Editing Knot (section)

==Knot theory==
{{main|Knot theory}}
[[Image:TrefoilKnot 01.svg|thumb|right|150px|A [[trefoil knot]] is a mathematical version of an [[overhand knot]].]]

Knot theory is a branch of [[topology]]. It deals with the [[mathematics|mathematical]] analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a [[knot (mathematics)|knot]] is a figure consisting of a single loop with any number of crossing or knotted elements: a closed curve in space which may be moved around so long as its strands never pass through each other. As a closed loop, a mathematical knot has no proper ends, and cannot be undone or untied; however, any physical knot in a piece of string can be thought of as a mathematical knot by fusing the two ends. A configuration of several knots winding around each other is called a ''link''. Various mathematical techniques are used to classify and distinguish knots and links. For instance, the [[Alexander polynomial]] associates certain numbers with any given knot; these numbers are different for the [[trefoil knot]], the [[Figure-eight knot (mathematics)|figure-eight knot]], and the [[unknot]] (a simple loop), showing that one cannot be moved into the other (without strands passing through each other).<ref>{{Cite journal |last1=Nakanishi |first1=Yasutaka |last2=Okada |first2=Yuki |title=Differences of Alexander polynomials for knots caused by a single crossing change |journal=Topology and Its Applications |volume=159 |issue=4 |pages=1016–1025 |doi=10.1016/j.topol.2011.11.023|year=2012 |doi-access=free }}</ref>