Why does Pi show up in so many diverse equations if it’s only related to a circle?

Question

Is Pi more than just a ratio for circles? Is there a easy way to understand the universality of Pi?

In: 1018

Answer 1

It isn’t quite only related to circles but instead also spheres and higher-dimensional versions of spheres as well as cylinders (and higher-dimensional versions of cylinders). The real trick is that when pi shows up, you can bet that there’s at least one way to reformat your question to ask about circles. 3Blue1Brown has done a few examples of this because of how satisfying to watch they are including [this recent one which actively acknowledges the oddness of pi showing up](https://youtu.be/cy8r7WSuT1I).

Edit: link formatting fix