Projective geometry is a topic of
mathematics. It is the study of geometric properties that are invariant with respect to
projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting,
projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has
more points than
Euclidean space, for a given dimension, and that
geometric transformations are permitted that transform the extra points (called "
points at infinity") to Euclidean points, and vice versa.