There probably is a direct correlation to your personal geekiness and the number of digits you know for PI. I think my first HP scientific calculator had 10 digits which I memorized very early. In a tunnel underneath I-75/85 at Georgia Tech, someone had written out PI to 26 or something digits, which I also memorized.
But I'm no competition for Supercomputers crack Sixty-Trillionth Binary Digit of Pi-Squared. A scientist for the Department of Energy - David H. Bailey, had developed an algorithm for computing PI, but it would have taken 1500 years on a single computer. Australian researchers partitioned the algorithm to run on IBM's "BlueGene/P" supercomputer and produced the result after only 110 "rack days".
On Bailey's PI blog, we learn that Archimedes of Syracuse was the first to show that the area of a circle is pi times the radius squared. He did this in 250 BCE, without the benefit of "BlueGene/P". Newton computed PI to 15 digits in 1666, admitting that he did it because he wanted to, not that there was a purpose. Bailey tells that computing PI to 40 digits is sufficient to express the circumference of the Milky Way with an error less than the size of a proton.
If you are interested, the wagon wheel algorithm is hosted on the Wolfram site. As you can see from the above, you sketch 2n+1 spokes evenly along the semicircle and also draw vertical bars for the semicircle, dividing it evenly into 2n+1 segments. The intersections of a spoke and bar truncate the spoke into length tk, where -n < K < n +1. t0 cannot be directly measured because the spoke and bar directly overlap. t0 has to be inferred from the pattern created by the other intersections. t0 approaches 2/pi and n -> infinity.
Courtesy of WolframAlpha, a pretty good estimate of PI is