Nothing I can tell you that a quick Google search won't tell you. But one thing you might want to be aware of is that pi is also
transcendental, meaning that it is the solution to no polynomial equation, or more precisely, "that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients." See: http://en.wikipedia.org/wiki/Transcendental_number
This, in contrast, for instance, to the Golden ratio, which is irrational, but not transcendental.
Incidentally, here is a link to another thread on this forum where the same issue was discussed at some length:
Looking for "Easy" proof of Pi Irrational
As for the below question...
It's kind of mind-bending, but if you were to snip a perfect circle and stretch it out in to a straight line along an x-axis demarcated into measurement increments as small as you please, then, while that line it would be "this long" and no longer, or "this short" and no shorter, well, good luck being able to locate, or rather, specify, where exactly the endpoint of that line is relative to your 0 point.