What is the arc length
of a space curve
$$\mathcal{C} = [ {\bf{r}} (t) ~| ~t \in I] \subset {\mathbb{R}}^3 $$
where ${\bf{r}}$ is the vector function $t \longmapsto {\bf{r}}(t) = \langle f(t), g(t), h(t) \rangle$ ?
Definition: arc length
Examples
Parametrizations
arc length parametrization
Definition: curvature
Intuition
Examples
velocity
acceleration
(Frenet Frame
)