Tuesday, March 14, 2017

it's Π day!


it's Π day!!

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

Π figures in these eleven wonderful mathematico-physical formulas:

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


What would math be without Π?

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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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