Pi stories

Apparently today, March 14th, is PI.-day (3.14, get it ?). Actually, as my Greek Calculus instructor once informed us, PI is correctly pronounced "P" (just like the equivalent English letter). [In a related story, a Greek physics grad student teaching assistant told me that he once got back evaluations from his students which said that he did a good job at everything except pronouncing the Greek alphabet correctly !]. But back to PI.

Not long ago I was called in to mediate a dispute between an 8-yr old girl (my cousin) and her mechanical-engineer father. My cousin's teacher had told her that if you wrote down the decimal expansion of PI, the sequence of digits would go on forever without repetition. Her dad then took out paper and pen and divided 22 by 7 and showed her that the digits did in fact repeat. I, of course, had to inform them that the teacher was right and that PI is only approximately equal to 22/7 and, in fact, is irrational (even transcendental) and therefore can not be expressed as an integer over another integer (in the process perhaps causing long term damage to the sacred bond of trust between father and daughter). I suspect the assumption that PI is exactly equal to 22/7 is more common among people who learnt math without calculators.

I'd like to say that I took out pen and paper and wrote out the proof of the irrationality of PI, but sadly they had to take it on faith. I did find it on the internet later though. Before I direct you to the proof, I hope you notice the time-stamp on this post. Getting the post in exactly at 3.14 1:59:26 was a complicated task involving synchronizing the clock on my PC to Blogger's clock and then making sure that the first key was hit just as the second digits turned to 26. Ok, here's the proof thanks to Helmut Richter.