Descrizione
With Sabetta Matsumoto and Saul Schleimer.
It seems impossible, but you can make a giant loop out of lots of little (not very stretchy) loops. So you can wrap a broken suitcase using hair ties, without any cutting or knotting. Or you can finish off a rubber band bracelet without using a clip and, again, without any cutting or tying knots. We explain the problem, the solution, and some of the mathematics behind it all.
Links and references:
Snappy - computer program for analysing knots, links, and manifolds - https://snappy.computop.org/
Mathoverflow question (by Anton Petrunin) -
https://mathoverflow.net/questions/424215/can-i-wrap-a-suitcase-with-hair-ties
Anton Petrunin - https://anton-petrunin.github.io/
Michael Freedman - https://en.wikipedia.org/wiki/Michael_Freedman
Larsen Linov - https://math.berkeley.edu/~linov/
Mathematics:
Hopf link - https://en.wikipedia.org/wiki/Hopf_link
Borromean rings - https://en.wikipedia.org/wiki/Borromean_rings
Hyperbolic geometry - https://en.wikipedia.org/wiki/Hyperbolic_geometry
Hyperbolic links - https://en.wikipedia.org/wiki/Hyperbolic_link
https://bookstore.ams.org/cdn-1598077516917/gsm-209
Linking number - https://en.wikipedia.org/wiki/Linking_number
Milnor invariants -
J. Milnor. Link groups. Ann. of Math. (2), 59:177–195, 1954
For an introduction to hyperbolic geometry and its application to knot theory we recommend Jessica Purcell's book "Hyperbolic Knot Theory" - https://users.monash.edu/~jpurcell/hypknottheory.html
Loom bracelets:
https://youtu.be/4rIQ77bpNEo - Fishtail Loom Bracelet - Tutorial || Rainbow Loom
https://youtu.be/VYcca5rC_10 - How to Make a Boxed Bow Bracelet - EASY design on the Rainbow Loom
https://youtu.be/ah2KQGi8Swk - Rainbow Loom! DIY 5 Easy Rainbow Loom Bracelets without a Loom (DIY Loom Bands)