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 Title Euclidean Plane and its Relatives: A Minimalist Introduction
 Author(s) Anton Petrunin
 Publisher: Independently published (December 24, 2019); eBook (arXiv, Creative Commons Edition)
 License(s): CC BYSA 4.0
 Hardcover/Paperback 206 pages
 eBook PDF
 Language: English
 ISBN10: 1650229674
 ISBN13: 9781650229676
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Book Description
The book is designed for a semesterlong course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist.
The content of the book is based on Euclid's five postulates of plane geometry and the most common theorems. It promotes the art and the skills of developing logical proofs. Most of the theorems are provided with detailed proofs.
 Euclidean geometry: The Axioms / Halfplanes / Congruent triangles / Perpendicular lines / Similar triangles / Parallel lines / Triangle geometry.
 Inversive geometry: Inscribed angles / Inversion.
 NonEuclidean geometry: Neutral plane / Hyperbolic plane / Geometry of hplane.
 Additional topics: Affine geometry / Projective geometry / Spherical geometry / Projective model / Complex coordinates / Geometric constructions / Area.
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 Geometry and Topology
 History of Mathematics
 Algebra and Abstract Algebra
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