AbstractPerspectivity 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 ContentsCross ratio. Harmonic conjugates. Perspectivity. Projectivity
Dessargue\( \prime \)s theorem
Theorems of Pappus and Pascal
Pole. Polar. Theorems of Brianchon and Brokard
2005-2018 IMOmath.com | imomath"at"gmail.com | Math rendered by MathJax
Home | Olympiads | Book | Training | IMO Results | Forum | Links | About | Contact us