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I seem to remember a proof by Euler, involving infinite series, which was really complex (for a maths hobbyist). I believe it was sent in a letter to someone, and that it ended up with $\pi = 0$ or something. I was just wondering if anyone has any idea what I'm talking about, or if it was someone else.

Thanks.

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  • $\begingroup$ I think you are confused with sin(2pi) = sin(0) or such ? $\endgroup$ – mick Oct 22 '14 at 21:40
  • $\begingroup$ I've heard of false proofs that show $1+2+3+\cdots=-1/12$ or an incorrect limit showing $\pi=2$, but I have never heard of a false proof that $\pi=0$. $\endgroup$ – Clayton Oct 22 '14 at 21:40
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    $\begingroup$ Take a Cricle. The ratio of the diameter of the circle and the circumference is pi. The circle looks like 0 therefore $\pi=0\ \square$ $\endgroup$ – Ali Caglayan Oct 22 '14 at 21:41
  • $\begingroup$ It's not either of those (I do quite like the -1/12 one) although it might be the incorrect limit of \pi=2. This was a proof that Euler knew was wrong but I think he wanted to see if the other person could figure out where? I'm not sure, but a link to the \pi=2 would be nice. $\endgroup$ – Oscar S Oct 22 '14 at 21:43
  • $\begingroup$ @alizter That's amusing but no thats not it :) $\endgroup$ – Oscar S Oct 22 '14 at 21:45
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$$e^{2i\pi}=1=e^0\quad=>\quad2i\pi=0\quad=>\quad\pi=\dfrac0{2i}=0.$$

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  • $\begingroup$ Or was it perhaps this ? $\endgroup$ – Lucian Oct 22 '14 at 23:19
  • $\begingroup$ I think it might be the generality of algebra thing, so I'm going to google around a bit more to find the exact thing im looking for. Thanks :) $\endgroup$ – Oscar S Oct 22 '14 at 23:28

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