In mathematics, plane geometry refers generally to geometry in a two-dimensional space called a plane.
Euclidean plane geometry, is the most common meaning; it includes Plane analytic geometry Plane synthetic geometry Plane projective geometry, the geometry of projective planes Geometry of finite planes, such as the Fano plane Affine geometry of affine planes Geometry of non-Euclidean planes, including hyperbolic planes, elliptic planes two-dimensional spherical geometry.
See also Plane curve Inversive geometry Geometrography