Brunnian link - Revision history

AnonMoos at 18:28, 29 April 2013

2013-04-29T18:28:16Z

← Older revision		Revision as of 14:28, 29 April 2013
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	The name Brunnian is after Hermann Brunn, whose 1892 article ''Über Verkettung'' included examples of such links.		The name Brunnian is after Hermann Brunn, whose 1892 article ''Über Verkettung'' included examples of such links.

	The best-known and simplest possible Brunnian link is the [[L6a4\|Borromean rings]], a link of three unknots. (This is also the only Brunnian link ~~contained~~ in ~~tables~~ ~~which~~ ~~don't~~ ~~include~~ ~~links~~ with 12 or ~~more~~ crossings.) However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some relatively simple three-component Brunnian links which are not the same as the Borromean rings:		The best-known and simplest possible Brunnian link is the [[L6a4\|Borromean rings]], a link of three unknots. (This is also the only Brunnian link with less than 10 crossings, and the only symmetrical Brunnian link with less than 12 crossings.) However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some relatively simple three-component Brunnian links which are not the same as the Borromean rings:

	<gallery>		<gallery>
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	==See also==		==See also==
			*[[L10a140]]
			*[[L11a434]]
			*[[L11n436]]
	*[["Rubberband" Brunnian Links]]		*[["Rubberband" Brunnian Links]]

			==Further reading==
	T.Kanenobu, Hyperbolic links with Brunnian properties. J. Math. Soc. Japan. Vol 38 No. 2, (1986) 295--308.		T.Kanenobu, Hyperbolic links with Brunnian properties. J. Math. Soc. Japan. Vol 38 No. 2, (1986) 295--308.

AnonMoos at 00:10, 9 July 2010

2010-07-09T00:10:48Z

← Older revision		Revision as of 20:10, 8 July 2010
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	==Non-Borromean-rings Brunnian links in real world symbols==		==Non-Borromean-rings Brunnian links in real world symbols==
	[[Image:Selo Rito Brasileiro.jpg\|thumb\|Brazilian Masonic emblem with three interlaced triangles]]		[[Image:Selo Rito Brasileiro.jpg\|thumb\|Brazilian Masonic emblem with three interlaced triangles]]
	A version of the three interlaced triangles (18-crossings Brunnian link) is also found ~~in the~~ in the sixth century Marundheeswarar Temple in Thiruvanmayur, South Chennai, India, associated with the goddess Tripurasundari,[http://www.liv.ac.uk/%7Espmr02/rings/maths.html] and is occasionally called "the star of the muses" as a minor symbol in some New Age / occultist / neo-pagan circles.		A version of the three interlaced triangles (18-crossings Brunnian link) is also found in the sixth century Marundheeswarar Temple in Thiruvanmayur, South Chennai, India, associated with the goddess Tripurasundari,[http://www.liv.ac.uk/%7Espmr02/rings/maths.html] and is occasionally called "the star of the muses" as a minor symbol in some New Age / occultist / neo-pagan circles.

	==See also==		==See also==

AnonMoos: /* Non-Borromean-rings Brunnian links in real world symbols */

2010-07-09T00:07:27Z

Non-Borromean-rings Brunnian links in real world symbols

← Older revision		Revision as of 20:07, 8 July 2010
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	==Non-Borromean-rings Brunnian links in real world symbols==		==Non-Borromean-rings Brunnian links in real world symbols==
	[[Image:Selo Rito Brasileiro.jpg\|thumb\|Brazilian Masonic emblem with three interlaced triangles]]		[[Image:Selo Rito Brasileiro.jpg\|thumb\|Brazilian Masonic emblem with three interlaced triangles]]
			A version of the three interlaced triangles (18-crossings Brunnian link) is also found in the in the sixth century Marundheeswarar Temple in Thiruvanmayur, South Chennai, India, associated with the goddess Tripurasundari,[http://www.liv.ac.uk/%7Espmr02/rings/maths.html] and is occasionally called "the star of the muses" as a minor symbol in some New Age / occultist / neo-pagan circles.

	==See also==		==See also==

AnonMoos at 00:04, 9 July 2010

2010-07-09T00:04:02Z

← Older revision		Revision as of 20:04, 8 July 2010
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	T. Kanenobu has proven there exist hyperbolic Brunnian links with arbitrarily many components.		T. Kanenobu has proven there exist hyperbolic Brunnian links with arbitrarily many components.

			==Non-Borromean-rings Brunnian links in real world symbols==
			[[Image:Selo Rito Brasileiro.jpg\|thumb\|Brazilian Masonic emblem with three interlaced triangles]]

	==See also==		==See also==

AnonMoos at 07:03, 4 July 2010

2010-07-04T07:03:04Z

← Older revision		Revision as of 03:03, 4 July 2010
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	Image:Three-triang-18crossings-Brunnian.gif\|18-crossing link.		Image:Three-triang-18crossings-Brunnian.gif\|18-crossing link.
	Image:Three-squares-Brunnian-24crossings.png\|24-crossing link.		Image:Three-squares-Brunnian-24crossings.png\|24-crossing link.
			Image:Three-interlaced-pentagons-Brunnian-30crossings.png\|30-crossing link.
	</gallery>		</gallery>

AnonMoos: add

2010-03-13T20:37:59Z

add

← Older revision		Revision as of 16:37, 13 March 2010
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	Image:Brunnian-3-not-Borromean.gif\|12-crossing link.		Image:Brunnian-3-not-Borromean.gif\|12-crossing link.
	Image:Three-triang-18crossings-Brunnian.gif\|18-crossing link.		Image:Three-triang-18crossings-Brunnian.gif\|18-crossing link.
			Image:Three-squares-Brunnian-24crossings.png\|24-crossing link.
	</gallery>		</gallery>

AnonMoos: /* Links */

2010-02-04T22:29:53Z

Links

← Older revision		Revision as of 18:29, 4 February 2010
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	==Links==		==Links==
	*[http://en.wikipedia.org/wiki/Brunnian_link Wikipedia article "Brunnian link"]		*[http://en.wikipedia.org/wiki/Brunnian_link Wikipedia article "Brunnian link"]
	*[http://www.mi.sanu.ac.yu/vismath/bor/bor1.htm "Are Borromean Links so Rare?", by Slavik Jablan]		*[http://www.mi.sanu.ac.yu/vismath/bor/bor1.htm "Are Borromean Links so Rare?", by Slavik Jablan] ([http://www.scipress.org/journals/forma/abstract/1404/14040269.html Original journal site])

AnonMoos at 13:35, 3 December 2009

2009-12-03T13:35:22Z

← Older revision		Revision as of 09:35, 3 December 2009
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	[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]		[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]
			[[Image:6Loops-Brunnian-link.png\|right\|200px\|thumb\|Six-component Brunnian link.]]

	A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).		A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).

Drorbn: Reverted edits by ChiolOorro (Talk); changed back to last version by Rybu

2008-12-17T11:52:12Z

Reverted edits by ChiolOorro (Talk); changed back to last version by Rybu

← Older revision		Revision as of 07:52, 17 December 2008
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	racmonlicboc
	[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]		[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]

	A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).		A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).

	The name Brunnian is after Hermann Brunn, whose 1892 article ''~~Ãber~~ Verkettung'' included examples of such links.		The name Brunnian is after Hermann Brunn, whose 1892 article ''Über Verkettung'' included examples of such links.

	The best-known and simplest possible Brunnian link is the [[L6a4\|Borromean rings]], a link of three unknots. (This is also the only Brunnian link contained in tables which don't include links with 12 or more crossings.) However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some relatively simple three-component Brunnian links which are not the same as the Borromean rings:		The best-known and simplest possible Brunnian link is the [[L6a4\|Borromean rings]], a link of three unknots. (This is also the only Brunnian link contained in tables which don't include links with 12 or more crossings.) However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some relatively simple three-component Brunnian links which are not the same as the Borromean rings:

ChiolOorro: cocnale

2008-12-17T02:48:49Z

cocnale

← Older revision		Revision as of 22:48, 16 December 2008
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			racmonlicboc
	[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]		[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]

	A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).		A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).

	The name Brunnian is after Hermann Brunn, whose 1892 article ''~~Über~~ Verkettung'' included examples of such links.		The name Brunnian is after Hermann Brunn, whose 1892 article ''Ãber Verkettung'' included examples of such links.

	The best-known and simplest possible Brunnian link is the [[L6a4\|Borromean rings]], a link of three unknots. (This is also the only Brunnian link contained in tables which don't include links with 12 or more crossings.) However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some relatively simple three-component Brunnian links which are not the same as the Borromean rings:		The best-known and simplest possible Brunnian link is the [[L6a4\|Borromean rings]], a link of three unknots. (This is also the only Brunnian link contained in tables which don't include links with 12 or more crossings.) However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some relatively simple three-component Brunnian links which are not the same as the Borromean rings:

← Older revision		Revision as of 09:35, 3 December 2009
Line 1:		Line 1:
	[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]		[[Image:Brunnian.gif\|right\|200px\|thumb\|This four-component link is a Brunnian link.]]
			[[Image:6Loops-Brunnian-link.png\|right\|200px\|thumb\|Six-component Brunnian link.]]

	A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).		A '''Brunnian link''' is a nontrivial link which becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops (so that there is no [[L2a1\|Hopf link]] between any two loops).