MA1004: Geometry
| School | Cardiff School of Mathematics |
| Department Code | MATHS |
| Module Code | MA1004 |
| External Subject Code | 100405 |
| Number of Credits | 10 |
| Level | L4 |
| Language of Delivery | English |
| Module Leader | Dr Timothy Logvinenko |
| Semester | Autumn Semester |
| Academic Year | 2022/3 |
Outline Description of Module
This module gives an introduction to elementary plane Euclidean geometry. We present this material in a way which emphasises axiomatic approach, logical thinking and rigorous proofs, as well as careful use of diagrams as an aid to understanding problems and finding solutions. In the latter half of the module we also introduce basic notions of spherical geometry, emphasising the differences between it and Euclidean geometry.
Free Standing Module Requirements: A pass in A-Level Mathematics of at least Grade A
On completion of the module a student should be able to
- Understand basic geometrical notions of lines, circles, triangles, distances, angles, tangents, bisects, isometries, similarities, etc.
- Prove geometrical figures to be congruent
- Being able to carry out classical geometrical constructions such as those of an inscribed and a circumscribed triangle
- Visualise non-Euclidean geometries using the geometry on a sphere as an example
- Compute areas and sums of internal angles of basic geometrical figures
How the module will be delivered
Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:
- Weekly face to face classes (e.g. labs, lectures, exercise classes)
- Electronic resources that you work through at your own pace (e.g. videos, exercise sheets, lecture notes, e-books, quizzes)
Students are also expected to undertake self-guided study throughout the duration of the module.
Skills that will be practised and developed
Constructing logical proofs based on a set of axioms and previously established results
Rigorous use of diagrams in the course of the proof
Developing geometrical intuition and visualisation in 2 and 3 dimensions
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Autumn Semester | 100 | Geometry - Autumn Examination | 2 |
Syllabus content
- Introduction: Euclid's axioms. Distances and angles
- Isometries and congruences.
- Triangle congruences: SAS, ASA and SSS. Isosceles triangles.
- Perpendicular bisects. Distance from a point to a line.
- Bisectors. Inscribed and circumscribed circles of a triangle.
- Spherical geometry: intro. Lines and angles.
- Parallel postulate. Sum of angles of a triangle / n-gon.
- Area. Ceva's Theorem.
- Spherical geometry: triangles on a sphere.
- Similarity. Pythagoras theorem.