Category:Single Point Characterization of Simple Closed Contour
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This category contains pages concerning Single Point Characterization of Simple Closed Contour:
Let $C$ be a simple closed contour in the complex plane $\C$ with parameterization $\gamma: \closedint a b \to \C$.
Let $t_0 \in \openint a b$ such that $\gamma$ is complex-differentiable at $t_0$.
Let $S \in \set {-1,1}$ and $r \in \R_{>0}$ such that:
- for all $\epsilon \in \openint 0 r$, we have $\map \gamma {t_0} + \epsilon i S \map {\gamma '}{t_0} \in \Int C$
where $\Int C$ denotes the interior of $C$.
If $S = 1$, then $C$ is positively oriented.
If $S = -1$, then $C$ is negatively oriented.
Pages in category "Single Point Characterization of Simple Closed Contour"
The following 4 pages are in this category, out of 4 total.