Talk:Brunnian link

RFE

the Borromean_rings artice mentions that you cannot make borromean rings from exact circles because it's a brunnian link, but there's no mention on this page of that. Would anyone care to eludicate? -- 01:17, 27 July 2008 User:Paul Murray

None of the images on this page are drawn with circles, or would be easy or natural to draw with circles. If something is only relevant to the Borromean rings (not to other Brunnian links), then it should be discussed there, not here... AnonMoos (talk) 12:46, 27 July 2008 (UTC)[reply]

Why Borromean simplest?

Wouldn't the link with two circles by Brunnian? (Or even just one circle, as a degenerate case?)--345Kai (talk) 00:45, 11 May 2009 (UTC)[reply]

It's the simplest non-degenerate case (I didn't think it necessary to add "non-degenerate", but do so if you see fit). People often find the properties of the Borromean rings to be surprising, but no one finds the analogous properties of two interlinked loops or one unlinked loop to be surprising... AnonMoos (talk) 02:40, 11 May 2009 (UTC)[reply]

Two more images from commons

Interlaced-Triangles Brunnian-link alternate.svg
Interlaced-Triangles quasi-Arabesque Brunnian-link.svg

They're not by me but they're nice. Hyacinth (talk) 10:26, 27 December 2009 (UTC)[reply]

Thanks, they're just ornamental versions of Image:Brunnian-3-not-Borromean.png... AnonMoos (talk) 13:23, 16 January 2010 (UTC)[reply]

It's not at all obvious to me that these are not just Borromean links. Why are you convinced that these are not each equivalent to the Borromean link?50.205.142.35 (talk) 20:33, 9 December 2019 (UTC)[reply]

50.205.142.35 -- File:Brunnian-3-not-Borromean.png has twelve basic crossings (the number cannot be reduced without destructive operations), while the Borromean rings have six basic crossings... AnonMoos (talk) 23:18, 21 September 2020 (UTC)[reply]

And of course I made a mistake in 2010: those two are ornate versions of File:Three-triang-18crossings-Brunnian.svg. It's File:Brunnian-link-12crossings-nonBorromean-quasi-Arabesque.svg which is an ornate version of Brunnian-3-not-Borromean.png ... -- AnonMoos (talk) 00:53, 23 September 2020 (UTC)[reply]

Where the word "simplest" means what, exactly?

It's a very bad idea to invent concepts without telling the reader what these concepts mean.

If by "simpler" all is meant is that the minimal number of crossings in a planar link diagram is fewer ... then please say so.

Otherwise it is far better not to mention such a concept unless it will be defined somewhere.50.205.142.35 (talk) 20:30, 9 December 2019 (UTC)[reply]

The Borromean rings have six crossings, while it seems exceedingly likely (though I'm not sure whether it's been strictly mathematically proven) that all other Brunnian links have 10 or more crossings. That seems fairly intuitive... AnonMoos (talk) 23:27, 21 September 2020 (UTC)[reply]