pi and "undefinable" numbers

pi is a very cool number. there are so many cool things about it that i don't really have time to list all of them, but here's one of my favorites:

(1/1)^2 + (1/2)^2 + (1/3)^2... = (π^2)/6

the explanation for why this is true is too long for me to write about, but if you want to know why you can read about the Basel problem and how it relates to the Riemann hypothesis, which is one of the biggest unsolved problems in mathematics right now.

anyway, another cool thing about pi is that it's irrational: it can't't be expressed