| Abstract: |
The center of mass of a body in space is not necessarily included
in the body, as can be easily seen when the body is not convex. But
if the body is convex, then the center of mass should be in the body.
Or should it? Well, I will show that this doesn't need to be the
case! For this I will define the center of mass in a way involving
finitely additive measures in an arbitrary bounded subset of a Hilbert
space H. Then I will justify why that should be the center of mass,
and finally I prove that if the body is not closed, then there is a mass
distribution for the body such that the center is not in the body (but
in its bounday). No particular prerequisites will be assumed, and
you can feel free to imagine R^n instead of H if you don't know what a
Hilbert space is. |