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

• Published in 2026
• Added on 2026-04-27

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.

Links

• https://arxiv.org/abs/2604.13799v1
• https://arxiv.org/pdf/2604.13799v1

Other information

BibTeX entry

@article{Allknotsaretrivialaproofbysleightofhand,
	key = {Allknotsaretrivialaproofbysleightofhand},
	type = {article},
	title = {All knots are trivial: a "proof" by sleight of hand},
	author = {Raphael Appenzeller and Jos{\'{e}} Pedro Quintanilha},
	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.},
	comment = {},
	date_added = {2026-04-27},
	date_published = {2026-04-27},
	urls = {https://arxiv.org/abs/2604.13799v1,https://arxiv.org/pdf/2604.13799v1},
	collections = {fun-maths-facts,the-groups-group,things-to-make-and-do},
	url = {https://arxiv.org/abs/2604.13799v1 https://arxiv.org/pdf/2604.13799v1},
	urldate = {2026-04-27},
	year = 2026,
	archivePrefix = {arXiv},
	eprint = {2604.13799},
	primaryClass = {math.GT}
}