  We analyze several continuum models of polymers: worm-like chains, ribbons
and Fourier knots. We show that the torsion of worm-like chains diverges and
conclude that such chains can not be described by the Frenet-Serret (FS)
equation of space curves. While the same holds for ribbons as well, their rate
of twist is finite and, therefore, they can be described by the generalized FS
equation of stripes. Finally, Fourier knots have finite curvature and torsion
and, therefore, are sufficiently smooth to be described by the FS equation of
space curves.
