
Visual proof of Euler's identity (vid) - nickb
http://ovablastic.blogspot.com/2008/12/eulers-identity.html
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zack
Wow, how was that visual proof?

For those who aren't looking forward to a lame video, the basic idea is this:

e^(pi)(i) = -1.

Why?

Because you can express e^x as a taylor series:

e^x = 1 + x + x^2/2! + x^3/3! + ... thus e^ix = 1 + ix + ix^2/2! + ix^3/3! +
.. e^ix = (1 - x^2/2! + x^4/4! + ..) + i(x - x^3/3!+x^5/5!+...) implies e^ix =
cosx + isinx

because those parenthetical quantities are the taylor series for cosx and sinx
respectively

So, e^i(pi) = cos(pi) + isin(pi). = -1 + i(0) = -1

