Definition:Curve Parameterized by Arc Length/3-Dimensional Real Vector Space

Definition
Let $\alpha : I \to \R^3$ be a smooth curve.

$\alpha$ is said to be parameterized by arc length :
 * $\forall t \in I : \norm {\map {\alpha'} t} = 1$

where:
 * $\alpha '$ denotes the derivative of $\alpha$
 * $\norm {\, \cdot \,}$ denotes the Euclidean norm on $\R^3$

Also known as
Some sources use the spelling parametrized.