  In considering the mathematical problem of describing the geodesics on a
torus or any other surface of revolution, there is a tremendous advantage in
conceptual understanding that derives from taking the point of view of a
physicist by interpreting parametrized geodesics as the paths traced out in
time by the motion of a point in the surface, identifying the parameter with
the time. Considering energy levels in an effective potential for the reduced
motion then proves to be an extremely useful tool in studying the behavior and
properties of the geodesics. The same approach can be easily tweaked to extend
to both the nonrelativistic and relativistic Kepler problems. The spectrum of
closed geodesics on the torus is analogous to the quantization of energy levels
in models of atoms.
