nLab barycenter

Barycenter of a simplex

Definition

If $\sigma = \{ v_0, \ldots, v_q\} \in K_q$, the set of $q$-simplices of a simplicial complex, $K$, then its barycentre, $b(\sigma)$, is the point

$$b(\sigma) = \sum_{0\leq i \leq q}\frac{1}{q + 1} v_i \in |K|.$$

For the use of barycenters in the barycentric subdivision, see classical triangulation or

• wikipedia: barycentric subdivision, barycentric coordinates

• barycentric coordinates homepage

• Wolframworld: [[barycentric coordinates](http://mathworld.wolfram.com/BarycentricCoordinates.html)