Barycentric coordinates

Abstract

A number triple defines, algebraically, a point in a plane; a number quadruple a point in space. The physical interpretation of these number groups vary, giving rise to the various systems of homogeneous coordinates. The particular case in which we are interested is that in which these numbers are interpreted as masses. It is at once evident that with an extended interpretation to the term "mass," we may define any point in space as the center of mass of four masses at four fixed points. It is further evident that the mutual ratio of these masses is sufficient to label this point . The configuration of four fixed points at which the masses are located is referred to as the base tetrahedron, and the four masses or more specifically, the ratios of these masses are called the barycentric coordinates of this point. The point itself is referred to as the barycenter of the four masses.