Classification of Curves
 Definition: If $\vec{r}(t)$ traces a curve $C$ for $a ≤ t ≤ b$, then $C$ is said to be a Closed Curve if $\vec{r}(a) = \vec{r}(b)$ and an Open Curve otherwise.
 Definition: If $\vec{r}(t)$ traces a curve $C$ for $a ≤ t ≤ b$, then $C$ is said to be Self-Intersecting if for $t_0, t_1 \in (a, b)$ and $t_0 \neq t_1$ we have that $\vec{r}(t_0) = \vec{r}(t_1)$. $C$ is said to be Non-Self-Intersecting if for $t_0, t_1 \in (a, b)$ and $t_0 \neq t_1$ then we have that $\vec{r}(t_0) \neq \vec{r}(t_1)$.