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orientation (Definition)

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$.



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See Also: sense-preserving mapping

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Cross-references: oriented, winding number, point, Jordan curve, rectifiable
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This is version 3 of orientation, born on 2002-08-14, modified 2002-08-14.
Object id is 3292, canonical name is Orientation.
Accessed 3522 times total.

Classification:
AMS MSC30A99 (Functions of a complex variable :: General properties :: Miscellaneous)

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