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

Raphael Appenzeller; José Pedro Quintanilha

doi:10.5802/crmath.843

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arXiv · 2604.13799

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

Raphael Appenzeller·José Pedro Quintanilha

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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.

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Raphael Appenzeller, José Pedro Quintanilha. 2026-04-15. All knots are trivial: a "proof" by sleight of hand. https://doi.org/10.5802/crmath.843

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