Euclidean plane and its relatives


The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist.

You can order a printed copy at amazon. Its exact copy can be downloaded at arXiv. (The older printings start from [v11]; the numbering of some statements has been changed).

Visual assignments can be used in addition to the traditional exercises in the book.

Table of contents:

1. Preliminaries

Euclidean geometry
2. The Axioms
3. Half-planes
4. Congruent triangles
5. Perpendicular lines
6. Similar triangless
7. Parallel lines
8. Triangle geometry

Inversive geometry
9. Inscribed angles
10. Inversion

Non-Euclidean geometry
11. Neutral plane
12. Hyperbolic plane
13. Geometry of h-plane

Additional topics
14. Affine geometry
15. Projective geometry
16. Spherical geometry
17. Projective model
18. Complex coordinates
19. Geometric constructions
20. Area

Write me a short message if you are teaching a course using this book. Also, write me if you see a mistake.

You can download the source files and use it as you want, see the license below.