Theres a video on YT that explains how Pi can be calculated by anyone with an Excel spreadsheet. Its called Pi Hiding in Prime Regularity.
Something like 1+1/1+1/2-1/3+1/5-1/7+1/11-1/13 etc. Alternative signs, and divisors that are incremental primes. This converges on Pi, so Pi is an expression of prime series. YouTube has some mind blowing number theory videos.
Or, if you were a pre-Excel math nerd, you might memorize a good chunk of it:
3.14159265358979323846264338327950288419716939937510...
My favorite pi approximator (for use with dollar store calculators with no Pi key) is 355/113, it was developed in medieval China I think, read about it in, hmm, L. Sprague de Camp?
sidebar:
http://turner.faculty.swau.edu/mathematics/materialslibrary/pi/pirat.html