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Euclidean Plane and its Relatives: A Minimalist Introduction
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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 BY-SA 4.0
  • Hardcover/Paperback 206 pages
  • eBook PDF
  • Language: English
  • ISBN-10: 1650229674
  • ISBN-13: 978-1650229676
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Book Description

The book is designed for a semester-long 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 / 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.
About the Authors
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