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Projective Plane

Alternate name

finite projective plane

Basic definition

The projective plane is the set of lines in the Euclidean plane that pass through the origin. It can also be viewed as the Euclidean plane together with a line at infinity.

Detailed definition

A projective plane, sometimes called a twisted sphere, is a surface without boundary derived from a usual plane by addition of a line at infinity. Just as a straight line in projective geometry contains a single point at infinity at which the endpoints meet, a plane in projective geometry contains a single line at infinity at which the edges of the plane meet. A projective plane can be constructed by gluing both pairs of opposite edges of a rectangle together giving both pairs a half-twist. It is a one-sided surface, but cannot be realized in three-dimensional space without crossing itself.

Related terms

affine plane | block design | Bruck-Ryser-Chowla theorem | complex projective plane | configuration | Fano plane | Lam's problem | map coloring | Moufang plane | oval | projective plane PK^2 | projective space | real projective plane | symmetric block design

Educational grade level

college level

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