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?

(In reply to re: solution by Tristan)

Then what has to happen is that the one that had been around the outer surface going through the hole in the center must become one on the inner surface that goes around the whole, and vice verso, so the rings are still linked.

Posted by Charlie on 2007-01-02 13:34:37