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Is it possible to derive pi from iterated stereographic projection of some kind? I ask because the link below shows an animation of pi 'unrolling' from a turning wheel, and it seems like there ought to be a way of describing pi as somehow the cumulative shadow of such a wheel with a light source.

https://en.wikipedia.org/wiki/Pi#/media/File:Pi-unrolled-720.gif

Svenn
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    See here; I’m not sure if this is what you’re after. One can define $2\pi$ to be the limiting value of the integral written there as $t_2\to \infty$ and $t_1\to -\infty$. – peek-a-boo Aug 25 '24 at 01:31
  • Is it possible? Yes, sure, no problem. But some effort: somebody must move the wheel, somebody must trace the axle's shadow with chalk or coal on the flor, and the one with the torch on top of the wheel must run backwards twice as fast as the wheel moves forward to stay on top of it. Just a matter of teamwork. -- You asked for stereographic projection. – m-stgt Aug 25 '24 at 04:14

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