## ::Coordinate system

### ::concepts

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

{{#invoke:redirect hatnote|redirect}}

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 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></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></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 << >>