Items related to Notes on Geometry
Synopsis
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.
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