Euclidean plane and its relatives


The textbook is designed for a semester-long course in Foundations of geometry and meant to be rigorous, conservative, elementary and minimalist. It is based on lectures for course MATH 427 given at the Penn State University.

You can order a printed copy at amazon. Its exact copy can be downloaded at arXiv; printings of this (third) edition start with v16. If you use the printed version in class, make sure everyone gets the latest printing directly from amazon (some number-labels of exercises and theorems might be shifted in the older printings).

In addition to the traditional exercises in the book, one can use visual assignments.

Table of contents:

   1. Preliminaries

Euclidean geometry
   2. The Axioms
   3. Half-planes
   4. Congruent triangles
   5. Perpendicular lines
   6. Similar triangles
   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.

Write me if you see a mistake.

Download the source files and use it as you want, see the license below.