# The True Meaning of Pi Day

## Beautiful math, strange history, and, of course, pie.

There are holidays like Mother’s Day, Earth Day, Thanksgiving Day. Even a Talk-Like-Shakespeare Day. But Friday is Pi Day.

Really! It’s official. The date March 14 (that is, 3/14) was designated Pi Day by House Resolution 224 of the first session of the 111^{th} Congress of the United States. It begins “Whereas the Greek letter (Pi) is the symbol for the ratio of the circumference of a circle to its diameter,” and is followed by 11 more *whereases* before it resolves to support the designation of “Pi Day” to encourage “schools and educators to observe the day with appropriate activities that teach students about Pi and engage them about the study of mathematics.”

It wasn’t the first government resolution to address that renowned Greek letter. In 1897, the state of Indiana passed House Bill 246 dictating that the mathematical constant pi would officially have the value 3.2. There was a duplicitous reason for this number: The fellow who lobbied for the bill was Edwin Goodwin, a country doctor from Solitude, Ind., a crank pseudo-mathematician with loony-toon visions of fame. He claimed to have solved a problem that had baffled great mathematicians for 2,000 years. He managed to have his proof, which required that pi be 3.2, published in the *American Mathematical Monthly*. It was unreserved gobbledygook. But with the credentials of a publication in the country’s leading journal of mathematics, he was able to convince his state representative, Taylor Record, to introduce a bill making Goodwin’s method for squaring the circle Indiana law. Goodwin offered his method as a “gift to the state of Indiana.”

The full House passed the bizarre bill 67 to 0. Had any of the 67 representatives even glanced at the bill? Fortunately, Clarence Abiathar Waldo, chairman of the mathematics department at Purdue University, by chance was visiting the statehouse at that time in support of appropriations for the Indiana Academy of Science. On his counsel, the Senate voted the pi bill down.

It seems that the U.S. 111^{th} Congress was more sensible in 2009. After all, we do want to teach students about pi and engage them in the study of mathematics. Of course, Congress didn’t appropriate any money for this wonderful day. But, hey, it’s a whole day dedicated to engaging students. We’ll take it.

Why pi? The mathematical constant that every schoolchild has at least heard of—I hope—seems to pop up in so many seemingly unrelated areas. Its mystique may be one of the engaging hooks that make a child a scientist. When pi is around, something circular is lurking about. That ever-present pi connects the mysterious infinite world to the finite; infinite loops to straight lines. We see it happen in the *Star Trek* episode “Wolf in the Fold” when the *Enterprise’s* computer tries to compute the last decimal of pi sending the computer into an infinite loop.

By definition, pi is a specific ratio, the circumference of a circle divided by its diameter. As a number, it as approximately equal to 3.14159—approximately, because to pin it down precisely, the decimals would have to go on forever. I like to stop at the 9 in the hundred-thousandths place because, well, that’s good enough for most things, and I can never remember decimals beyond the 9.

It is rigidly linked to the beautiful circle, that consummate representation of perfect symmetry. But it can masquerade in many forms. It appears as a beautiful infinite sum, as an infinite product, or even as an infinitely repeated fraction. Through the wave formulas for light and sound, it tells us which colors should appear in a rainbow and how middle C should sound on a piano. It explains which direction the proverbial needle will fall when it hits the haystack. You will find it describing the morphology of the apple and the energy of stars. It sits deep in the wave functions describing the quantum state of the hydrogen atom. It even plays a significant role in analyzing survey predictions for the next president. And it’s entrenched in Heisenberg’s uncertainty principle, the equation that tells us just how precisely we can ever know the state of the universe.

My favorite, and one of the most surprising relations, is about how pi connects river flow with bird flight. Imagine a river flowing in uniformly erodible sand under the influence of a gentle slope. The sand can be moved—though not easily—by the pressures of the river flow. Over time, the river’s actual length, divided by the straight-line distance from beginning to end (that is, as the crow flies), will tend toward pi. If you guessed that the circle might be a cause, you would be right. Once again, there is that ubiquitous pi lurking about. Over time, the edges of the river tend to dredge themselves to smoothen out any sharp curves. Pi, and by extension circles, are deeply rooted in our perception of the universe.

The symbol π had no meaning in Euclid’s time, other than it being the 16th letter of the ancient Greek alphabet. Only in the 18^{th} century did the Welsh mathematician William Jones use it to denote the ratio of the circumference to the diameter of a circle.

As I explain in my book *Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers*, over the centuries many people approximated pi, starting with the Babylonians. Archimedes in the 2^{nd} century B.C. got it accurately to three decimal places. By the 17^{th} century, the German-Dutch mathematician Ludolph van Ceulen, who spent a lifetime calculating pi, succeeded in getting it to a colossal 35 decimals, 3.14159265358979323846264338327950288... , which is engraved on his tombstone.

Today pi has been calculated to 10 trillion decimal places. You can even smell it. In its modern olfactory form, it is a cologne.

When I asked my 12-year-old twin grandchildren how they celebrated Pi Day last year, they said, “We ate pie and memorized digits.”

“Do you know what pi is?” I asked.

“No,” they said. “It has something to do with a circle.”

With all the magic of pi, and its ubiquity in mathematics, is eating pie and memorizing digits what the 111^{th} Congress had in mind? Surely we can do more.