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This question already has an answer here:

When I first saw:

$$\frac{\pi}{4}=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}\mp\cdots.$$

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.

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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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