Editing Coordinate system (section)

{{Short description|Method for specifying point positions}}
{{redirect|Coordinate|coordinates on the Earth|Spatial reference system|other uses|Coordinate (disambiguation)}}
[[File:3D Spherical.svg|thumb|The [[spherical coordinate system]] is commonly used in ''physics''. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance ''r'', polar angle ''θ'' ([[theta]]), and azimuthal angle ''φ'' ([[phi]]). The symbol ''ρ'' ([[rho]]) is often used instead of ''r''.]]
In [[geometry]], a '''coordinate system''' is a system that uses one or more [[number]]s, or '''coordinates''', to uniquely determine and standardize the [[Position (geometry)|position]] of the [[Point (geometry)|points]] or other geometric elements on a [[manifold]] such as [[Euclidean space]].<ref>Woods p. 1</ref><ref>{{MathWorld|title=Coordinate System|urlname=CoordinateSystem}}</ref> The order of the coordinates is significant, and they are sometimes identified by their position in an ordered [[tuple]] and sometimes by a letter, as in "the ''x''-coordinate". The coordinates are taken to be [[real number]]s in [[elementary mathematics]], but may be [[complex number]]s or elements of a more abstract system such as a [[commutative ring]]. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of [[analytic geometry]].<ref>{{MathWorld|title=Coordinates|urlname=Coordinates}}</ref>