Related pages

Projective closure
Affine derivative
An incidence structure is called an affine plane if the following three axioms hold.

Two lines a and b of an affine plane are defined to be parallel if either a=b or . We will write in this case. The relation of parallelism defines a parallelism on . In fact, this is the unique parallelism on .

All point rows and all parallel classes of an affine plane have the same cardinality n, called the order of . Moreover, if p is a point of , then .

Primary examples of affine planes are the affine planes over a vector space. More general affine planes are koordinatized over ternary fields.

See also

Contributed by Hauke Klein
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