two-dimensional space
geometric model of the planar projection of the physical universe
plane
flat, infinite two-dimensional surface
surface
two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space
algebraic surface
algebraic variety of dimension two
real projective plane
a compact non-orientable two-dimensional manifold
ellipse
ellipse in descriptive geometry
affine plane
Euclidean space of dimension 2 that is axiomatically defined
projective plane
geometric concept of a 2D space with a "point at infinity" adjoined