I’ve lately become a fan of the famous BORROMEAN RINGS; since they’re so exciting, we’ll call them Bor. Rings for short, and cut right to the chase.
They look like they’re tightly knotted, but if you look closely you’ll see that no two rings are linked with each other. Maybe it’s obvious why this is… For starters, the OVER-UNDER-OVER-UNDER pattern we use to draw them seems to suggest a sort of EVEN-ODD-EVEN-ODD pattern; and since each ring encounters first ONE other ring and then THE OTHER other ring and then back to the ONE other ring, it’s always either OVER or UNDER any other single ring, but never both.
Maybe it would help to have the rings in color so we could see this working at each crossing…
So what if we have two rings? Strangely enough, our EVEN-ODD rule goes out the window, and now the rings are ALL linked with every other ring…
And what if we were to have three rings woven together like so?
You guessed it — now they’re NOT linked with any other single ring once again.
Hmmm, I guess I’ll never get bored of the rings….
The three rings woven together are so pretty. Your drawing ability and descriptions are amazing. I could never picture what is happening here with only the Wikipedia explanation.
As with art, so with math… It’s all about exploration & questioning & discovery! I was up in the coffee fields of Nicaragua drawing rings with the kids between math classes yesterday at La Hermandad, Nicaragua ( https://marekbennett.com/tag/la-hermandad )…
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