Definition:Staircase Contour

Definition
Let $C$ be a contour that is a concatenation of the directed smooth curves $C_1, \ldots, C_n$.

Suppose that for all $i \in \left\{ {1, \ldots, n}\right\}$, $C_i$ can be parameterized by a smooth path $\gamma_i : \left[{0 \,.\,.\, 1}\right] \to \C$ such that either:


 * $\gamma_i \left({t}\right) = z_i + tr_i$

or


 * $\gamma_i \left({t}\right) = z_i + itr_i$

for some $z_i \in \C, r_i \in \R$ for all $t \in \left[{0 \,.\,.\, 1}\right]$.

Then $C$ is called a staircase contour.

Illustration
A picture of a staircase contour can be found in the proof of the theorem Connected Domain is Connected by Staircase Contours.