Author | Rees, Elmer G. author |
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Title | Notes on Geometry [electronic resource] / by Elmer G. Rees |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1983 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61777-5 |
Descript | VIII, 114 p. online resource |
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 Poincarรฉ Model -- The Local Metric -- Areas -- Trigonometry -- Hyperbolic Trigonometry -- Lines and Polarity -- Isometries -- Elliptic Trigonometry -- Problems -- Further Reading -- List of Symbols