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What is pie ?


What is π?

It's the ratio of the circumference of a circle to its diameter. Or it's the area of a circle of radius 1 or something like that. Everyone knows that. Wrong.

Well, it's not exactly wrong. It is true that π

has these properties. But that's not its essence, it's not what it fundamentally π is. The stuff with the circles is just one aspect of π and not the most profound one.

π somehow depends on the geometry of our universe or the way we measure angles, or lengths, or areas. There are tons, believe me). That's false, of course. π

π doesn't care at all about the structure of the universe or real-life circles.

Euler's formula e^iπ+1=0

What then, is π? And why is it so ubiquitous?

The answer lies with a profound, incredible, and beautiful (complex) exponential function. #pie 


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