A projective plane consists of a set of lines, a set of points, and a relation between points and lines called incidence, having the following properties:
- Given any two distinct points, there is exactly one line incident with both of them.
- Given any two distinct lines, there is exactly one point incident with both of them.
- There are four points such that no line is incident with more than two of them.
The second condition means that there are no parallel lines. The last condition excludes the so-called degenerate cases (see below). The term "incidence" is used to emphasize the symmetric nature of the relationship between points and lines. Thus the expression "point P is incident with line l " is used instead of either "P is on l " or "l passes through P ".
Read more about Projective Plane: Vector Space Construction, Subplanes, Affine Planes, Degenerate Planes, Collineations, Plane Duality, Correlations, Finite Projective Planes, Projective Planes in Higher Dimensional Projective Spaces
Famous quotes containing the word plane:
“At the moment when a man openly makes known his difference of opinion from a well-known party leader, the whole world thinks that he must be angry with the latter. Sometimes, however, he is just on the point of ceasing to be angry with him. He ventures to put himself on the same plane as his opponent, and is free from the tortures of suppressed envy.”
—Friedrich Nietzsche (1844–1900)