Euclidean plane and its relatives; a minimalist introduction

TL;DR

This book offers a rigorous, minimalist introduction to Euclidean and non-Euclidean geometries, covering foundational axioms, transformations, and advanced topics like inversion and projective geometry in a concise, semester-long course format.

Contribution

It provides a comprehensive, elementary, and conservative overview of various geometries, integrating classical and modern topics within a minimalistic framework.

Findings

Clear exposition of Euclidean axioms and properties

Introduction of inversion and non-Euclidean geometries

Integration of projective and complex coordinate methods

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.