Let $S \subset\mathbb R^n$ be rectifiable with nonzero volume. The centroid of $S$ is the point $c(S) \in \mathbb R^n$ whose $k$th coordinate is given by the integral \(c_k(S) = \frac{1}{\text{vol}(S)} \int_S \pi_k,\) where $\pi_k:\mathbb R^n \to\mathbb R$ is such that $(x_1,\dots,x_n)\mapsto x_k$.
Wikidata ID: Q511093