# Online Encyclopedia

# Fundamental theorem of projective geometry

In mathematics, the **fundamental theorem of projective geometry** states that if *P*^{n} is a projective space and *F* and *F′* are frames of *P*^{n}, then there exists a unique projective transformation sending *F* to *F′*.

In case *n* = 1 this comes down to saying that given two ordered triples of distinct points, there is a projective transformation of the projective line taking the first triple to the second. This is a basic result on Möbius transformations, saying that the group they form is "triply" transitive.

Last updated: 01-19-2005 00:42:09