If $f$ is a continuous function on a open set $U\subseteq \mathbb C$ and $\Delta$ is a triangle which lies in $U$, what does $$ \oint_{\partial \Delta} f(z) dz $$ exactly mean ? Path integral requires a parametrization of the boundary of $\Delta$ but it can be oriented counter-clockwise or clockwise... so how to define a piecewise smooth path $\gamma$ depending on $\Delta$ with arbitrary fixed orientation, given by a function which takes a triangle as an input and return a path at output, therefore we may denote such a path by $\partial \Delta$ to be convenient ?
Thanks for help :)