torus games!
Torus is the mathematical name for a donut shaped surface.
The torus has a special class of curves like the great circles on a sphere
which locally are the paths in the surface which have the shortest length
between two points in the surface.
See an animation of one of these here:

http://www34.homepage.villanova.edu/robert.jantzen/maple/examples/torusgifs.htm
And here is a game you can play by executing the whole worksheet and they by
trial and error try to discover the closed such curves on the torus.

http://www34.homepage.villanova.edu/robert.jantzen/notes/torus/torusdemo.mw
These curves are "quantized" into states like the quantum states of
atoms with a discrete listing by the pair of loops the curves make around
the vertical axis and around the torus crosssections. The simplest ones are
the analog of the equator on a sphere, or the circular crosssections of the
surface with quantum numbers (1,0) and (0,1) for the number of loops around
the vertical axis and around the crosssections.
Starting from a point on the "equator", one aims up at a certain angle to
see if after one loop around the vertical axis the cure returns close to its
point of origin. Then one adjusts the angle up or down until you hit the
point of departure!
For math nerds like bob, see here for more details
than you care to know about torus and its geodesics.