Projective geometry
Projective geometry can be thought of informally as the geometry which
arises from placing one's eye at a point. That is, every line which intersects
the "eye" appears only as a point in the projective plane because the eye cannot
"see" the points behind it. Projective geometry has also been a useful tool in
proving a number of theorems from Euclidean
geometry.
Whatever the precise foundational status, projective geometry did include
basic incidence properties. That means that any two distinct
lines L and M in the projective
plane intersect in exactly one
point P. The special case in analytic geometry
of parallel lines has been subsumed in the smoother form of a line at infinity
on which P will lie in that case. The point is then that the line at infinity is
a line like any other in the theory: it is in no way special or distinguished.
See also