Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Ok this is probably the most absurd question you'll ever read, but it came to my mind, and I cant shake it off. Eulers Identity states that: $e^{i\pi}+1=0$. So my ridiculous question is why was it stated this way? Why couldnt it have been $e^{i\pi}=-1$? Are there any reasons for this, or it could have been either of the two, but this one was chosen?

share|cite|improve this question
Sorry I wasnt sure what to tag this at all, so I chose calculus. Please fix as needed. – maq Feb 13 '11 at 2:29
Well, I've seen it stated both ways. – Calle Feb 13 '11 at 2:44
It's just an aesthetic matter. I prefer the second one, though I think there's not much merit in this "identity" anyhow. – Yuval Filmus Feb 13 '11 at 2:55
I would call $e^{i\pi}+1=0$ an ${\it equation}$ and use the term ${\it identity}$ only for equations with a free variable in it, e.g. $e^{i\phi}=\cos(\phi) + i\sin(\phi)$. – Christian Blatter Feb 13 '11 at 11:18
@Yuval: "...there's not much merit..."? Really? – Mitch Feb 13 '11 at 15:29
up vote 11 down vote accepted

The reason is to get just the $5$ "fundamental" numbers $\pi,e,i,0,1$ into one equation.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.