When is a knot not a knot?
• Take a piece of string. Tangle it, and thread it though itself, in any way you choose. Glue the ends together. You may well have created a KNOT.
• Take a piece of string. Glue the ends together, tangle it, and thread it though itself, in any way you choose. You may well have created an UNKNOT.
For a succinct introduction to unknots, the simplest possible version of which is illustrated above right, see : Untangling the Unknot, authored for Colby (College) Liberal Arts Symposium by Amar Šehić in 2015.
Further reading : Visual algebraic proofs for unknot detection
Research research by Martin Gardiner