  The two-mode Bose-Hubbard model in the mean-field approximation is revisited
emphasizing a geometric interpretation where the system orbits appear as
intersection curves of a (Bloch) sphere and a cylinder oriented parallel to the
mode axis, which provide a generalization of Viviani's curve studied already in
1692. In addition, the dynamics is shown to agree with the simple mathematical
pendulum. The areas enclosed by the generalised Viviani curves, the action
integrals, which can be used to semiclassically quantize the N-particle
eigenstates, are evaluated. Furthermore the significance of the original
Viviani curve for the quantum system is demonstrated.
