In collaboration with Pizza Hut, John Horton Conway is providing a pathway to fame, riches, and pizza. On Monday–3.14 if you write your dates with dots–the mathematician will issue questions three, and a limited number of correct respondents will earn pizza for a year, and maybe an interview from a local TV station. I was a little surprised at a chain restaurant latching onto the math-y-ness of Pi Day, but hey, I’m not complaining. Presumably the questions won’t be as easy as, “What… is your name?” “What … is your quest?” and “What … is your favorite colour?”… Well, now that I think about it, these questions were pretty tough on a few of King Arthur’s cohorts…. But I digress.
Nobody really knows the number pi through its decimal form 3.14159265… because to do so would entail a knowledge of all of the infinitely many digits following the point. Alexander Yee And Shigero Kondo have determined the first 12.1 trillion decimal digits of pi; there are boatloads of published papers about this wonder number; and there are lots of questions about it for which no one has an answer.
Back in 1988 Larry Shaw at the San Francisco Exploratorium organized what seems to have been the first significant observation of Pi Day. Since then, it’s become a de facto national holiday, celebrated by school kids, collegians, and others with pie eating contests, pie throwing contests, digit recitation contests, lectures and who knows what else. When I was a college professor, my students once celebrated the day by bidding on pies that they then threw at me or smashed into my face.
Pi actually comes from geometry–it’s the ratio of the circumference to the diameter
of a circle. That’s its definition. So why not call it C/D Day? Not so obvious when it should be. There are fractions that approximate this number 3/1, 7/2, 10/3, so it might make sense to celebrate on March 1, July 2, and October 3. There are other, better, approximations like 22/7 that you learn about somewhere along the way, but sadly these better approximations don’t correspond to any dates. Plus, it may violate the spirit of things to celebrate an irrational number like pi with a rational number. Of course the number 3.14 is a rational exactly equal to 157/50, but the resemblance of “3.14” to a date is simply irresistible.
All this got me to thinking how tied most of us are to representing numbers in decimal form and wondering if the celebration might be extended a bit by varying the representation. We might want to make March Pi Month, as it turns out that the dates 3.02, 3.03, 3.05, 3.06, 3.11, 3.12, 3.14, 3.16, 3.18, 3.21, 3.24, 3.26, and 3.29 all correspond to good approximations of pi in different bases. If humans instead had only four fingers, then we would almost certainly represent numbers using base four, and so the number pi would look like 3.012003332…..; if instead we had five fingers (three on one and two on the other?), then we would likely use base five to represent numbers, and the number pi would look like 3.0323222…; and so on. Truncating these quaternary, quinary, etc. representations to two places after the point gives the dates I’ve listed, and if you re-interpret the symbols in decimal, then voila, many Pi Days in March!
I’ll be eager to see what Conway’s problems are, and maybe I’ll take a stab at them. But for sure I’m committing myself to Eat Mor Pizza during the month of March. It’s Pi Month, folks; dig in. Just try to make sure your pies are round!