Projective geometry

Summary

Projective geometry studies the properties of figures that survive projection, such as incidence and the cross-ratio. Length and angle are not among them. Its spaces are projective spaces, where any two lines of a plane meet. It can be built either from linear algebra or from incidence axioms. In it, points and hyperplanes play symmetric roles, which gives the principle of duality. It underlies perspective drawing, algebraic geometry and computer vision.