MA2219



Introduction to Geometry

This module gives a first introduction to various kinds of geometries ranging from elementary Euclidean geometry on the plane, inversive geometry on the sphere, as well as projective geometry and Non-Euclidean geometry. Topics covered include: Conics, Quadric surfaces, Affine geometry, Affine transformations, Ceva's theorem, Menelaus' theorem, Projective geometry, projective transformations, homogeneous coordinates, cross-ratio, Pappus' theorem, Desargues' theorem, duality and projective conics, Pascal's theorem, Brianchon's theorem, Inversions, coaxal family of circles, Non-Euclidean geometry, Mobius transformations, distance and area in Non-Euclidean geometry.

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