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; version [v12] is the current second printing and [v11] is the first printing (the numbering of some statements has been changed). You can also download the very last version.

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. Parallel lines and similar triangles
7. Triangle geometry

Inversive geometry
8. Inscribed angles
9. Inversion

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

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

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

If you would like to contribute, you will have to use Git and LaTeX. The following command will create a local copy of the source code for you.

git clone

You can also create an alternate version, see the license below.