez Galarza, Jos� Seade

List price: $59.99
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Description:

This book develops the geometry intuition of the reader by examining the symmetries (or rigid motions) of the space in question. This approach introduces in turn all the classical geometries: Euclidean, affine, alliptic, projective and hyperbolic.
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Book details

List price: $59.99
Copyright year: 2007
Publisher: Birkh�user Boston
Publication date: 3/20/2007
Binding: Paperback
Pages: 220
Size: 6.50" wide x 9.00" long x 0.50" tall
Weight: 0.990

Preface
List of Symbols
Euclidean geometry
Symmetries
Rigid transformations
Invariants under rigid transformations
Cylinders and tori
Finite subgroups of E(2) and E(3)
Frieze patterns and tessellations
Affine geometry
The line at infinity
Affine transformations and their invariants
Projective geometry
The real projective plane
The Duality Principle
The shape of P[superscript 2](R)
Coordinate charts for P[superscript 2](R) (and for P[superscript 1] (C))
The projective group
Invariance of the cross ratio
The space of conics
Projective properties of the conics
Poles and polars
Elliptic geometry
Hyperbolic geometry
Models of the hyperbolic plane
Transformations of the hyperbolic plane
Steiner network
The hyperbolic metric
First results in hyperbolic geometry
Surfaces with hyperbolic structure
Tessellations
Appendices
Differentiable functions
Equivalence relations
The symmetric group in four symbols: S[subscript 4]
Euclidean postulates
Topology
Some results on the circle
Bibliography
Index