In
geometry, a
real projective line is an extension of the usual concept of
line that has been historically introduced to solve a problem set by visual
perspective: two
parallel lines do not intersect but seem to intersect "at infinity". For solving this problem,
points at infinity have been introduced, in such a way that in a
real projective plane, two different projective lines meet in exactly one point. The set of these points at infinity, the "horizon" of the visual perspective in the plane, is a real projective line. It is the circle of directions emanating from an observer situated at any point, with opposite points identified. A model of the real projective line is the
projectively extended real line. Drawing a line to represent the horizon in visual perspective, an additional
point at infinity is added to represent the collection of lines parallel to the horizon.