[HN Gopher] Knot Theory and its Applications [pdf]
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Knot Theory and its Applications [pdf]
Author : jpcooper
Score : 57 points
Date : 2021-01-17 12:51 UTC (10 hours ago)
(HTM) web link (www.maths.ed.ac.uk)
(TXT) w3m dump (www.maths.ed.ac.uk)
| mjul wrote:
| One of my favourite applications of knot theory is to classify
| all aesthetic tie knots, using topology to uncover unknown
| sartorial gems. It is a great piece of research from Cambridge, a
| short and accessible paper called "Tie knots, random walks and
| topology" by Thomas M.A. Fink and Yong Mao published in Physica A
| 276 (2000) 109-121.
|
| It is available on the authors' home page:
|
| http://www.tcm.phy.cam.ac.uk/~tmf20/
| amenghra wrote:
| http://www.tcm.phy.cam.ac.uk/~tmf20/TIES/PAPERS/paper_physic...
| carapace wrote:
| Hey, they wrote a book!
|
| https://en.wikipedia.org/wiki/The_85_Ways_to_Tie_a_Tie
| EarthIsHome wrote:
| Thanks for sharing this! I've gotten into knot tying in the new
| year, and keep finding applications and things to do with knots.
|
| Here are some other resources I've used: Ashley Book of Knots
| [0], Grog's animated knots [1], and youtube.
|
| A lot of useful knots build on basic knots and variations of
| basic knots. More complex knots used to be daunting to me (trying
| to memorize how to tie the whole thing). But they become easier
| when you can recognize the basic knots used in the complex ones.
| Learning the use cases for the knots also helped.
|
| [0]: https://archive.org/details/TheAshleyBookOfKnots/mode/2up
|
| [1]: https://www.animatedknots.com/
| mb7733 wrote:
| I think learning and tying knots is cool too, but just a heads
| up, the mathematical knot theory discussed in the OP is not
| related to that. It's a branch of topology that studies the
| possible shapes and transformations of closed curves in 3-space
| (without self intersection).
|
| It's not concerned with practical properties of knots tied with
| rope, like strength, stability, ease of use, etc.
| amelius wrote:
| But the title says "... and its Applications". Is tying
| actual knots not an application of knot theory?
| gjm11 wrote:
| The applications mentioned in the book are to chemistry and
| to molecular biology. (As well as another, mentioned only
| fairly briefly, elsewhere in pure mathematics, to what's
| called the classification of 3-manifolds.)
| jpcooper wrote:
| Thanks for the links. I memorised a number of decorative knots
| as a kid, but it never really occurred to me then that they
| were formed of smaller parts. That didn't seem to be necessary
| at the time. Also, you do have prime knots, which are not
| decomposable in a certain way.
| noman-land wrote:
| I've always loved knots and have learned a few cool ones
| throughout my life, some useful, some just cool. But I've
| always wanted to learn the discipline more holistically. I
| wanna "get" knots and be able to think in knots.
|
| What kind of cool uses have you found for your new knot skills?
|
| Any recommendations for learning how to "get" knots other than
| just looking at knots in books?
| niccl wrote:
| I end up using knots quite a lot. I cycle so when I need to
| transport stuff I reach for the piece of parachute cord I
| keep in my backpack and tie things to bike rack with
| harvester's hitch, bowline, round turn and two, clove hitch,
| as appropriate. Also, instead of using a ratchet tie down ona
| trailer load, try using knot skills to keep things in place.
| That way you get a really practical feel for what type of
| know does what, and then Ashley or other things can take you
| further in a particular direction
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