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
It’s just the ratio of a circle’s diameter to its circumference.
This comes up a lot in various disciplines because so many things move in circles, oscillate around a central value in a circular manner, or collapse into circle/spheres as the simplest shape.
Your classic sinusoidal wave is just moving around a circle that’s also moving, and so pi pops up in all manner of wave behaviors and vibrations from the smallest electron to the chaotic magnetic fields of giant stars.
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