Despite the fact that non-Euclidean geometry has found its use in numerous applications (the most striking example being 3-dimensional topology), it has retained a kind of exotic and romantic element. This course intends to be a businesslike introduction to non-Euclidean geometry for nonexperts.
Curriculum:
- Prerequisites from linear algebra, point set topology, group theory, metric spaces.
- Axioms for plane geometry.
- The inversive models.
- The hyperboloid and the Klein model.
- The geometry of the sphere.
- Some computations in the hyperbolic plane and on the sphere.
- Hyperbolic isometries.
- Convex polygons.
- Isoperimetric inequality in non-Euclidean geometry.
- Hyperbolic surfaces.
Textbooks
- I. S. Iversen, Hyperbolic geometry, Cambridge Univ. Press 1993.
- H. S. Coxeter, Non-Euclidean Geometry, Toronto Univ. Press, 1957.
