Let $\alpha$ be a rectifiable, Jordan curve in $\mathbb{R}^{2}$ and $z_{0}$ be a point in $\mathbb{R}^{2} - \operatorname{Im}(\alpha)$ and let $\alpha$ have a winding number $W [ \alpha : z_{0} ]$ Then $W [ \alpha : z_{0} ] = \pm 1$ all points inside $\alpha$ will have the same index and we define the orientation of a Jordan curve $\alpha$ by saying that $\alpha$ is positively oriented if the index of every point in $\alpha$ is $+1$ and negatively oriented if it is $-1$