One way of showing that a knot diagram represents a knot equivalent to an unknot is to show that the diagram can be transformed into one without crossings by a sequence of atomic moves, known as Reidemeister moves. The relevant background fact is Reidemeister’s theorem, which links the visualizable diagrammatic changes to the mathematically precise definition of knot equivalence: Two knots are equivalent if and only if there is a finite sequence of Reidemeister moves taking a knot diagram of one to a knot diagram of the other. Figure 4 illustrates.  Each knot diagram is changed into the adjacent knot diagram by a Reidemeister move; hence the knot represented by the leftmost diagram is equivalent to the unknot.