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, transformations of the plane, congruent triangles, the axiom of parallels, quadrilaterals and parallelograms, similar triangles, area, Ceva’s Theorem, circles, Ptolemy’s Theorem.. Parametrization and length of a curve.
Non-Euclidean Geometry:
Examples of geometries in which the axiom of parallels is false, geodesic paths, the punctured plane.
Spherical Geometry:
Geodesics and distance on the sphere, converting from spherical to rectangular coordinates, spherical distance, spherical trigonometry, spherical version of Pythagoras’ Theorem, angles and area in spherical geometry
Lectures supported by tutorials
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |