The animation in the article looks like a simplified diagram of a rotary engine or a drill that will cut polygon-shaped holes instead of round holes.
The article mentions a connection to the Fourier transform, which makes sense because nested rotations are essentially summed sine waves in a different coordinate space.[1]
Is there more of a connection than that between the Kakeya conjecture, physical machines like rotary engines, and additive wave synthesis, or are they all fairly different branches of "interesting things one can do with nested rotations / summed sine waves"?
I'm curious if proving the conjecture opens up new possibilities in mechanical engineering or sound/EM wave synthesis/analysis, in other words.
[1] Apologies in advance if I mauled this description.
The article mentions a connection to the Fourier transform, which makes sense because nested rotations are essentially summed sine waves in a different coordinate space.[1]
Is there more of a connection than that between the Kakeya conjecture, physical machines like rotary engines, and additive wave synthesis, or are they all fairly different branches of "interesting things one can do with nested rotations / summed sine waves"?
I'm curious if proving the conjecture opens up new possibilities in mechanical engineering or sound/EM wave synthesis/analysis, in other words.
[1] Apologies in advance if I mauled this description.