Anthonares

Here’s a short article that I wrote for DamnInteresting.com, but I finished it a bit late in the day so I’m not sure that it will get published:

Mathematicians (I won’t call them math geeks) are not generally considered wild partiers. Positioned in front of whiteboards endlessly writing arcane proofs and derivations, they seem more the quiet type. But today, on March 14th, the entire math world sets down their dry-erase markers, breaks out the party hats and eats a slice of pie. Why? Because it’s Pi Day!

But math geeks worldwide (there, I said it) aren’t just celebrating the happy coincidence of the date and the first few digits of pi (3.14159265…). Pi day gives them a chance to celebrate the deep mystery of the universe, along with marvelous history of mathematics, by paying homage to that little greek letter that appears in so many equations.

Pi is defined as the ratio of the circumference of a circle to its diameter. That’s a simple enough sentence to say, and it gives pi an exact value. But calculating that value is another matter. A reasonable approximation of pi is 22/7, but 333/106 is better, and 355/113 is closer still. In fact there is no ratio of finite rational numbers that exactly equals pi, unless of course you happen to be counting in base-pi.

It turns out that the decimal value of pi is a sequence of non-repeating values at least 1 trillion digits long (supercomputers are continuously working to calculate more digits). This puts pi into a very special class of mathematical oddities called transcendental numbers: those without any algebraic solution (read the Mathworld explanation below, for more). On a side note, a combination of two transcendental numbers makes for one of the most marvelous equations in all of mathematics: ei*pi=1

Mathemeticians currently suspect, though there is no accepted proof, that the digits of pi will continue to infinity while never repeating a sequence. But why do the digits of pi continue so? Why isn’t the value exactly 3.14, or something like it? Why did Professor Frink shock his colleagues in The Simpsons when he shouted “Pi is exactly 3!”

It turns out that Professor Frink is right; pi is exactly 3. Just not in a Euclidean universe like ours. Because pi relates a linear measure to an area, its exact value depends on the curvature of spacetime. We believe that our universe has no inherent curvature, or at least the three largest dimensions do not. However, if every dimension of our universe were spherical or hyperbolic, then pi could be exactly 3. Strangely enough, it could also be negative or infinite.

Celebrators of Pi Day in a spherical universe might be particularly dissapointed. Firstly, pi might be a negative number. Second, it would be very hard to slice a pie with a negative circumference but a positive area!

Speculating on the question of why our universe has the shape it does led visionaries such as Carl Sagan or Arthur Clarke to suggest (not entirely seriously) that deep within the digits of pi lie the basic instructions for the creation of the universe. Perhaps whoever, or whatever, caused us and everything to be embedded a fingerprint deep within pi so that only an advanced civilization, presumably one capable of handling such an enormous discovery without collapse, could detect it.

So, while you enjoy a slice of your favorite pie with your geeky friends, step back a moment and contemplate infinity. That’s what the folks at the University of Waterloo did at the very first Pi day bash. Unfortunately, the supreme Pi Day (at least to those observing the Julian calendar) probably went uncelebrated. It occured on March 14th, 1592 at 6:53 AM and 58 seconds (pi to twelve digits). But, a 10-digit Pi Day is coming up on March 14th, 2015 at 9:26 AM and 53 seconds (3.14.15 9:26.53), so start making plans!

Further Reading:
A random Pi-worshipper at Upenn wrote out 1881 digits in chalk (from Anthonares.net)
Wikipedia entry on Pi
Pi in Non-Euclidean Universes