\begin{definition}[Definition:Centroid/Surface]
Let $S$ be a surface.
Let $S$ be divided into a large number $n$ of small elements.
Consider one point of each of these elements.
Let a weight function be associated with this set of points.
Let $G$ be the centroid of each of these weighted points.
Let $n$ increase indefinitely, such that each element of $S$ converges to a point.
Then the limiting position of $G$ is the '''centroid''' of $S$.
\end{definition}