  We establish a fundamental connection between smooth and polygonal knot
energies, showing that the Minimum Distance Energy for polygons inscribed in a
smooth knot converges to the Moebius Energy of the smooth knot as the polygons
converge to the smooth knot. However, the polygons must converge in a ``nice''
way, and the energies must be correctly regularized. We determine an explicit
error bound between the energies in terms of the number of the edges of the
polygon and the Ropelength of the smooth curve.
