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You’re probably reading this because you like Pi Day. Once a year, your office, your classroom or your group of friends partake in pies of lemon meringue or pumpkin or apple… You’re joined by people across the nation, nay the world, basking in the hilarity of eating circular food while celebrating the mathematical constant of a circle, pi. Here at the NewsHour, we’ve been known to celebrate with a selection of Pi Day pies.
Yet if you peel back the crust and take a deeper look at pi, one finds an imperfect hero. Much like Christopher Columbus day, Pi Day’s faults are masked by the crushing weight of heritage and popular opinion. Pi isn’t as unique as believed, and mathematically, it’s more trouble than it’s worth.
Here’s why in three simple lessons based on claims by pi lovers.
1. “Pi is infinite. That’s so special!”
Wrong, it’s quite ordinary. School teachers indoctrinate kids with the idea that pi wanders on forever behind its decimal. 3.1415926535…and beyond. But there are plenty of numbers with infinite digits. For example, 18, which has an infinite number of zeros behind it in decimal notation.
Plus even though pi has infinite digits, it is still finite. If you draw a number line, pi will always land between three and four. Pi isn’t boundless or wandering into infinity. It has always possessed the same number of digits today, yesterday, last year and a thousand years ago, and those digits have always been stuck squarely between three and four. If you don’t believe me, watch this:
2. “Pi is the circle constant. That’s so special!”
Except pi is a confusing circle constant.
Let’s start with the schoolyard definition of a circle. All points on a circle are the same distance from its center. This distance is the radius, and the length around a circle is the circumference. Society’s favorite constant for a circle would be defined by these two attributes: the radius and the circumference. This constant could be tossed into a math equation and any circumference and radius to instantly describe a circle.
But it isn’t. Pi fails at this mission. If you divide the circumference of a circle by its radius, you don’t get pi. You get two times pi. There’s an extra step of multiplying by two. Rather than define a circle’s circumference by its simplest element — the radius — tradition has taught us to use a circle’s diameter.
But that’s confusing for kids learning math. You know what’s a lot less confusing: tau. Tau is two times pi, or double pi. The equation for circumference goes from C = 2 times pi times radius to just C = tau times radius. Rather than one revolution being equivalent to 2π, as pictured below, it’s now equal to one tau.
A complete revolution is 2π radians, shown here with a circle of radius one and thus circumference 2π. Could life be easier with tau? Photo by John Reid
People have written whole manifestos behind the constant tau (τ), given its ability to simplify the understanding of circles whilst alleviating the headaches of kids learning geometry and trigonometry.
3. “Pi doesn’t repeat itself. That’s so special!”
“That’s a cop out, Nsikan,” you say. “We love pi because it’s an irrational number, and its trailing digits don’t repeat.” Pi is an irrational number, sure, because it can’t be expressed as a fraction or ratio. 22/7 will get you close to pi, but not quite there. When written as a decimal number, pi’s digits wander off without repeating. So special.
Except that’s just like the golden ratio φ (pronounced “phi”), which is arguably even cooler than pi. The golden ratio is defined as the diagonal of a regular pentagon divided by the length of its side. The result is 1.618033988749…, a number viewed as beautiful throughout human history. The Great Pyramids, The Parthenon, The Taj Mahal and Notre Dame feature architecture set to the golden ratio. The aesthetic appeal of the golden ratio crosses cultures, time and even nature. Flower petals, fingers and spiral galaxies follow the golden ratio too.
To understand why, take a look at Fibonacci numbers: 1, 2, 3, 5, 8, 13, 21, 34… Each number in the sequence is the sum of the two preceding numbers. It’s an elegant pattern, but the real mathematical magic happens when you divide those numbers into each other:
2/1 = 2
3/2 = 1.5
5/3 = 1.666666666…
8/5 = 1.6
13/8 = 1.625
233/144 = 1.618055556…
Notice, the answers are heading increasingly toward the golden ratio (1.618033988749…). But you don’t have to start with 1 and 2. This trend happens even if you pick two random numbers to start the Fibonacci sequence, like 3 and 14:
Sequence: 3, 14, 17, 31, 48, 79, 127….
14/3 = 4.66666666666…
17/14 = 1.21428571429
31/17 = 1.82352941176
48/31 = 1.54838709677
79/48 = 1.64583333333
127/79 = 1.60759493671
Totally cool, right? An irrational number seemingly defined by aesthetic order. And yet, where is the yearly celebration on January 6 for phi?! We could make fudge! or phyllo dough!
Or we could share libations on February 7 as a eulogy for Euler’s number ‘e’ (2.71828…) — the irrational number that characterizes exponential relationships. Or maybe, we should make marshmallow squares to mark the innumerable dates defined by the square root of 2 and other non-perfect square numbers.
People have been enjoying Pi Day, ever since scientists at San Francisco’s Exploratorium invented the concept in 1988, and likely even before that. But the celebration feels a tad arbitrary. Last year’s Pi Day was hailed as a once-a-century marvel because it hit the first five digits of pi — 3/14/15 — but if we were rounding, today would actually fall much closer to the mark.
Don’t misunderstand me. Pi has brilliant qualities, but why should we shackle our dessert-themed holidays to March 14, when there is so much tasty math to enjoy?
Nsikan Akpan is the digital science producer for PBS NewsHour and co-creator of the award-winning, NewsHour digital series ScienceScope.
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