# Plane (geometry)

In mathematics, a **plane** is a Euclidean (flat[1]), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with one of a room's walls, infinitely extended, or they may enjoy an independent existence in their own right, as in the setting of two-dimensional[2] Euclidean geometry. Sometimes the word *plane* is used more generally to describe a two-dimensional surface, for example the hyperbolic plane and elliptic plane.

When working exclusively in two-dimensional Euclidean space, the definite article is used, so *the* plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, often in the plane.