Centroid

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure. Informally, it is the point at which a cutout of the shape could be perfectly balanced on the tip of a pin. In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure. Informally, it is the point at which a cutout of the shape could be perfectly balanced on the tip of a pin. The definition extends to any object in n-dimensional space: its centroid is the mean position of all the points in all of the coordinate directions. While in geometry the word barycenter is a synonym for centroid, in astrophysics and astronomy, the barycenter is the center of mass of two or more bodies that orbit each other. In physics, the center of mass is the arithmetic mean of all points weighted by the local density or specific weight. If a physical object has uniform density, its center of mass is the same as the centroid of its shape. In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center. The term 'centroid' is of recent coinage (1814). It is used as a substitute for the older terms 'center of gravity,' and 'center of mass', when the purely geometrical aspects of that point are to be emphasized. The term is peculiar to the English language. The French use 'centre de gravité' on most occasions, and others use terms of similar meaning.