Projective geometry

Projective geometry studies properties of figures that remain unchanged (invariant) under projective transformations, such as central projection. It extends classical geometry by adding 'points at infinity' so that parallel lines meet at a point at infinity, making many theorems simpler and more general.

Important properties

• Parallel lines meet at a point at infinity in projective geometry.

• Projective transformations (also called homographies) map lines to lines and preserve incidence (which points lie on which lines).

• Classical theorems like Desargues' and Pappus' Theorems are naturally stated in projective geometry.

• Projective geometry ignores measurements like distance and angle, focusing instead on collinearity and concurrency.