My problem with Pi Day
Restoring the essence of our most revered constant
What I’m about to say is unlikely to win me friends. It may well cost me a few.
It is the week that marked Pi Day. On March 14th, or 3.14, everyone in the maths world goes nuts for their favourite constant, π. Everyone, it seems, but me. Out of my own love for π, I can’t bring myself to partake in the festivities.
Don’t get me wrong — I welcome any attempt to drum up interest in mathematics. I can even look past the fact that π earns the attention by virtue of phonetic happenstance —I’m a sucker for pie, all variants thereof. It’s hard hard to think up a tasty treat for e-day or i-day.
My concern is that it all feels rather trivial. I have witnessed only rare attempts to use the occasion of Pi Day to shed light on the most essential characteristics of our chosen constant.
The date is already a compromise too far. In settling for π’s two decimal point approximation, we disconnect from all that makes it holy: a forever expanding, never repeating decimal form. The same irony is lost on students — and adults — who labour towards memorising umpteenth digits of π, barely stopping to reflect on the fact that for all their toil, they remain infinitely far away from capturing its full form. It is the elusiveness of Pi’s decimal expansion that warrants our celebration, not its disfigured two decimal point representation.
Our shallow embrace of Pi only reinforces the most narrow mathematical stereotypes — that, for example, genius belongs to those who can memorise scores of digits.
The only debate around Pi Day (that I am aware of) centres on the choice between March 14th and June 28th (the latter, 6.28, corresponding to the equally disfigured approximation of τ, the constant corresponding to 2π).
What if, instead, we probed the genuine depths of π?
I am reminded of one student, who, upon receiving news of π’s irrational nature, pondered on the distribution of digits in its decimal expansion. He asked if we can expect each digit to arise as frequently as one another, and whether there is any predictably at all in certain strings of digits appearing.
These are the probing, insightful questions that amplify the mystery and intrigue of π. We should ask more of them. In that vein, here are five ways of showcasing the enduring majesty of π:
- The fact that π is a constant should not be taken lightly. It results in the most fascinating consequences, such as the delightful conclusion to the string around the earth problem:
Imagine a piece of string wrapped around the Earth’s equator. How much more string would you need for it to sit 15cm above the ground, all the way around? Assume that the equator is a circle.
- Instead of debating the choice of date, try to pinpoint a moment in time that corresponds to Pi’s exact value. Accepting 3.14 to correspond to the month and year, perhaps the remaining digits, 1592653…, can represent hours, minutes, seconds and whatever other time intervals we would have to create to capture more of π. We would soon confront the paradox of capturing π in a single moment in time — what better way to magnify its quirks?
- Pi Day marked the passing of legends. Stephen Hawking, you know about. Jim Bowen, I presume less so — unless, like me, you grew up on Bullseye, the gameshow hosted by Bowen that combined darts with trivia. In homage of Jim, consider how, with appropriate assumptions,we can approximate π using a dartboard (one approach can be found here — Kudos to the creators for raising the bar on Pi Day).
- If you are seeking still deeper truths to π, I can offer no better than 3Blue1Brown’s stunning geometric solution to the Basel problem, which offers an illuminating proof of the infinite series representation of π²/6.
- Lastly, if you want to understand the historical significance of π, a brief foray into past attempts to approximate its value will reveal mankind’s eternal fascination with this constant.
π is worthy of our celebration — heck, every day should be Pi Day. But let’s pour our efforts into celebrating all that makes π so special, rather than settling for its paltry imitations.
Until March 14th 2019 (or, if you insist, June 28th 2018).
