Talk:Borromean rings

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Can this arrangement be twisted about into a Mobius Strip? THAT would be weird. Same surface continuity, no two rings connected, yet "one" complex. I can't get my mind around that! bt -- unsigned comment by anonymous IP 68.102.13.50, 06:48, 26 August 2006

[edit] clarification

Why wouldn't you be able to form this figure from regular circles? Or should it say from two-dimensional figures, as the linkages require overlap? -- nae'blis _(talk) 20:27, 1 February 2006 (UTC)

No -- you can't do it with exact geometric circles. Take a close look at the picture. Michael Hardy 21:19, 1 February 2006 (UTC)

I can assure you that I designed my tattoo [1] using geometric circles as the basis - can you explain that to me again? Is the 2.ε-dimensional overlap the 'impossibility', or the shape of the ellipse/circle? -- nae'blis _(talk) 23:28, 1 February 2006 (UTC)

I didn't mean you can't make 2-dimensional pictures of it with exact circles. In the first place, any two of the circles would have to be in two different planes; otherwise they would have common points rather than being linked. That means we need to embed them in a three-dimensional space. I was speaking of the actual circles, not of pictures of them. So is this article. Michael Hardy 23:46, 1 February 2006 (UTC)

Thanks, I'll make a small clarification to the opening paragraph for those who aren't as adept at topology. -- nae'blis _(talk) 15:12, 2 February 2006 (UTC)

OK, I've found a reference: B. Lindström, "Borromean Circles are Impossible", American Mathematical Monthly, volume 98 (1991), pages 340—341. I'm going to add that to the article.

But anyway, it seems you had in mind 2-dimensional pictures in which the circles are perfect circles. No one has said that those are impossible, and you already see those in the article. Michael Hardy 23:59, 1 February 2006 (UTC)

I've not seen the Math Monthly article, but I learned about it first from a short note by Ian Agol. The proof is fairly simple but ingenious. I don't know if we need two references, but this has the advantage of being freely available through the Internet (instead of say, through JSTOR). --Chan-Ho (Talk) 01:34, 2 February 2006 (UTC)

I made a variation of Borromean Rings with a tangle toy. Each ring is pringle shaped, though.

[edit] Recent edits

The recent edits have, in my opinion, been rather lacking. Poor wording and even misleading statements have been inserted. --Chan-Ho (Talk) 20:33, 12 March 2007 (UTC)

I do like the introduction of gallery tags. Anyway, I changed some things. --Chan-Ho (Talk) 00:04, 14 March 2007 (UTC)