Eden,

Its exact value is given in many ways: circumference/diameter for a circle, arccos(-1), the area of a unit circle, and the limiting value of many different infinite but convergent series and products.

The problem is that there are many ways in which pi cannot be given. For instance, there is no terminating decimal, repeating decimal, or fraction that is equal to pi (though some are excellent approximations.) It cannot be constructed with compass and straightedge. And indeed there is no polynomial with integer coefficients that has a root equal to pi.

There are surprisingly efficient algorithms that can find specific digits of pi, in some cases without finding all the ones in between. You might find the following interesting:

http://www.cecm.sfu.ca/~jborwein/pi-slides.pdf

Good Hunting!
RD