In
geometry, an
affine plane is a two-dimensional
affine space. Typical examples of affine planes are
- Euclidean planes, which are affine planes over the reals, equipped with a metric, the Euclidean distance. In other words, an affine plane over the reals is a Euclidean plane in which one has "forgotten" the metric (that it one cannot talk of lengths nor of angle measures).
- Vector spaces of dimension two, in which the zero vector is not considered as different from the other elements
- For every field or division ring F, the set F2 of the pairs of elements of F
- The result of removing any single line (and all the points on this line) from any projective plane
All the affine planes defined over a field are
isomorphic. More precisely, the choice of an
affine coordinate system (or, in the real case, a
Cartesian coordinate system) for an affine plane
P over a field
F induces an isomorphism of affine planes between
P and
F2.