Typically one would want an equal probability of any number being returned by a random number generator, and their being no petterns in the sequence of numbers returned.
Just becuase pi does not repeat, does not say that pi contains an equal distrubuation of the numbers 0-9, or even that there is no pattern. The number
1.121121112111121111121111112
does not repeat but the pattern is simple, and the distribution is awful.
I don't know enough about pi to even thing about how to prove that it could be used for random number generation, so I'd leave it well along and look at other algorithms.
You actually don't need to use any fancy math, trig functions etc to get a pretty decent random number sequence from a seed. This for the most part is all you'll ever need. The seed can be generated by so many different parts, you can be sure you have a decent seed value.
For example, I'd use a combination of the following.
Current time (low resolution)
Time since system was started (low resolution)
Current CPU timer value (high resolution)
These should be available to everyone.
If however you wanted to add more truely random numbers
Ping time to
www.yahoo.com
Current mouse position
Time since last key press
Current microphone sample. (Check there is a microphone attached.)