Definition:Centroid/Solid Figure
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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 $F$.
Sources
- 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Centroids: $10$. Centroids of area and volume