Taking a word like "geek" and trying to define exactly what it means is an activity bound to frustration. MaximumPC was completely undaunted when it released this set of necessary conditions for geekness: 50 Skills Every Real Geek Should Have. Jean-Marc will be please to see that reciting digits of pi made it on the list. Here's the entry.
Recite pi to 23 Decimal Places
3.14 may have been enough accuracy for 10th grade geometry, but it’s just not going to win you any respect from the other nerds. We consider 23 places the bare minimum for pi memorization.
If you’re having trouble dealing with all that, try “chunking” your memory. That is to say, instead of simply trying to remember each number in sequence (a task that humans tend not to be very good at) try to remember the numbers in groups or chunks that have more significance for you. If that’s not doing it for you, consider piems—stories and poems structured around digits of pi.
For the record, pi is: 3.141592653589793238462643...