Beginner's introduction to various types of non-Euclidean geometry through
concrete models (no axioms). Emphasis is on the role of transformations, and on
how the technique of modern mathematics is utilized to get comprehensive
understanding of different classical geometric systems.
- Affine geometry: affine transformations of the plane, affine invariants, linear
algebra and affine geometry. Orthogonal matrices and Euclidean geometry.
Spherical geometry: spherical triangles and trigonometry, structure of
Inversive geometry: inversions, Möbius transformations, and their invariants,
Projective geometry: the projective plane, homogeneous coordinates, projective
transformations, cross ratio, conics, polarity.
Hyperbolic geometry: Projective, conformal, and quadratic form models of
hyperbolic plane. Transformations, distance, angle, area. Some formulas of