Have your pi and eat it too

“It made an incredibly strong impression on me,” Daubechies said. “I remember my father let me touch [the] circles I would otherwise never have been allowed to, like the precious china plates hanging on our wall. I got to take them down and measure them. My mother was very worried.”

Today is a day of celebration for Daubechies and her colleagues and students in Fine Hall, and not just because it’s the last day of midterms. March 14 is celebrated in math classes across the country to honor the number pi — 3/14 mirrors the first three digits of pi, 3.14.

Pi Day is a time of rejoicing — a time for pie-eating contests, pi-digit-recitation competitions, pi-themed clothing, pi jokes (What do you get when you divide the circumference of the sun by its diameter? Pi in the sky!) and other forms of unabashed nerdiness.

“What’s fun about pi is that everyone knows the number,” Daubechies said. “We all see it in elementary school. People feel they have an appreciation for what it means.”

Pi and popular culture

Popular television shows, like “The Simpsons” and “Star Trek,” have helped spread pi’s appeal to mainstream audiences.

In perhaps its most heroic role, pi saves the USS Enterprise starship in the “Star Trek” episode “Wolf in the Fold,” when the evil Redjac takes over the computer running the ship.

Spock tells the computer to “compute to the last digit the value of pi,” destroying the computer with this impossible demand and thereby freeing the ship.

In an episode of “The Simpsons,” “Lisa’s Sax,” two school girls play a patty-cake-style hand game while chanting: “Cross my heart and hope to die, Here’s the digits that make pi: 3.1415926535897932384...”

In another “Simpsons” episode, “Marge in Chains,” Kwik-E-Mart proprietor Apu testifies that he can recite pi to 40,000 decimal places. “The last digit is one!” Apu says, correctly.

“Mmmm, pie,” Homer says.

In preparation for the episode, “Simpsons” writers wrote to NASA asking for the 40,000th digit of pi, and NASA responded by sending back a printout of the first 40,000 digits.

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One trillion digits!

Forty thousand may seem like a lot of digits, and in fact, 40 decimal digits are all that we really need for practical calculations, Daubechies said.

She referenced a 1996 article about pi, in which lead author David Bailey, the chief technologist at the Lawrence Berkeley National Laboratory, wrote that the “value of pi to 40 digits would be more than enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton.”

The first 40,000 digits, however, are barely the tip of the computational iceberg that has helped researchers calculate more than one trillion digits of pi in the past few decades. Yasumasa Kanada at the University of Tokyo has computed more than 6.4 billion digits and currently holds the world record.

Not everyone, however, has been eager to see pi grow so long.

In 1897, the Indiana House of Representatives passed a bill proposing three formal — and inaccurate — definitions of pi. The bill was based on the work of a Dr. Goodwin, who fancied himself an amateur mathematician and claimed he had definitively computed three official values for pi: 3.2, 3.23 and four. Goodwin also copyrighted his ideas and announced that he would allow only schools in Indiana to teach them for free and that everyone else in the country would have to pay him a royalty if they wished to teach or use these “facts.”

The bill was approved by the Senate Education Committee, but Purdue mathematician C.A. Waldo put an end to it before it could be passed into law.

Perhaps the most famous truncation of pi is in the “Second Book of Chronicles.” King Solomon is constructing the Temple of Jerusalem, and he builds a tub of “ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about” (1 Kings 7:23). In other words, the circular tub has a diameter of 10 cubits and a circumference of 30 cubits, in which case pi would equal exactly three.

The rabbi Nehemiah, in 150 AD, pointed out that while the diameter of the tub had been measured from the outer rim of the thick stone, the circumference measure was taken along the inner circle, and it was this discrepancy that accounted for the inaccurate portrayal of pi.

A brief history of a lengthy number

The first of pi’s trillion calculated digits date back to the ancient Egyptians and Babylonians, who used 3.16 and 3.125, respectively, as rough estimates of pi.

Mathematicians across the globe have been computing more and more accurate estimates of pi for centuries since, but it was a set of mid-20th-century advances in computing that allowed for the discovery of billions and billions of digits.

John von Neumann, one of the first faculty members at the Institute for Advanced Study in Princeton, played a crucial role in designing ENIAC, the first electronic computer, which in 1949 more than doubled the number of known digits by correctly calculating 2,037 of them.

Today, calculating long values of pi is a common method for testing new computer chips, Daubechies said. A great deal also remains unknown about pi, she added, most notably the question of whether its decimal expansion is normal, that is, whether each digit occurs with relatively equal random frequency in pi.

Irrational holiday

Lillian Pierce ’02 GS said she usually celebrates Pi Day at 3:14 p.m. in 314 Fine Hall or the common room next to it. In the annual pi-reciting and pie-eating contests held in Fine, Pierce added, the physics team usually beats the math team at eating.

“Pi itself is one of the fudnamental constants of mathematics. So you could say that it is very important. But it’s also very beautiful,” Pierce said. “Pi Day is a great way for mathematicians to poke fun at themselves. If everyone else is always poking fun at us, it’s only fair we should have a turn too.”

The first Pi Day celebration at Princeton took place in 1988, said Yang Mou ’10, president of the undergraduate math club. This year’s celebration is today at 2 p.m. in the Fine Hall common room.

Pierce also makes a pi dress every year for the occasion. In the past, she has embroidered roughly 50 digits of pi around the hem of a dress. This year, however, she is going for “sheer quantity of digits.” If she uses small enough numbers, she estimates, she may be able to fit as many as 1,000 digits around a skirt.

Pierce, like Daubechies, first discovered the joys of pi as a girl when she read a 1992 New Yorker article about pi by Richard Preston.

“I’d always liked numbers, but reading about this many numbers all strung out in an infinitely long, beautiful sequence was incredibly inspiring,” Pierce said.