Since it’s Pi Day (at least in the US)I decided to jump on the bandwagon and contribute my own thoughts. Pi is fascinating. It’s such a simple definition - the ratio of a circle’s circumference to it’s diameter - yet it’s both irrational and transcendental and impossible to actually express as a simple number. People have been trying to get more accurate estimates for multiple millennia with multiple great mathematicians trying to derive their own approximation.

Srinivasa Ramanujan's Pi approximation

Looking at a Wikipedia article for Pi approximations is itself overwhelming. How Ramanujan was able to come up with his approximations is tough to understand - they seem so ridiculously esoteric that it’s hard to imagine someone was able to come up with such a formulation. Since then there have been improved approximations and Pi’s been calculated to 12.1 trillion digits. I can’t think of any real reason why we’re spending countless computer cycles to get better approximations but that’s the allure of Pi: incredibly simple to explain while being infinitely expressive.