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MATH301 Advanced Geometry

10 cp
Prerequisites MATH105/205 Geometry
Teaching Organisation 4 hours per week for twelve weeks or equivalent. There will be two hours of lectures and two hours of tutorials per week. One tutorial hour per week for six weeks will be on using Geometers Sketchpad.

The unit has two distinct sections: Euclidean and non-Euclidean geometry. We review Euclidean geometry from a standpoint of logic and the logical processes involved in writing formal proofs. We look at the classical definition of constructible and study the famous three impossible constructions. A review of formal logic leads to the study of finite geometries and Euclidean geometry as a deductive system. Alternatives to Euclids fifth postulate give rise to hyperbolic and Riemannian geometries. Use of the software package Geometers Sketchpad is included in the unit: students will be encouraged to demonstrate heuristically theorems which are prove axiomatically.

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