Delightful video on the lambda calculus and other compution concepts https://www.youtube.com/watch?v=RcVA8Nj6HEo
Reminds me of a Pynchon novel or my favorite lyrics from The Dismemberment Plan.
"So in the end, whatever, we die, we dissolve / Equations unbalanced, riddles unsolved / And we were never connected or involved / Except for the intersections and crazy mathematics / With no time and no space and no schedule and no place."
However, my best rank was 12. That’s twelve, in case you misunderstand the numbers. I was literally the worst player in the entire league.
I don’t think that there’s anyone out there who is much worse than I am.
I was curious what they used to generate the graphic's and it's their own tool:
BRB going to go make hyperbolic outer billards art
From Tabachnikov's book Geometry and Billiards:
Classical mechanics and geometrical optics, discussed in this chapter, are intimately related. The configuration trajectories of mechanical systems are extremals of a variational principle, similar to the trajectories of light. In fact, mechanics can be described as akind of geometrical optics; this was Hamilton’s approach to mechanics(see [3] for details). The brachistochrone problem is a good example of this optics-mechanics analogy.
Could also be the Stars of David (1m46s) and swastikas (2m24s) that end up drawn by the repeating patterns.
Personally I found that the videos instantly made some group theory aspects of this stand out. Maybe I'm completely off, and that's not really how this is approached, but now I have a question/idea as a foil which I can use to look a bit deeper. In any case, the animation SW came from a researcher in the field, I don't think they are doing this to generate junk food, but to solve actual problems in their field.
Outer billiards is a basic dymamical system which serves as a toy model for celestial mechanics....
I tried as hard as possible to write a proof that is independent from Billiard King [the visualization SW], but still the reader of this paper would get a much greater appreciation for what is going on by learning to use Billiard King. A few minutes playing with Billiard King is worth hours of reading the paper.
https://arxiv.org/pdf/math/0702073
edit:
ah, and here is a Dogru & Tabachnikov paper where they make the connection between this problem and celestial mechanics clear. Very readable!
https://drive.google.com/file/d/1sm47vPUwDqfcY-IGEKSoKIBqyqr...