March 14^th is Pi Day, which for once we get to post about ahead of the fact. Even though Geeky Domain here is given over to the definition of “geek” as being a media fan, Pepperidge Farm and Penguin Pete remember when “geek” meant an affinity for STEM topics. So here’s a fun fact sheet about the most iconic mathematical constant.

Pi is too popular for its own good

The number π is merely representative of the ratio between a circle’s circumference and its diameter. Since Pi is integral to such a basic shape found everywhere in nature, it captured humanity’s fascination early on and has since been subject to all manner of bizarre speculation. Or, to put it more bluntly, pseudoscience and mathematical quackery.

There’s dozens of stories about ancient people trying to work Pi out to be rational, or theories of how generations of engineers just called Pi “3” and have done with it. The Christian Bible gives the measurements for Solomon’s temple to imply that he calculated integer 3 as Pi’s value; however, we have to remember that Archimedes wouldn’t be born for another 680 years and measurements in Solomon’s time were done with knotted ropes and stakes.

The mathematician Albert Eagle just about made a career out of trying to replace Pi with Tau, which is merely the ratio between a circle’s radius and its circumference, but this is just as irrational and solves nothing. There’s also the famous Indiana Pi Bill which tried to establish the value of Pi and force an amateur mathematician’s method of “squaring the circle” into law, and yes, that really happened. “Pi denial” is popular in the same circles with the flat-Earther types.

Pi has since been proven forwards, backwards, and sideways to be both irrational and transcendental, which means it is a ratio (a mixed-number fraction, so to speak) which neither terminates nor repeats, and that it also not a number which can be expressed in algebraic terms using integers. But even those who have made their peace with Pi still seem to derive considerable pleasure form fiddling with it.

Piphilology is the hobby of trying to memorize as many digits of Pi as possible. Despite this mental sport, you only need about eight decimal places of Pi – 3.14159265 – to construct a hoop around planet Earth that would only be off by a few inches. NASA interviews confirm the most Pi digits they use is 15. So if you know Pi to fifteen decimal places – 3.141592653589793 – you literally have enough Pi digits for rocket science.

Pi Day is also Albert Einstein’s birthday!

Einstein was born March 14^th, a fact perhaps subtly referenced in Wikipedia’s choice of a photograph for the article…

Why, that is a circle on the blackboard behind him! I see what you did there.

Einstein wasn’t particularly associated with circles or Pi, but it doubtless would have come up in many calculations, what with his physics work and all.

There’s the “Pi” song

Hard ‘n’ Phirm was a UCLA nerd rock duo which released this video in 2005:

The video is a loving parody of public access TV educational shows, this time teaching us all about Pi. Besides the mind-blowing feat of making a catchy song out of random digits, the song has a rap bridge which covers a few digits of Pi “forwards and backwards” using a mnemonic story. The length of the song is just about exactly 3.14 minutes long, give or take some appropriate fade-out at the end. Oh, the linking book prop they use in the video? Myst reference!

Then there’s Darren Aronofsky’s Pi (1998)

Pi is indie film’s gift to geeks (366Weird review here). It is the only movie you can describe as a “mathematical thriller.” It’s about Max, a paranoid, computer-addicted, troglodyte mathematician bent on discovering the ultimate number that solves Life, the Universe, and Everything. He’s almost got it too, but he’s hampered by an array of goons from both Big Business and Big Religion, who are after his work for their own reasons. Draw your own symbolism; the story keeps its nose in the trenches and lets you worry about the macrocosm.

The movie’s a real treat, recommended for every geek as well as university philosophical films courses. Don’t flinch from Aronofsky’s name; this is the one good movie he did before curdling into a Narcissistic turd. There is, however, one scene which starts math wonks into a flame war to this day:

Soon after the above conversation, Max blanches at the rabbi’s story and rebukes them all saying they must have written down and intoned every possible 216-digit number, and gotten nowhere with it. This is wrong; there has not been enough time in recorded human history to have even intoned all combinations of 216 digit numbers.

BUUUUT: Max isn’t necessarily mistaken here. He has shown himself to be clever and resourceful in wriggling out of tight situations before. You could suppose that Max is lying, intentionally bluffing the religious group who don’t have his expertise. They buy his bluff, too, discouraged and shrugging. Even though they haven’t intoned every number, Max is convincing them that it would do no good to have it. He’s already been stalked, beaten up, and kidnapped at this point. He’s not beyond a desperate measure.

The digits of Pi have useful applications

For instance, say you need a method to remember a password, combination, encryption key, or PIN. All you have to do, for example, is remember “9999999” and then head for the Pi search engine, which tells you that the sequence occurs at the 1,722,776th digit. Of course if you only searched for six 9s, that’s the Feynman Point. Go ahead, search for your phone number, social security number, or just about any other number you can come up with!

For teacher educational resources, visit PiDay.org.

Pi has a nature as a mathematical constant whose digits are widely known and with several methods of calculating approximations. This makes it a good test subject for computers, programming languages, and other number-crunching aspects. Yes, despite the reputation that computers have with math, floating-point arithmetic does produce a few errors for certain calculations, Pi included.