Excerpted from Math for English Majors by Ben Orlin. September 2024, Black Dog and Leventhal Publishers. Published with permission.
Every March 14, the mathematical world observes its favorite holiday by canceling lessons, gorging itself on pie, and reciting the decimal expansion of math’s most revered constant. Young and old, pure and applied, algebraist and analyst, we all gather to celebrate Pi Day.
Except…Okay, I take that back. Most of us celebrate. A few grinches prefer to grumble about it.
We’ll come back to them, but first: What is pi? It’s the number of diameters (the distance across a circle) you’d need to equal the circumference (the distance around a circle). Roughly speaking, three acrosses equal one around.
More specifically, the around is about 3.14 times the across. Even more specifically, it’s about 3.141 592 653 589 793 times. Hyperspecifically, it’s 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117…
I can get more specific, but never specific enough, because this number, known as π or pi, is irrational. As in, not a ratio. No fraction can express it. No decimal either. We can’t even pull a trick like when we wrote 0.3̅ for 1⁄3, because π’s digits don’t settle into a repeating pattern. Around every corner is a new, never-before-seen digit sequence. I have heard 12-year-olds recite a hundred digits from memory. And that’s nothing compared to the 70,030 digits reeled off by Suresh Kumar Sharma in October 2015, over the course of 17 (presumably agonizing) hours.
So why does this drive mathematicians batty? With apologies to Dr. Seuss, I find it easiest to express their lack of holiday cheer through rhyme.
Every kid in the classroom liked Pi Day a lot.
But the Grinch in the faculty lounge did not!
This, to the Grinch, was the dumbest of seasons,
and asked or unasked, he would rattle off reasons:
“In the US, it’s said the date 3 slash 14
is March the 14th. That’s what ‘Pi Day’ must mean.
But the rest of the world gives the day, then the month!
So 3 slash 14 is the 3rd of Kerplumph,
a month, I assure you, that does not exist.
And that is just one of the gripes on my list.
This horrible day that transfixes the nation,
is built on a lousy approximization.
22 over 7 comes closer to pi.
So let’s wait till that date, out in mid-late-July.
Besides which, old pi is an artifact now.
The cool mathematicians all venerate tau.
And have I brought up how it eats me alive,
the 3 point 1 4 1 5 9 2 6 5?
How it just rambles on, and it fills me with hate.
3 5 8 9 7 9 3 2 3 8!All those meaningless digits!
The hot wasted breath!
Oh, it bores me to tears.
No, it bores me to death.
I’ve said it before, and I’ll say it again:
Those numbers mean nothing outside of base ten.
Besides which, the digits are ones no one needs.
Past 30 or 40, they’re useless as Thneeds.
For a circle a million light-years in width,
your digits could stop at the mere 25th,
and still you could calculate out the circumference
down to the span of a nano-non-umference,
a distance one-thousandth the width of a hair.
For digits past that, I quite simply don’t care.
I’m speaking the truth when I firmly assert:
Pi Day’s an excuse
to swap math for dessert.”
Setting aside calendrical arguments to focus on mathematical ones, I see two strong points in the grinches’ favor.
First, irrational numbers are not rare. Throw a dart at the number line, and you’ll hit one. If what we care about is irrationality, then we might as well replace Pi Day with √_17 Day on April 12, or _3e day on 7 January 16. Yes, π is more important than these numbers, but dwelling on its irrationality is like centering MLK Day celebrations on Martin Luther King Jr. having been 5′7′′. Kind of missing the point.
Second, even if irrational numbers were rare, then memorizing their digits would still be a silly pastime. You can typically round π to 3.14159, or 3.14, or even 3. For all practical purposes—and even for impractical ones—π might as well be rational.
That said, few grinches follow this logic to its terrible conclusion: irrationals don’t exist.
Infinite precision is impossible. No ruler, scale, or stopwatch can give you unlimited decimal places. Sooner or later, you must round. And once you round, the irrational number is gone, replaced with a boringly rational approximation.
So in what sense do irrationals exist, except in our imaginations?
For 364 days of the year, we must accept the dreary reality that beyond the first handful, an irrational’s digits are empirically (if not existentially) meaningless. But one day each year, the world indulges our fantasy that irrational numbers exist. For one day, the world stops to admire a number that escapes description, a noun that can never be uttered.
Plus, we get to devour fistfuls of pecan pastry. What’s not to love?
And what happened then? In some circles, they say the Grinch’s small heart grew three sizes that day. And elsewhere, they say that it grew a bit more: maybe 3 point 1 sizes, or 3 point 1 4…
Math for English Majors is out September 3, 2024 and available for pre-order now.