Classifying knots: topology and invariants | Tangente

Take a piece of string and join its two ends: you now have an unknot, also known in knot theory as the trivial knot. If you tie the string before joining its ends, you get a trefoil knot. So knots are easy to make.

For a mathematician, a knot is simply a closed curve in three-dimensional space with no self-intersections. Two knots are said to be equivalent if one can be deformed into the other without ever cutting the string. Since a knot's strands are flexible by definition, mathematicians have developed a theory of knots within topology, the study of malleable shapes—a kind of "rubber-sheet geometry," as it is sometimes called.

Three moves are all it takes --------------------------------