  The notion of center of mass, which is very useful in kinematics, proves to
be very handy in geometry (see [1]-[2]). Countless applications of center of
mass to geometry go back to Archimedes. Unfortunately, the center of mass
cannot be defined for sets whose total mass equals zero. In the paper we
improve this disadvantage and assign to an n-dimensional affine space L over
any field k the (n+1)-dimensional vector space over the field k of weighty
points and mass dipoles in L. In this space, the sum of weighted points with
nonzero total mass is equal to the center of mass of these points equipped with
their total mass. We present several interpretations of the space of weighty
points and mass dipoles in L, and a couple of its applications to geometry. The
paper is self-contained and is accessible for undergraduate students.
