Euclidean Plane and its Relatives: A Minimalist Introduction (Anton Petrunin)

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Euclidean Plane and its Relatives: A Minimalist Introduction (Anton Petrunin)

The book is intended to be rigorous, conservative, simple, and minimalist for a semester-long Foundations of Geometry course.

The five-plane geometry postulates of Euclid and the most popular theorems serve as the foundation for the book's content. It encourages the practice of creating logical arguments as an art and skill. The majority of the theorems come with thorough 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.

Ebook Details

Published Date / Year
(December 24, 2019); eBook (arXiv, Creative Commons Edition)
CC BY-SA 4.0
206 pages
eBook Format

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