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I don't know if this visualization is really useful for those who know that

  circumference = diameter * pi
the visualization isn't meant for those who know that.
It rolls so quickly, I would find it difficult for anyone who doesn't know this to grasp the fact. It took me a second, and I'm awesome at basic mathematics. BTW, diameter here = 1.

Anyone else thought that π(n) was referring to a graph of the density of prime numbers? :P

It took me three watchings to figure out what they were trying to demonstrate. Between the colors (not to harp on the color blindness thing, but those color choices were dreadful) and the speed of the animation, its relatively difficult to even understand what is happening the first few times through.
If you didn't know that, HN probably isn't the right place to start learning it.
I think the point is that even if you "know" that, you might not "get" it intuitively. This animation is supposed to help you "get" it, and even though it's a bit too fast, I think it does a great job.
I wonder why they chose a wheel with seven spokes. I don't recall ever seeing one with an odd number.
Wheels with an odd number have less variance in how much weight they can support along their edge. An even number of spokes makes a wheel with "weaker" points midway between the spokes, where the wheel won't hold as much weight.
Thanks. For some reason I was thinking of old-fashioned wooden wheels rather than modern car wheels. I guess someone figured out the physics at some point and there was no looking back.
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Pi = cheese wrapped in sausage.
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