\begin{definition}[Definition:Contour/Length]
{{mergeto|Definition:Arc Length}}
Let $\R^n$ be a real cartesian space of $n$ dimensions.
Let $C$ be a '''contour''' in $C$ defined by the (finite) sequence $\sequence {C_1, \ldots, C_n}$ of directed smooth curves in $\R^n$.
Let $C_i$ be parameterized by the smooth path $\rho_i: \closedint {a_i} {b_i} \to \R^n$ for all $i \in \set {1, \ldots, n}$.
The '''length''' of $C$ is defined as:
:$\ds \map L C := \sum_{i \mathop = 1}^n \int_{a_i}^{b_i} \size {\map {\rho_i'} t} \rd t$
\end{definition}