A three-torus is the boundary of the solid three torus, just like the two-torus is the surface of a solid donut. You can imagine it as a cubical room where each wall/ceiling/floor is a portal to the opposite-facing wall (i.e. the wall to your right is a portal that sends you to your left), but preserves orientation (when you walk out of the portal, your heart is still on your left).
You can also think of it as a world where your position is described by three coordinates (like x, y, and z in Euclidean space), but each coordinate corresponds to an angle on the unit circle. If you go far enough in one coordinate, you loop back to where you started (360 degrees is the same as 0 on a circle).
No comments:
Post a Comment