Euler's Identity Song

A song about the coolest identity around!

Download the song for free:
http://thesingingnerd.bandcamp.com/al...

Lyrics:
E to the i pi is equal to negative one
Man, that is crazy, this equation can't be outdone

How'd all those con con con con constants get into one...equation
It's like a re re re reunion -- special occasion

e's the limit (as n approaches zero) of (1 + 1/n)
to the power oh oh oh to the power of n (2.71)

well, its 2.7182818284590452353602874

E to the i pi plus one is equal to zero
Forget the batman -- euler was a real life hero

I's not a real real real real number it's the square root -- of minus one
And pi's a ra ra ra ra ratio of c to d I know you're stunned

All these constants are popular (the bomb)
But this one time oh oh oh oh, but this one time we see them ensemble

E to the i pi is equal to negative one
Man, that is crazy, this equation can't be outdone
E to the i pi is equal to negative one

• Category

  Music

[lirothen]

e^(i * tau) = 1. much cooler :P

[TheSingingNerd]

Yeah, I've actually been convinced that in the grand scheme of things tau makes more sense.  However, I would have had to explained what tau was first, since most people are much more familiar with pi. I guess I'm just part of the problem.

[DisfunctionalMisfunc]

Wouldn't e^i*tau be a little problematic since tau= 2pi? It would be e^i*tau/2 then.

[TheSingingNerd]

e^(i*pi) = -1 but e^(i*tau) = 1 so they are both beautiful.

[Aidan Haslam]

how can it be an identity, if there are no variables?

[TheSingingNerd]

As long as the equation is always true, its an identity. It's a less interesting identity since you can't plug lots of numbers into it, but its still a tautology and therefore an identity. But you make a good point.

[TheSingingNerd]

binary solo?

[speadskater]

Alright, so this comes from e^(ix)=cosx+i*sinx, notice that at pi, sin is 0 so the complex term goes away. When solving a differential equation involving sine or cosine, it is easier to use this identity, then solve for the real or imaginary component. Using this, you can also form an identity for cos(x) or sin(x) in terms of e,i, and a few constants. This in turn becomes a powerful machine for generating trig identities (ever see an identity, and wonder "how did they get that?", that's how

[DisfunctionalMisfunc]

Oh wow! Now I'm even more impressed.

[woo216]

Happy 306th birthday Euler!

[TheSingingNerd]

I saw?

[minishoorange]

I came.