- #1

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e

^{πi}+1=0

But what I finally understood is that this is not a relation between those numbers. It is just the result of the function exp(z) when you extend the exponential function to the complex numbers and you supose analyticity (I don´t know if that is well said).

In other words, there is no simple calculation that I can make to the number "e" (I mean, something to put in the calculator) that will give as a result the number π.

The question would be: Is this last statement true?

I hope it isn´t because it was more romantic when I thought that e and pi where linked like the flowers and the bees or like Jack and Rose!

Thanks in advance for you usual help!

Ps: I also thought about the relation:

∫

_{-∞}

^{+∞}e

^{-x2/2}dx=√π

But that comes from squaring the integral, transforming it in a doble integral and noting the rotational symmetry of the integrand. Everything that has rotational symmetry will give something times π, that's not properly related to the number e. It felt like cheating. I know that this is not precisely stated but I hope that you'll be able to capture the spirit of my question and to help me find an answer about whether we can say that e and π are related or not.