Content: This module begins with a quick tour through elementary plane Euclidean geometry. We emphasise proof, and the careful use of diagrams as an aid to understanding problems and finding proofs. Plane geometry then provides the setting for an introduction to the geometry of the sphere and of polyhedra.

Aims:

• To learn and enjoy Euclidean geometry of the plane, the sphere and of three-dimensional space.
• To learn to visualise geometrical problems, and to draw diagrams which represent them accurately.
• To learn to reason from diagrams, and use them as an aid to writing rigorous proofs.
• To learn to construct proofs, and to set them out clearly and convincingly.

Objectives: You will gain familiarity with

• Plane Euclidean geometry: isometries, congruence and similarity; theorems on triangles, circles, tangents and angles; ruler and compass constructions.
• Polyhedra: the Euler characteristic; classification and construction of regular polyhedra.
• Spherical geometry: the angle-sum formula for spherical triangles; stereographic projection and its relation with inversion; conformal (angle-preserving) maps.

Books:

Notes for the module will be available at cost price from the departmental office.

Also relevant: G.A. Jennings, Modern geometry with applications, Springer-Verlag (a fine book with many challenging exercises, but useful only as a complement to the course).