Editing Surface (topology) (section)

==In general==
{{Further|Surface (mathematics)}}

In [[mathematics]], a '''surface''' is a geometrical shape that resembles a deformed [[plane (geometry)|plane]]. The most familiar examples arise as boundaries of solid objects in ordinary three-dimensional [[Euclidean space]] '''R'''<sup>3</sup>, such as [[sphere]]s. The exact definition of a surface may depend on the context. Typically, in [[algebraic geometry]], a surface may cross itself (and may have other [[singular point of an algebraic variety|singularities]]), while, in [[topology]] and [[differential geometry]], it may not.

A surface is a  [[dimension|two-dimensional space]]; this means that a moving point on a surface may move in two directions (it has two [[degrees of freedom]]). In other words, around almost every point, there is a ''[[coordinate patch]]'' on which a two-dimensional [[coordinate system]] is defined. For example, the surface of the Earth resembles (ideally) a two-dimensional [[sphere]], and [[latitude]] and [[longitude]] provide two-dimensional coordinates on it (except at the poles and along the [[180th meridian]]).

The concept of surface is widely used in [[physics]], [[engineering]], [[computer graphics]], and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the [[aerodynamics|aerodynamic]] properties of an [[airplane]], the central consideration is the flow of air along its surface.