Borromean Rings & Hopf Links

 

Three loops, each one linked to both of the others, is called by mathematicians the “Hopf Links”.

Amazingly it is possible to have three rings, none of which is linked to either of the others, and yet in combination cannot be separated.  This is called the “Borromean Rings” and was used as the logo of a famous brand of beer.

Hopf Links

This is a rectilinear rendering of these two links.  Look carefully at the Borromean Rings.  If any one of the three links is removed, the other two can then be separated.

Borromean Rings