Editing Euclidean space (section)

==Usage==
Since the [[Greek mathematics|ancient Greeks]], Euclidean space has been used for modeling [[shape]]s in the physical world. It is thus used in many [[science]]s, such as [[physics]], [[mechanics]], and [[astronomy]]. It is also widely used in all technical areas that are concerned with shapes, figure, location and position, such as [[architecture]], [[geodesy]], [[topography]], [[navigation]], [[industrial design]], or [[technical drawing]].

Space of dimensions higher than three occurs in several modern theories of physics; see [[Higher dimension]]. They occur also in [[configuration space (physics)|configuration space]]s of [[physical system]]s.

Beside [[Euclidean geometry]], Euclidean spaces are also widely used in other areas of mathematics. [[Tangent space]]s of [[differentiable manifold]]s are Euclidean vector spaces. More generally, a [[manifold]] is a space that is locally approximated by Euclidean spaces. Most [[non-Euclidean geometries]] can be modeled by a manifold, and [[embedding|embedded]] in a Euclidean space of higher dimension. For example, an [[elliptic space]] can be modeled by an [[ellipsoid]]. It is common to represent in a Euclidean space mathematical objects that are ''a priori'' not of a geometrical nature. An example among many is the usual representation of [[Graph (discrete mathematics)|graphs]].