PlanetPhysics/Centre of Mass of Polygon
Let be an -gon which is supposed to have a constant surface-density in all of its points, the centre of mass of the polygon and the origin. Then the position vector of with respect to is
We can of course take especially\, ,\, and thus
In the special case of the triangle we have
The centre of mass of a triangle is the common point of its medians.\\
Remark. An analogical result with (2) concerns also the homogeneous tetrahedron , and any -dimensional simplex (cf. the midpoint of line segment:\, ).