\begin{definition}[Definition:Curvilinear Coordinate System/Cartesian Representation]
The relation between curvilinear coordinates and Cartesian coordinates can be expressed as:
{{begin-eqn}}
{{eqn | l = x
      | r = \map x {q_1, q_2, q_3}
}}
{{eqn | l = y
      | r = \map y {q_1, q_2, q_3}
}}
{{eqn | l = z
      | r = \map z {q_1, q_2, q_3}
}}
{{end-eqn}}
where:
:$\tuple {x, y, z}$ denotes the Cartesian coordinates
:$\tuple {q_1, q_2, q_3}$ denotes their curvilinear equivalents.
\end{definition}