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Why Knot? An Introduction to Knot Theory
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- Опубліковано 17 сер 2024
- A short introduction to topology & knot theory, in particular crossing number, Reidemeister moves, and applications of knot theory.
Special thanks to Bob Davis who taught my Knot Theory course, Brandon Carter for reviewing the script, and DJ Moore for lending his notes.
Works Cited
Budworth, Geoffrey. The Knot Book. Right Way, 2012.
Farhi, Edward, et al. “Quantum Money from Knots.” Proceedings of the 3rd Innovations in Theoretical Computer Science Conference on - ITCS '12, 2012, doi:10.1145/2090236.2090260.
Konczakowski, Feliks Tomasz. “Money Business.” Tumblr, Konczakowski, 16 Oct. 2016, 66.media.tumblr.com/ac8fceabc9c88e5748d8a8a2b2d1dc59/tumblr_oafo2gQSWJ1txeruoo1_500.gif.
Reichmann, Alexander. “How to Identify Counterfeit Bills.” ITestCash.com, ITestCash.com, 16 Oct. 2018, www.itestcash.com/blogs/news/how-to-identify-counterfeit-bills.
Reidemeister, L. Kurt Reidemeister. 1930.
“Supercoil Me! The Art of Knotted DNA Maintenance.” Phys.org - News and Articles on Science and Technology, Phys.org, 6 July 2018, phys.org/news/2018-07-supercoil-art-dna-maintenance.html.
Weisstein, Eric W. “Reidemeister Moves.” From Wolfram MathWorld, mathworld.wolfram.com/ReidemeisterMoves.html.
I like the way the video is organized. And how important information is clearly shown. Wonderful!!!
I’ve watched 10 videos regarding knot theory, and this was the first one that clearly explains it for me. Thanks!
Im so glad to hear it! Glad you enjoyed :)
I was looking at knots on google images and accidentally stumbled into knot theory. This video was way helpful (much better than wikipedia). Thanks!
That is exactly how I found this video
I'm glad that I could help!
Fascinating!
These videos are very well made! I can't believe you have only 8 subscribers
Could you possibly do a video on the hanging-a-painting puzzle? Where you must hang a painting on n hooks such that removing any k of them (but no less) causes the painting to fall? I would very much love to see one
I didn't know about the hanging-a-painting puzzle before, but that looks super interesting! I'll look into making a video about it soon :)
Why knot
Great video!
low sound
Can you show us how to calculate the Jones polynomial?
aplication?(so that i can decide to take course or not)
What got you interested in knot theory?
I took a summer course in knot theory and fell in love with it... would you be interested in more videos like this?
@@abbygeigerman I'm personally a big fan. Knot theory is a great introduction to topology imo. I've actually been working on an unknotting algorithm to untangle knots using Reidemeister moves for the past couple of months. It's been a wild ride. My suspicion is that the unknotting problem is actually solvable in polynomial time, but no better way to find out than to solve it! I would love to correspond with you about my ideas surrounding knot theory. I literally have no one to talk to. :)
HARIZ Knot theory is relatively easy to get into is you understand a little about Topology, Set Theory, and Recursion (for Johnson Polynomials). I’m not the best expert, but knot theory is often praised for being understandable without an extensive mathematical background. Watch some UA-cam video from Math at Andrews University and you should get a good overview. Also search for Johnson Polynomials for Dummies, which is a great didactic resource
love knot theory too, I just don`t like this 3rd Riemann move. it's really complicated and there's a whole thing called virtual knots that I found looking for stuff to analyze them.
Came to see the effects of knots in stress strain curve and ended in knot theory
😂😂😶
She's so quiet