These parallel lines appear to intersect in the
"at infinity". In a projective plane this is actually true.
mathematics, a projective plane is a geometric structure that extends the concept of a
plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two distinct lines in a projective plane intersect in one and only one point.
Renaissance artists, in developing the techniques of drawing in
perspective, laid the groundwork for this mathematical topic. The archetypical example is the
real projective plane, also known as the extended Euclidean plane.
 This example, in slightly different guises, is important in
projective geometry where it may be denoted variously by PG(2, R), RP2, or P2(R) among other notations. There are many other projective planes, both infinite, such as the
complex projective plane, and finite, such as the
A projective plane is a 2-dimensional
projective space, but not all projective planes can be embedded in 3-dimensional projective spaces. Such embeddability is a consequence of a property known as
Desargues' theorem, not shared by all projective planes.