geometric concept of a 2D space with a "point at infinity" adjoined From Wikipedia, the free encyclopedia
A projective plane is like a plane. The difference is that every line in a projective plane meet at some point. This is not true in a plane. There are some lines that do not meet there. These lines are called parallel lines. In a projective plane, two lines that look parallel meet at a really far away point. This point is called the point at infinity. This means that every line in a projective plane meet somewhere.
The first people to think about projections are Renaissance artists. They want to draw perspective good, so they worked very hard. A common example of a projective plane is the real projective plane.[1]
A projective plane has lines and points. Points and lines can be incident. Incidence has these properties:
The second condition means that there are no parallel lines. The last condition means there are no degenerate projective planes (see below). We say "incident" because if a point is incident with a line, then that line is incident with the point.
Degenerate planes are not projective planes. This is because they are very boring. Without the third condition, they would be projective planes. (Albert & Sandler 1968) says there are seven kinds of degenerate planes. They are:
A degenerate plane can be multiple of these cases at once.
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