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User avatar #90 - anonymoose (09/14/2013) [-]
Y'ALL BETTER HOLD ON TO YOUR SEATS. MATHS IS GOING DOWN!!!:

- e^(iπ)+1=0 known as Euler's identity. It's considered by some as the most beautiful equation.
- e is a mathematical constant. It's approx. 2.718. It's the sum to infinity of 1/(n!) (1/1)+(1/(1*2))+(1/(1*2*3))+(1/(1*2*3*4)) ... and so on
- e^x can be written as the sum to infinity of this is where it gets hard to write it down ((x^(n-1)))/(n!) 1 + (x^1)/(1) + (x^2)/(1*2) + (x^3)/(1*2*3) etc.
- i is a number that doesn't exist but we use it in maths anyway because WE ENJOY CONFUSING PEOPLE. It is the sqrt(-1)
- Sub iπ as x for e^x 1 + ((iπ)^1)/(1) + ((iπ)^2)/2 + ((iπ)^3)/(6) etc.
- Because (i^2) = -1 we can change the equation above into 1 + iπ - (π^2)/2 - (i(π^3))/6 + (π^4)/24 etc.
- That **** up there is known to be the same as cos(π) + isin(π)
- cos(π) = 1 sin(π) = 0 meaning we can get rid of the i there and we're left with just 1

tl;dr When you sub iπ into the formula for e^x you end up with it turning into the same formula for cos(x)+isin(x) which turns out to be 1
#101 to #90 - iluvnutella (10/09/2013) [-]
I completely understand what you just said!
User avatar #94 to #90 - mahnamesjakers (09/14/2013) [-]
That's exactly what I was thinking.
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