  Bending of worm-like polymers carries an energy penalty which results in the
appearance of a persistence length l such that the polymer is straight on
length scales smaller than l and bends only on length scales larger than this
length. Intuitively, this leads us to expect that the most probable value of
the local curvature of a worm-like polymer undergoing thermal fluctuations in a
solvent, is zero. We use simple geometric arguments and Monte Carlo simulations
to show that while this expectation is indeed true for polymers on surfaces (in
two dimensions), in three dimensions the probability of observing zero
curvature anywhere along the worm-like chain, vanishes.
