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

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### Famous quotes containing the word plane:

“It was the most ungrateful and unjust act ever perpetrated by a republic upon a class of citizens who had worked and sacrificed and suffered as did the women of this nation in the struggle of the Civil War only to be rewarded at its close by such unspeakable degradation as to be reduced to the *plane* of subjects to enfranchised slaves.”

—Anna Howard Shaw (1847–1919)