Olympiad training materials (main page)

Projective Geometry

Milivoje Lukić


Perspectivity is the projection of objects from a point. A quantity that is preserved by this map, called the cross-ratio, naturally appears in many geometrical configurations. This map and its properties are very useful in a variety of geometry problems. We study the pole of a line, polar of a point, cross ratio, perspectivity, and we prove theorems of Desargue, Pappus, Pascal, Brianchon, and Brokard.

Table of Contents

No.Title and link
1. Cross ratio. Harmonic conjugates. Perspectivity. Projectivity
2. Desargue's theorem
3. Theorems of Pappus and Pascal
4. Pole. Polar. Theorems of Brianchon and Brokard
5. Problems