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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 $-1$




"orientation" is owned by CWoo. [ owner history (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 4596 times total.

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

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