“Now go on, boy, and pay attention. Because if you do, someday, you may achieve something that we Simpsons have dreamed about for generations: you may outsmart someone!” –Homer Simpson
Today, March 14th, is known tongue-in-cheek as Pi Day here in the United States, as 3.14 (we write the month first) are the first three well-known digits to the famed number, π. As you know, it’s the ratio of a perfect circle’s circumference to its diameter.
It’s also very, very, very hard to calculate exactly, because it’s impossible to represent π as a fraction. (You may remember that’s part of the definition of an irrational number.) But that doesn’t mean we haven’t tried!
The easiest way to try is to either inscribe or circumscribe a regular polygon around a circle of radius 1, and calculate the polygon’s area. The more sides you make, the closer you’ll get.
Archimedes, who discovered the fraction 22/7 (which is why Pi Day is July 22 in Europe), took the equivalent of a 96-sided polygon to do this, and found that π was between 220/70 and 224/71, which is not bad for two thousand years ago!
But it’s hardly the most impressive approximation for π from back then. That honor goes to the Chinese mathematician, Zu Chongzhi.
He discovered — in the 5th Century — the approximation Milü, which is 355/113. Which is equal to, for those of you at home, 3.1415929… meaning you have to go to the eighth digit to see the difference between this number and π. In fact, if we look at the best fractional approximations of π…
we wouldn’t find a better one until 52163/16604! (Exclamation point, not factorial!) That was the world’s best approximation for π for something like 900 years, until this guy came along. Pretty impressive!
But what if you wanted to calculate π, but wanted to do as little math as possible? No geometry, just basic counting and four-function mathematics? Well, if you can play darts, you can do it!
It will only get you to π very slowly, but throwing darts (randomly) at a circle with a square of area equal to the circle’s radius will allow you to calculate π! How so? Count the darts that land in the circle, divide by the number of darts that land in the square, and that’s how you calculate π. (For those of you who write a computer program that can do this, congratulations, you’ve just written your first monte carlo simulation!)
But let’s say you wanted to be more efficient, but you wanted to get to π with arbitrary accuracy, given enough time. Have I got a fun method for you: you can represent it as a continued fraction, and the farther you continue it, the more accurate you’ll get!
Pi Day is also a special day for anyone interested in astronomy and space! Four famous astronomy and space heroes have their birthday on Pi Day; can you name them all from their pictures?
(Okay, okay, one of them is easy!)
As far as the pies go, I’m still no good at making pie crust, but I do have a special treat that I can make, with a circumference and a diameter and everything.
Yes, it’s a Leche Flan! Hope your day is as sweet as they come, hope that you enjoyed all the fun facts about pi, and if you’re up late over the next couple of nights, enjoy the Pi Day miracle of the Jupiter-Venus conjunction in the night sky!
Happy Pi Day!
(And your birthday boys are, from L-R, Albert Einstein, Apollo 8 Commander Frank Borman, Astronomer Giovanni Schiaparelli, and last-man-on-the-Moon Gene Cernan.)