Closed contour

A contour whose starting point and ending point are the same.

A contour is closed if its parametrization $z(t)$ , $a\le t\le b$ , satisfies $z(a)=z(b)$ -- it starts and ends at the same point. A simple closed contour is closed and otherwise non-self-intersecting; by the Jordan curve theorem, such a contour splits the plane into a bounded inside and an unbounded outside, the setting for nearly every theorem in this course about integrating around a region's boundary.

Examples

The boundary of a triangle, traced from one vertex back to itself, is a simple closed contour.
$z(t) = 2e^{it}$ , $0\le t\le 4\pi$ , is closed but not simple -- it traces the same circle twice.