Pi Day


Much of the world at large renders dates with a method that appears alien to many Americans: DD/MM/YY. This approach avoids many ambiguities and, if we’re being honest, is most likely the superior technique. At least one indisputable data point in the date format wars, however,  falls squarely in favor of the MM/DD/YY camp.

We get Pi Day!

14/3 simply does not have the cachet of 3/14. First celebrated in 1988, Pi Day is now an annual day of rejoicing among lovers of mathematics and connoisseurs of baked goods. Let’s explore a bit of this “illogical” holiday!

A creme pie created for Pi Day - image by Vellus Aureum

The mathematical concept pi is named for the 16th letter of the Greek alphabet. It’s often represented by the symbol π, which is the lowercase form of the letter in Greek. Of course, the concept was not always denoted in this manner. The Welsh mathematician William Jones first attributed the Greek letter to the concept in 1706. Prior to that date, many people called it “Archimedes’ Constant.”

Many ancient civilizations utilized the concept thousands of years ago, but Greek mathematician Archimedes worked to approximate pi using polygons circa 250 BCE. His algorithm monopolized academic usage for a millennium, leading to the nomenclature in his honor.

But what is the mathematical concept of pi?

If you recall your days in geometry, the most common definition of pi is the ratio of a circle’s circumference to its diameter. In other words, the length of the outside of a circle divided by the length of the line that goes across a circle through its center. In every circle, this ratio is pi. Written in decimal form, pi approximately equals 3.14, hence the celebration of Pi Day on March 14.

The anatomy of pi - graphic by Kjoonlee
Circumference unrolled onto diameters - image by John Reid

Of course, mathematicians love fiddling with things and making up new realities, so other definitions for pi have arisen in the modern era that divorce it from Euclidean Geometry and circles. No matter the tomfoolery injected into its technical meaning, we still have a constant whose first 10 post-decimal digits display as 3.1415926535.

Why do we refer to pi as an approximation? That’s a rational question with an irrational answer. Pi is an irrational number. An irrational number is one that cannot be expressed as the ratio of two integers. You can take any two integers and attempt to divide them by each other and you will never exactly produce pi. 22/7 is close, but not quite right. Because of this irrational attribute, the digits of pi never repeat and never end. (Is that a countable infinity or an uncountable infinity? A little mathematics joke for everyone. The question itself is not a joke. The mathematicians who huff and puff about joking about the difference between countable and uncountable infinities are what is funny here! Sorry to all the mathematicians in my life!)

Since pi’s digits never seem to stop, we can never quite pin it down, but that’s not really a problem. As the digits sprawl to the right, we quickly become very precise when it comes to engineering. In fact, NASA only uses 15 digits of pi for all its calculations. For the entire observable universe, we only need 39 or 40 digits to do all the calculations for which pi is required.

Infinity is a lot bigger than 40, so pi’s irrationality is a boon for someone who might want to do a lot of memorization. One activity held by schools and geek organizations each year is a contest to display how many digits of pi one can recall. 

The recognized world record is 70,000 digits, achieved by Rajveer Meena in 2015. Blindfolded, he achieved the feat in 10 hours. Several efforts not officially endorsed by the Guinness World Records exceed this tally. In 2006, Akira Haraguchi spent 16 hours to hit 100,000 digits, stopping only for bathroom visits and onigiri. Haraguchi uses a mnemonic system in which he translates digits into syllables, allowing him to create stories. The digits of pi are represented as a tale. Beautiful!

In 1988, at the first Pi Day, which occurred at the San Francisco Exploratorium, a physicist named Larry Shaw led staff in circles while eating fruit pies. As you are likely aware, pi is a homophone of the English word pie. A tradition was born. Many celebrate Pi Day each year by baking and/or consuming copious amounts of pie.

Some adherents to the DD/MM/YY format observe Pi Day on July 22, as that matches the approximation of 22/7. Fair enough. However, 22/7 = 3.142857, which deviates from pi on just the third post-decimal digit.

22/7 could never produce the Super Pi Day, which occurred in 2015. That year’s Pi Day was 3/14/15, matching the first four post-decimal digits.

Pi Day also displays a bit of cosmic convergence. On 14 March 1879, Albert Einstein arrived on our planet. Perhaps only a Pi Day birthdate for Archimedes himself would be more apropos!

Mathematicians also note that pi is a transcendental number. This definition means it is not the root of a non-zero polynomial of finite degree with rational coefficients. In Carl Sagan’s classic science fiction novel Contact, a celestial message is concealed within the myriad digits of pi. That sounds like a better sort of transcendence I can get behind!

Further Reading and Exploration


Pi – Wolfram Mathworld

10 million digits of Pi – Princeton University

What is pi? – LiveScience

Pi World Ranking List

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