Felix Klein viewed Geometry as the study of properties invariant under a group of transformations on a space. From this viewpoint two-dimensional Euclidean geometry is the study of isometries of the plane. Changing the group of transformations leads to other interesting and more exotic geometries: projective, spherical, hyperbolic and Minkowskian (this last being the natural geometry of spacetime in Einstein's special relativity). The object of this project would be to explore the properties of (a selection of) these non-Euclidean geometries.
Prerequisites: Level 2 linear algebra (MATH 2200, MATH 2080, or equivalent), and MATH 1022 Introductory Group Theory.