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# Centroid

In geometry, the centroid or barycenter of an object X in n-dimensional space is the intersection of all hyperplanes that divide X into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of X.

In physics, the centroid can, under some circunstances, coincide with an object's center of mass and also with it's center of gravity. In some cases this leads to the usage of those terms interchangingly. For a centroid to coincide with the center of mass, the object should have uniform density or the matter's distribution through the object should have certain properties, such assymmetry. For a centroid to coincide with the center of gravity, the centroid must coincide with the object's center of mass and the object must be under the influence of a uniform gravitational field.

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 lines extending from each vertex of a triangle to the mid-point of the opposite sides are called medians.

The three medians of a triangle intersect at a common point. This is called the centroid of the triangle.

This point is also the triangle's center of mass, if the triangle is made from a uniform sheet of material.