A torus is a surface shaped like a donut. Imagine that I've painted two rings on a torus. One is on the outer surface, and goes through the hole in the center, coming around from the other side. The other ring is on the inner surface, and goes all the way around the hole in the center. These two rings of paint are linked.

I then cut a small hole in the torus. Through this hole, I turn the torus inside-out.

In the process, the rings of paint switch from the outer surface to the inner surface and vice versa. Therefore, they have become unlinked. How?

This isn't as complicated as it first seems. Two perpendicular rings are painted, on different surfaces, around a torus. When the torus is turned inside out, the ring on the inner surface remains in the hole, but on the outside surface. The ring that had gone through the hole on the outside surface is now on the inside surface, so it doesn't exactly go "through" the hole anymore. The rings are now unlinked.

Posted by Bean on 2007-01-06 18:16:09