AS/SC/MATH4150C.03W
Topics in Geometry: Geometries from a
transformation point of view
We shall begin this course with the discussion of fundamental transformations
of Euclidean plane geometry, that is, with motions or distance preserving
transformations. One can, in fact, define geometry as the study of those
properties of the figures that are not changed by motions. For example, the
diagonal of a square with area 2 is of length 2 regardless of the position of
the square in the plane. One may, however consider geometry as study of those
properties of the figures that are not changed by similarity transformations.
This approach (known as the Klein's Erlangen programme) is generalized, by
defining two figures to be equivalent relative to a certain group of
transformations if they can be mapped onto each other by a transformation from
that group. The geometry associated with the group of transformations is then
the study of those properties of figures which are preserved under the
transformations of the group.
Topics to be covered are:
Geometry of the Euclidean plane (including the classification of isometries and
similarities)
Affine geometry (including Ceva's and Menelaus's theorems)
Real projective plane (including a brief study of conics)
Geometry on the sphere
Hyperbolic plane geometry
There will be no text for this course, but Coxeter's Introduction to
Geometry will be used as one of the references.

Prerequisites: AS/SC/MATH2022.03 or AS/SC/MATH2220.03; a major
MATH course (6 credits) at the 3000 level; or permission of the
Course Coordinator.

Coordinator: A. Ivic Weiss