projective geometry
Noun
Meaning
the geometry of properties that remain invariant under projection
Source: WordNetSynonyms
Hypernyms
Examples
Earlier, Menger and Birkhoff had axiomatized complex projective geometry in terms of the properties of its lattice of linear subspaces.
"One might say, with some justice, that projective geometry, in so far as present day research is concerned, has split into two quite separate fields.
Efforts were well under way by the middle of the 19th century, by Karl George Christian von Staudt (1798–1867) among others, to purge projective geometry of the last superfluous relics from its Euclidean past.
They showed how rich was the projective geometry of curves defined by algebraic equations and thereby gave an enormous boost to the algebraic study of curves, comparable to the original provided by Descartes.
The fundamental theorem of projective geometry says that all the collineations of PG(2,K) are compositions of homographies and automorphic collineations.
The field planes are usually denoted by PG(2,q) where PG stands for projective geometry, the "2" is the dimension and q is called the order of the plane (it is one less than the number of points on any line).