Mathematics & statistics
Euclidean plane and its relatives
Anton Petrunin
Anton Petrunin · arXiv version 19 (May 21, 2021) · English · Published 2021
An axiomatic introduction to Euclidean geometry and related geometries, with an emphasis on reasoning and proofs.
- Learning stage
- College introduction
- Prerequisites
- Comfort with mathematical proofs, elementary geometry and algebra; some exercises are advanced.
- PDF pages
- 204 in this file
- Editorial review
- 2026-10-29
Contents
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Introduction
1 Preliminaries
2 Axioms
3 Half-planes
4 Congruent triangles
5 Perpendicular lines
6 Similar triangles
7 Parallel lines
8 Triangle geometry
9 Inscribed angles
10 Inversion
11 Neutral plane
12 Hyperbolic plane
13 Geometry of the h-plane
14 Affine geometry
15 Projective geometry
16 Spherical geometry
17 Projective model
18 Complex coordinates
19 Geometric constructions
20 Area
Hints
Index
Used resources
Sources and permissions
The author and publisher remain the source of this textbook. Permission information applies to the specific files in this edition.
Author, publisher, and discovery sources
Authors: Anton Petrunin
Publisher: Anton Petrunin
- Discovered through Open Textbook Library: Source record · Checked 2026-10-27
- Discovered through Open Textbook Library: Source record · Checked 2026-10-25
CC BY-SA 4.0
Anton Petrunin, Euclidean plane and its relatives: A minimalist introduction, arXiv:1302.1630v19, May 21, 2021. CC BY-SA 4.0.
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Checked 2026-10-29