English

Euclidean plane and its relatives; a minimalist introduction

History and Overview 2025-07-08 v25 Metric Geometry

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.

Keywords

Cite

@article{arxiv.1302.1630,
  title  = {Euclidean plane and its relatives; a minimalist introduction},
  author = {Anton Petrunin},
  journal= {arXiv preprint arXiv:1302.1630},
  year   = {2025}
}

Comments

third edition, tenth printing, ISBN: 978-1650229676

R2 v1 2026-06-21T23:22:19.941Z