Desarguesian plane

Summary

A Desarguesian plane is a projective plane in which Desargues's theorem holds. These are exactly the planes $\mathbb{P}^2(D)$ built from a division ring $D$, so they are the planes that come from linear algebra. Every finite Desarguesian plane is $\mathbb{P}^2(\F_q)$ for a finite field $\F_q$. Planes in which the theorem fails are called non-Desarguesian planes.