Editing Writhe (section)

{{Short description|Invariant of a knot diagram}}
In [[knot theory]], there are several competing notions of the quantity '''writhe''', or <math>\operatorname{Wr}</math>. In one sense, it is purely a property of an oriented [[link (knot theory)|link]] diagram and assumes [[integer]] values. In another sense, it is a quantity that describes the amount of "coiling" of a [[knot (mathematics)|mathematical knot]] (or any [[curve|closed simple curve]]) in three-dimensional space and assumes [[real numbers]] as values. In both cases, writhe is a geometric quantity, meaning that while deforming a curve (or diagram) in such a way that does not change its topology, one may still change its writhe.<ref name=bates_dnatopology_2005 />