I understand the mathematical definition of Pi, but why does it end up being used in so many formulas and applications in math, engineering, physics, etc? What does it unlock?
Edit: I understand Pi is the ratio of circumference to diameter. But why is that fact make it important and useful. For example it shows up in the equation for standard normal distribution. What does Pi have to do with a normal distribution. That’s just one example.
In: 3
3blue1brown is a great YouTube channel for this. Basically, pi is like the definitive property of a circle. You can’t have a circle without pi being there.
But the reverse is pretty much always true: you can’t have pi without a circle hiding somewhere in the background. If an equation features pi or a problem has pi in the answer, there’s almost always a way to represent some part of the question with a circle. And since a circle is the most simple geometric shape (you can draw one with a pencil and a piece of string!), circles appear everywhere, therefore so does pi.
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