Overview

This book offers a concrete and accessible treatment of Euclidean, projective and hyperbolic geometry, with more stress on topological aspects than is found in most textbooks. The author's purpose is to introduce students to geometry on the basis of elementary concepts in linear algebra, group theory, and metric spaces, and to deepen their understanding of these topics in the process. A large number of exercises and problems is included, some of which introduce new topics.

Full Product Details

Author:   Elmer G. Rees
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1st ed. 1983. 6th printing 2005. 2005
Dimensions:   Width: 17.00cm , Height: 0.60cm , Length: 24.20cm
Weight:   0.454kg
ISBN:  

9783540120537

ISBN 10:   354012053
Pages:   114
Publication Date:   01 November 1982
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I: Euclidean Geometry.- The Linear Groups.- The Relationship Between O(n) and GL(n,R).- Affine Subspaces and Affine Independence.- Isometries of Rn.- 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.- 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.- III: Hyperbolic Geometry.- The Parallel Axiom.- The Beltrami (or projective) Model.- Stereographic Projection.- The Poincaré Model.- The Local Metric.- Areas.- Trigonometry.- Hyperbolic Trigonometry.- Lines and Polarity.- Isometries.- Elliptic Trigonometry.- Problems.- Further Reading.- List of Symbols.

Reviews

From the Reviews: This book is meant to fill a certain gap in the literature. Namely, it treats the classical topics of Euclidean, projective and hyperbolic geometry using the modern language of linear algebra, group theory, metric spaces and elementary complex analysis. In each of those geometries the main constructions are fully explained and the reader can check his understanding with the sets of problems included. The mixture of classical and modern material which is so difficult to find in the textbooks nowadays makes of this nice little book an enjoyable and profitable reading. <br>A. Dimca, Revue Roumaine de MathA(c)matiques Pures et AppliquA(c)es (No. 5/1985)

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