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

Triangles and circles. The simplest fundamental shapes and you can draw a circle touching all 3 points of any triangle. The circle is a perfect shape. The best way to think about it isn’t that circles are everywhere so that means pi is everywhere. Pi is a perfect fundamental mathematical constant. A circle is a perfect shape created from that ratio.

So the circle is like a sterile environment for us to discover that mathematical constant.

There is actually a movement among many mathematicians that tau or 2(pi) is actually the more fundamental mathematical constant and gives a more intuitive description of the unity of mathematics.