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Geometry (MATH124)

Constructions using the straightedge and compass alone. Remarkable points and lines connected with a triangle: Ceva’s theorem, the incircles and excircles, the orthic triangle, the Euler line. Some properties of circles: the radical axis of two circles, the Simpson line, first Ptolemy’s theorem. Collinearity and concurrence: cyclic quadrangles, Menelaus’s theorem, Pappus’s theorem, Desargues’s theorem, Pascal’s theorem. Transformations: translations, rotations, half-turn, reflections, dilatation. Inversive Geometry: Separation, Cross ratio, Inversion, the second Ptolemy theorem. Elements of projective geometry: Reciprocation, Conics, Projective plane. Elements of non-Euclidean geometry.

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