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 a number that shows up frequently in many different places.
It shows up frequently in many different formulae because it is related to circles, and circles and spheres are related to lots of other things, sometimes in not-so obvious ways.
Anything related to angles and rotations for example is obviously related to circles, but it turns out that powers in imaginary numbers are also related to rotations, which means that pi shows ups wherever complex numbers do. Spheres have something to do with how energy diffuses or radiates in space, so pi shows up in a lot of physics. Diffusion, in turn, has something to do with normal distributions, so pi shows up in statistics. Circles are also related to waves, so pi shows up in formulae about waves.
Latest Answers