# What is the incorrect proof by Euler that $\pi = 0$ (or something like that)?

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.

• I think you are confused with sin(2pi) = sin(0) or such ? – mick Oct 22 '14 at 21:40
• 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 $\pi=0$. – Clayton Oct 22 '14 at 21:40
• Take a Cricle. The ratio of the diameter of the circle and the circumference is pi. The circle looks like 0 therefore $\pi=0\ \square$ – Ali Caglayan Oct 22 '14 at 21:41
• 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. – Oscar S Oct 22 '14 at 21:43
• @alizter That's amusing but no thats not it :) – Oscar S Oct 22 '14 at 21:45

$$e^{2i\pi}=1=e^0\quad=>\quad2i\pi=0\quad=>\quad\pi=\dfrac0{2i}=0.$$