Monday, March 14, 2016

it's Π day!


it's Π day!!

your highness Π is at once irrational & transcendent! (another in this league is e)

Π figures in these eleven wonderful mathematico-physical formulas:

1- Mont Carlo methods,
2- Euler's formula, 
4- Cauchy's integral formula, 
5- the gamma function,
6- Riemann's zeta function,
7- Gaussian integral, 
8- Plank's constant,
9- Einstein field equation, 
10- Stokes' law, 
11- Fourier's transform, 

One could ask why is Π so pervasive? Instead, I'd like to ask this:

What would math be without Π?

________________________
note: how about mixing these e and π? you get the gelfond constant.

 e^\pi = (e^{i\pi})^{-i} = (-1)^{-i}, which is a transcendental number!

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