Online Textbook for Braid groups and knots and tangles(matthematics.com)
matthematics.com
Online Textbook for Braid groups and knots and tangles
https://matthematics.com/redoak/redoak.html
5 comments
Wait, Matthew Salomone is the lead of Klein Four!
https://youtube.com/watch?v=BipvGD-LCjU
https://youtube.com/watch?v=BipvGD-LCjU
This is really cool. I've always found braids & knots very fascinating (Wonder if that says anything about my particular strain of Autism)
Probably (k)not.
I like them too, including the math of weaving. They are very interesting structures. I spend an unhealthy amount of time playing with my belt *, twisting and knotting them and buckling them shut... reanimating Dirac's trick.
I don't think I am autistic. ADHD, very likely yes.
* Try this. Hold the loop of your buckled belt, so that the buckled is in your right hand and the mid-lengths of your belt in your left hand. Keep your thumbs up and pinky down as you hold the two. Now with your thumb of your left hand, push the top edge inwards to impart one half twist. Do that again. Now your belt will look quite twisted. Now exchange your hand position by moving your right hand towards left and left hand towards right. When you cross let the right hand pass below your left hand.
If you do this right, there might be a surprise waiting. You might have to do it a few times to get it right. Belts have natural variations in their preferred twistings, so it might take a few tries.
I like them too, including the math of weaving. They are very interesting structures. I spend an unhealthy amount of time playing with my belt *, twisting and knotting them and buckling them shut... reanimating Dirac's trick.
I don't think I am autistic. ADHD, very likely yes.
* Try this. Hold the loop of your buckled belt, so that the buckled is in your right hand and the mid-lengths of your belt in your left hand. Keep your thumbs up and pinky down as you hold the two. Now with your thumb of your left hand, push the top edge inwards to impart one half twist. Do that again. Now your belt will look quite twisted. Now exchange your hand position by moving your right hand towards left and left hand towards right. When you cross let the right hand pass below your left hand.
If you do this right, there might be a surprise waiting. You might have to do it a few times to get it right. Belts have natural variations in their preferred twistings, so it might take a few tries.
Man, I got my rope out for this..
On a related note, I was very pleasantly surprised to stumble upon the mojo language GPU Puzzles [0] and to see that they include manim animations for many of the puzzles, and include the source for these in the repo [1]. In this case, they are entirely separate from the actual language constructs, but I imagine that it would be very feasible to have the algebraic structures fully integrated with the code for their visualizations.
[0] https://puzzles.modular.com/
[1] https://github.com/modular/mojo-gpu-puzzles/blob/main/book/s...