why Pi is important?

Question

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

Answer 1

So, Pi is, by definition, related to circles and therefore to spheres as well.

So anything circular, like planetary orbits, is also related to Pi.

And things that are cyclic, like [simple harmonic motion](https://en.wikipedia.org/wiki/Simple_harmonic_motion).

And a sphere is the collection of all points that are a certain distance from a central point. So anything that propagates equally in all directions (such as gravitational and electric fields) also deals with spheres, and therefore relate to Pi.

There are many more such examples.