  Optimal geometrical arrangements, such as the stacking of atoms, are of
relevance in diverse disciplines. A classic problem is the determination of the
optimal arrangement of spheres in three dimensions in order to achieve the
highest packing fraction; only recently has it been proved that the answer for
infinite systems is a face-centred-cubic lattice. This simply stated problem
has had a profound impact in many areas, ranging from the crystallization and
melting of atomic systems, to optimal packing of objects and subdivision of
space. Here we study an analogous problem--that of determining the optimal
shapes of closely packed compact strings. This problem is a mathematical
idealization of situations commonly encountered in biology, chemistry and
physics, involving the optimal structure of folded polymeric chains. We find
that, in cases where boundary effects are not dominant, helices with a
particular pitch-radius ratio are selected. Interestingly, the same geometry is
observed in helices in naturally-occurring proteins.
