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When I first saw:


I was puzzled that such an expression could have anything to do with circles. There are tons more and it seems like a very large amount of summations will end up having to do with $\pi$. My question is how come $\pi$ finds its way into so many formulas, and could the above equation be thought of geometrically.


marked as duplicate by Nate Eldredge, Zev Chonoles, Hans Lundmark, user91500, Daniel W. Farlow Jul 27 '15 at 6:16

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  • $\begingroup$ It appears in that formula because it has to do with a trig function which is geometric. How often "should" you see something somewhere you don't expect it? $\endgroup$ – Race Bannon Jul 27 '15 at 6:00
  • $\begingroup$ A related question. $\endgroup$ – Lucian Jul 27 '15 at 8:16

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