# orientation

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 $-1$.

Title orientation Orientation 2013-03-22 12:56:09 2013-03-22 12:56:09 CWoo (3771) CWoo (3771) 6 CWoo (3771) Definition msc 30A99 SensePreservingMapping