Friday, January 27, 2012

Borromean Rings

I recently figured out that I could take Lilli's teething rings [1] and link them together to make Borromean Rings. Borromean rings are three rings that are interlocked in such a way that no two rings intersect each other.[2] Consider the diagram to the right. If you erase the blue ring, the red and green rings are not linked. But as long as the blue ring is there, none of the rings can be removed. The same is true for erasing the green or red ring. Blacksmith puzzles often work on a similar principle, as do braids and the monkey's fist knot. Ancient drawings or carvings of complete Borromean rings have been found in Italy, Afgahnistan, and Norway (where it is called a valknut); partial Borromean rings are even more common.[3]

Because of the way they're interlinked, it's impossible to make Borromean rings out of true rings. But Lilli's teething rings are actually ellipsoid, so I was able to get away with it. I still can't lay them completely flat, though (top).


[1] She hasn't started teething, yet, but she still likes to play with them.

[2] See rings for a more in-depth treatment.

[3] See rings#History.

Image attributions:

Borromean Rings is by Jim.belk, available at Rings Illusion.png. 

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