the most beautiful equation ever

Euler's identity

e^{i(π)}+1 = 0

Paul Nahin's "Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills" states:

I think [Euler's Identity] is beautiful because it is true even in the face of enormous constraint. The equability is precise: the left hand is not 'almost' or 'pretty near' or 'just about' zero, but exactly zero. That five numbers each with vastly different origins, and each with roles in mathematics that can not be exaggerated, should be connected by such a simple relationship, is just stunning. It is beautiful. And unlike the physics or chemistry or engineering of today which will surely appear archaic to technicians of the future, Euler's equation will still appear, to the arbitrarily advanced mathematicians ten thousand years hence, to be beautiful and stunning and untarnished by time.

Breaking down the equation:

**Zero**(0) which can be added to any number and the number is unchanged**One**(1) which can be multiplied to any number and the number is unchanged**Pi**which appears everywhere from trigonometry on to the most abstract domains of mathematics**e**which is the base of natural logarithms. It is also a number which 'just shows up' again and again in the exploration of mathematics**i**which is the fundamental imaginary number. There is no number which when multiplied by itself gives a negative result i.e. 1*1 = 1; (-1)*(-1)=1. So someone just invented a new number: i = Square Root(-1). They called it imaginary (cause it is) and so much mathematical magic suddenly appeared as to almost defy imagination. How can an imaginary number be so central to mathematics?"

In 1997, Brazilian soccer player Roberto Carlos scored on a free kick that first went right, then curved sharply to the left in what looked like a physics-defying fluke. French scientists - the goal was scored against France [French goalkeeper Fabien Barthez too stunned to react] have finally calculated the physics equation that shows the goal was no fluke. Check out all the details of the equation.

Here's another example of the curl

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