UID:
almahu_9947363137802882
Format:
VIII, 114 p.
,
online resource.
ISBN:
9783642617775
Series Statement:
Universitext,
Content:
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.
Note:
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.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783540120537
Language:
English
DOI:
10.1007/978-3-642-61777-5
URL:
http://dx.doi.org/10.1007/978-3-642-61777-5
