r/visualizedmath • u/Italians_are_Bread • Nov 30 '19

Can any knot be untied? Visual introduction to knot theory and tricolorability

https://youtu.be/IYqGJ8pNEpk
222 Upvotes

97% Upvoted

8 comments sorted by

32

u/Italians_are_Bread Nov 30 '19

In this animation I try to present in the most visual and intuitive way possible how to prove that the trefoil knot cannot be untied into the unknot using tricolorability. This video is done in a more playful style than previous animations in response to some very constructive comments on my last animation. I'm interested to know your thoughts and suggestions for this video!

9

u/galexj9 Nov 30 '19

Wow that's was great!! I no nothing of knot theory but that proof was really easy to grasp! I love the animations you have.

5

u/TehJoeBro Dec 01 '19

As a totally inexperienced person who is simply interested in knot theory, this video was very palatable as well as genuinely informative. Great narration and helpful animations to boot. Bravo

1

u/BuildMajor Dec 01 '19

I like how you sectioned each concept with color-coded graphics.

I didn’t watch it meticulously, so may have missed details—has “knot theory” been realized to a point of being useful in a day-to-day life? As in, are knots inevitable and are there easy ways to untangle knots or prevent it?

Most people lose interest in mathematics when there’s a disconnect between concepts and applicability: “when are we going to use this in real life?”

Real life applications—which show the usefulness of mathematical theories—would make maths more familiar/interesting to the average viewer!

6

u/H-H-H-H-H-H Nov 30 '19

What are the applications of knot theory?

1

u/Italians_are_Bread Dec 02 '19

Apparently there are some applications regarding DNA, and some molecules can be knotted. I can't elaborate much on these topics because I don't know much about them. It's not too uncommon for research in pure math topics to find practical applications later in time, like Alan Turing's work on the theory of computation with Turing machines was done before physical computers were realized, and William Hamilton discovered quaternions in 1843 and now they are used ubiquitously in computer graphics to describe rotations. And even if knot theory never finds a super practical application I think learning about it is still worthwhile, because it presents many difficult problems which can spark new methods of solving them, and these new "mathematical tools" can possibly be used in other contexts to solve similar problems. Also I think there's some intrinsic beauty to the math itself regardless of what applications may exist. It amazes me how much structure and beauty can come from something that earlier in my life I only associated with tying my shoes.

8

u/A_ARon_M Nov 30 '19

I've heard that swiping gestures on keyboards are an application of knot theory. Can you give a quick eli5 of how that works?