2013/02/07 by Anton Petrunin, Petrunin, Anton · 1 citation
Mathematics · #51-01 #51M05 #51M10 #Absolute geometry #Affine geometry #Affine plane (incidence geometry) #Affine space #Affine transformation #Analytic geometry #Differential geometry #Euclidean geometry #FOS: Mathematics #Foundations of geometry #Geometry #History and Overview (math.HO) #Hyperbolic geometry #Inscribed figure #Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Non-Euclidean geometry #Ordered geometry #Plane (geometry) #Projective geometry #Projective plane #Regular polygon #Synthetic geometry
paper · pdf · doi:10.48550/arxiv.1302.1630
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2013/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.