## ::Coordinate system

### ::concepts

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In geometry, a **coordinate system** is a system which uses one or more numbers, or **coordinates**, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space.<ref>Woods p. 1</ref><ref>Weisstein, Eric W., "Coordinate System", *MathWorld*.</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 numbers in elementary mathematics, but may be complex numbers 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>Weisstein, Eric W., "Coordinates", *MathWorld*.</ref>

**Coordinate system sections**

Intro Common coordinate systems Coordinates of geometric objects Transformations [[Coordinate_system?section={{safesubst:#invoke:anchor|main}}{{safesubst:#invoke:anchor|main}}Coordinate_curves_and_surfaces|{{safesubst:#invoke:anchor|main}}{{safesubst:#invoke:anchor|main}}Coordinate curves and surfaces]] Coordinate maps Orientation-based coordinates See also References External links

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System::point Systems::space Title::first ''r''::example Polar::geometry Plane::three

{{#invoke:redirect hatnote|redirect}}

In geometry, a **coordinate system** is a system which uses one or more numbers, or **coordinates**, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space.<ref>Woods p. 1</ref><ref>Weisstein, Eric W., "Coordinate System", *MathWorld*.</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 numbers in elementary mathematics, but may be complex numbers 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>Weisstein, Eric W., "Coordinates", *MathWorld*.</ref>

**Coordinate system sections**

Intro Common coordinate systems Coordinates of geometric objects Transformations [[Coordinate_system?section={{safesubst:#invoke:anchor|main}}{{safesubst:#invoke:anchor|main}}Coordinate_curves_and_surfaces|{{safesubst:#invoke:anchor|main}}{{safesubst:#invoke:anchor|main}}Coordinate curves and surfaces]] Coordinate maps Orientation-based coordinates See also References External links

PREVIOUS: Intro | NEXT: Common coordinate systems |

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