Centroid
In geometry, the centroid or barycenter of an object <math>X<math> in <math>n<math>-dimensional space is the intersection of all hyperplanes that divide <math>X<math> into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of <math>X<math>.
In physics, these words designate the center of mass or center of gravity of an object. These points coincide if the object is in a uniform gravitational field, and they coincide with the geometrical centroid if the object has uniform density.
Note that a figure's centroid need not necessarily lie within it; the centroid of a crescent, for example, lies somewhere in the central void.
The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). This point is also the triangle's center of mass, if the triangle is made from a uniform sheet of material.
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