MATH5785 is a Mathematics Level V course, but its main prerequisite is some mathematical maturity.
This course will cover exciting new developments in metric geometry arising from Wildberger's recent book
"Divine Proportions: Rational Trigonometry to Universal Geometry", and will include modern algebraic formulations of spherical and hyperbolic geometrics, as well as an introduction to chromogeometry.

We will be having a close look at the ancient Greek approach to Euclidean geometry and how it fits in with a more modern Cartesian framework, in such a way as to easily derive the main laws of rational trigonometry and extend them to a relativistic setting.

The projective version of these laws will be derived and form the basis for a simplified and unified approach to both spherical and hyperbolic geometries, emphasising the Klein model. We'll apply these theorietical results to
problems from surveying, physics and two and three dimensional geometry, including Platonic solids and the ZOME construction kit.

We'll also introduce the remarkable new theory of chromogeometry, which unifies Euclidean and relativistic geometries, and mention connections with special functions and number theory.

The approach is algebraic, combinatorial and computational. Students are expected to work on problem sets as well as on a topic of original investigation.

See the course overview below.

Units of credit: 6

Prerequisites: Core higher second year course or permission of the lecturer:A/Prof N J Wildberger (n.wildberger@unsw.edu.au)

Cycle of offering: Course not offered every year - see School for more details.

Graduate attributes: the course will enhance your research, inquiry and analytical thinking abilities.

More information: these recent course outlines (pdf) contain information about course objectives, assessment, course materials and the syllabus.

The course will cover the following topics: