Definition:Centroid/Solid Figure

Definition
Let $F$ be a solid figure.

Let $F$ 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 $F$ converges to a point.

Then the limiting position of $G$ is the centroid of $F$.