All knots are trivial: a "proof" by sleight of hand

TL;DR

The paper explores a mathematical analogy to a magic trick involving knots, introducing 'knotholder diagrams' to show all knots can be represented similarly, thus generalizing the trick to all knots.

Contribution

It introduces 'knotholder diagrams' and proves that every knot admits such a diagram, enabling a universal magic trick analogy for all knots.

Findings

All knots can be represented by knotholder diagrams.

The trick can be generalized to produce any knot from the unknot.

The approach links knot theory with a visual, magic trick analogy.

Abstract

We take a close look at a classical magic trick performed with a string, where a trivial knot is seemingly isotoped into a trefoil, and generalize it to a family of magic tricks for transforming the unknot into other knots. We encode such a trick by depicting the target knot as a special type of knot diagram, which we call a "knotholder diagram". By proving that all knots admit knotholder diagrams, we obtain variants of the trick for producing every knot.