Leena Thuy Dung: Inversive Geometry

Abstract

Inversive Geometry is the study of a transformation known as inversion which maps circles or lines to circles or lines and preserves the magnitude of angles between intersecting curves. The purpose of the thesis is to define Inversive Geometry and study its fundamental properties. In order to do that, an introduction of inversion and its properties will be provided from the beginning of the thesis. Central concepts will be systematically investigated such as generalized circles, the extended plane, Möbius transformations and so on. To summarize, the thesis will present some interesting applications of Inversive Geometry.

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