Online Encyclopedia Search Tool

Your Online Encyclopedia


Online Encylopedia and Dictionary Research Site

Online Encyclopedia Free Search Online Encyclopedia Search    Online Encyclopedia Browse    welcome to our free dictionary for your research of every kind

Online Encyclopedia

Fundamental theorem of projective geometry

In mathematics, the fundamental theorem of projective geometry states that if Pn is a projective space and F and F′ are frames of Pn, 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