Introduction to Classical Geometries

Name: Introduction to Classical Geometries
Availability: InStock
ISBN: 9783764375171

ISBN-10: 3764375175

ISBN-13: 9783764375171

Edition: 2007

Authors: Ana Irene Ramirez Galarza, Josï¿½ Seade

List price: $54.99

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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.

Book details

List price: $54.99
Copyright year: 2007
Publisher: Springer Basel AG
Publication date: 3/20/2007
Binding: Paperback
Pages: 220
Size: 6.69" wide x 9.61" long x 0.19" tall
Weight: 1.826



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