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/torus-demo.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 cross-sections. The simplest ones are the analog of the equator on a sphere, or the circular cross-sections of the surface with quantum numbers (1,0) and (0,1) for the number of loops around the vertical axis and around the cross-sections.
  
  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.