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Euclidean plane and its relatives; a minimalist introduction (1302.1630v25)
Published 7 Feb 2013 in math.HO and math.MG
Abstract: The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: The Axioms / Half-planes / Congruent triangles / Perpendicular lines / Similar triangles / Parallel lines / Triangle geometry. Inversive geometry: Inscribed angles / Inversion. Non-Euclidean geometry: Neutral plane / Hyperbolic plane / Geometry of h-plane. Additional topics: Affine geometry / Projective geometry / Spherical insights / Projective model / Complex coordinates / Geometric constructions / Area.
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