2015•arXiv (Cornell University)Open access

Euclidean Plane and its Relatives: A minimalistic introduction

Anton Petrunin

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 geometry / Projective model / Complex coordinates / Geometric constructions / Area.

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Key concepts: Foundations of geometry, Non-Euclidean geometry, Absolute geometry, Geometry, Ordered geometry, Projective geometry, Hyperbolic geometry, Euclidean geometry