This module develops a deep understanding of Euclidean Geometry and introduces the student to non-Euclidean Geometry.
Geometry and the Euclidean Plane
The axiomatic approach to geometry, angle and area, triangles, circles and quadrilaterals. Trigonometry. Similarity and congruence. Ceva’s Theorem.
Geometry of the Complex plane
Lines and circles in the complex plane. Mobius transformations. Stereographic projection and the Riemann sphere.
Non-Euclidean Geometry
Geodesics and distance on the sphere, spherical distance, spherical trigonometry, sum of the angles of a spherical triangle. Spherical version of Pythagoras’ Theorem, area in spherical geometry.
Lectures supported by tutorials and/or laboratory sessions including use of mathematical software
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |