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Topic: Unknot

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	PlanetMath: unknot
		The unknot is the knot with a projection containing no crossings, or equivalently the knot with three vertices.
		This is version 3 of unknot, born on 2002-12-19, modified 2002-12-20.
		Object id is 3777, canonical name is Unknot.
	planetmath.org /encyclopedia/Unknot.html (66 words)

	Definition of unknot - Merriam-Webster Online Dictionary
		Learn more about "unknot" and related topics at Britannica.com
		Find more about "unknot" instantly with Live Search
		See a map of "unknot" in the Visual Thesaurus
	www.m-w.com /cgi-bin/dictionary?book=Dictionary&va=unknot (38 words)

	[No title] (Site not responding. Last check: )
		Even > with this improvement, however, the algorithm is not one you would want in > the inner loop of a program." Joel Hass told me that the unknot, drawn with a single crossing, was input into said program, and after three days the computer said (correctly) that it was the unknot.
		It is interesting to note that Haken's algorithm only recognizes the unknot.
		However, while unknot recognition is in NP, their algorithm for genus has higher complexity, maybe P^#P -- their paper in the proceedings of FOCS '97 says PSPACE but I think Pippenger said something smaller at the actual conference talk.
	www.math.niu.edu /~rusin/known-math/97/unknot.progs (502 words)

	Problems in Knot Theory
		Is it true that every unknotting number 1 knot (which is 1-adjacent to the unknot) is 2-adjacent to the unknot?
		For example, is it true that a double knot is 2-adjacent to the unknot iff it is the trefoil or the figure eight knot?
		Suppose K, K' both are unknots in R, is there a sequence of unknots in R such that
	math.ucr.edu /~xl/knotprob/knotprob.html (909 words)

	Read This: Why Knot? An Introduction to the Mathematical Theory of Knots
		After the trefoil knot is introduced, it is carefully noted that no amount of fiddling with the knot and not being able to untie it can show that it is not equivalent to the unknot.
		The existence of such a coloring is unchanged by Reidemeister moves and hence is a knot invariant.
		Since the unknot clearly does not have such a coloring, the trefoil and the unknot are indeed distinct.
	www.maa.org /reviews/whyknot.html (868 words)

	Unknot Equivalence
		denote the trivial (0-crossing) diagram of the unknot.
		M* denote the set of diagrams which may result when a finite sequence of moves from the set M is applied to D.
		conjecture 3 : any unknot diagram with crossings can be simplified by locating a line segment with a sequence of all-over or all-under crossings with endpoints in the infinite planar region, removing the segment and replacing it with an arc in the infinite planar region [proved false by counter-example - e.g.
	f2.org /maths/kt/unknoteq.html (1078 words)

	UNKNOT Links On The Homeless Search Engine - Fighting Homelessness & UNKNOT With unknot Resources (Links) (Site not responding. Last check: )
		Please submit a URL related to unknot that could help out others in the future.
		The unknot is a loop of rope without a knot in it.
		A knot theory might describe the unknot as the standard embedding of the circle, though any knot that can be 'untied' to give this would
	www.sparesomechange.com /search/engine/?find=unknot (236 words)

	Research Page (Site not responding. Last check: )
		The simplest example of a knot, a single unknotted loop, is called an unknot.
		No matter how the strands of a rubber band are twisted, poked, or slid, it will remain topologically equivalent to an unknot since we can untwist, unpoke, and unslide the rubber band back into a single unknotted loop.
		No matter how we twist, poke, or slide the strands of the trefoil knot, it never looks like the single unknotted loop of the rubber band.
	www.uwosh.edu /faculty_staff/pricek/Talks_files/Knots.html (198 words)

	unknot - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "unknot" is defined.
		Unknot : Online Plain Text English Dictionary [home, info]
		Words similar to unknot: unpick, unravel, unscramble, untangle, disentangle, more...
	www.onelook.com /?w=unknot&ls=a (147 words)

	Unknot Registry (Site not responding. Last check: )
		The unknot is the simplest knot: just a loop.
		This Unknot Registry catalogues some unknot diagrams - knot pictures which can be untangled completely.
		Decided that exploration of unknot projections is in order.
	f2.org /maths/kt/unknotreg.html (118 words)

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