Pi Day

In schools throughout the United States, March 14 is Pi Day. Why? March is the third month, so if we express "March 14" as a decimal, we get 3.14, which is the approximation for the number pi we learned all those years ago. The purpose of Pi Day is simply to celebrate the important and mysterious number pi.

In the St. Bonaventure Department of Mathematics, Pi Day festivities begin precisely at 1:59 p.m. and end precisely 2 hours 65 minutes later. Like the date of Pi Day, these figures are derived from the digits of pi: to eight digits beyond the decimal point, pi is about 3.14 159 265. Our celebrations occur in and near De La Roche 301 and include pie (naturally), pi-ounce bags of m&m's (really), Pi Day songs (naturally), a giant Pi Day

display, and an opportunity to find your birthday in the digits of pi. Pi Day at SBU is sponsored by the SBU Student Chapter of the MAA. In the fall, the SBU Student Chapter sponsors Integral Day.

On this page, you'll find more about Pi Day at SBU and more about the fascinating number pi. The Pi Day page is maintained by Dr. Chris Hill (chill@sbu.edu).

Pi is defined to be the ratio between the circumference C of a circle and its diameter d. Thus, π = C/d. Implicit in this definition is a fact from geometry: in the Euclidean plane, the ratio of the circumference of a circle to its diameter is the same for every circle.

Calculus has been used to prove that pi is irrational, which implies that the digits of pi go on forever without settling into a repeating pattern. Using powerful mathematics and powerful computers, pi has been computed to over one trillion digits. The digits of pi do not appear to have any pattern whatsoever---they seem to be random. It's remarkable that from such simplicity (π = C/d) comes such complexity (the digits of pi).

The idea of "Pi Day" originated with physicist Larry Shaw, who organized the first Pi Day celebration at the San Francisco Exploratorium in 1988. Almost exactly twenty-one years later, on March 11, 2009, the U.S. House of Representatives passed a resolution proclaiming March 14 to be National Pi Day. The resolution encourages schools to teach their students about pi and to "engage them about mathematics." On behalf of the thousands and thousands of people who have enjoyed Pi Day and were, as a result, engaged about mathematics, thank you Mr. Shaw!

The largest number of decimal digits of pi ever computed is 10,000,000,000,050, that is, ten trillion fifty. This staggering achievement was completed in 2011 by Alexander Yee and Shigeru Kondo using a custom-built PC. The total time of the computation was 371 days, although 180 days of this were lost time due to hardware failures.

The digits were never printed out, but if they were, what would ten trillion digits look like? If every book in the Friedsam Memorial Library were replaced by a book containing only digits of pi, we would need 34 Friedsam Libraries to hold all of the books required to contain ten trillion digits*. What is the ten trillionth digit of pi? 5.

 
* We assume that the SBU library contains 250,000 books, that a typical book has 400 pages, and that a typical page holds 3000 digits.

The largest number of digits of pi that you will ever need is 41. To compute the circumference of the universe with an error less than the diameter of a proton, you need 41 digits of pi**. It seems safe to conclude that 41 digits is sufficient accuracy in pi for any circle measurement problem you're likely to encounter. Thus, in the over one trillion digits of pi computed in 2002, all digits beyond the 41st have no practical value. The burgundy pi approximation in the middle of each section header on this page has exactly 41 digits of accuracy. Tuck that number away in your wallet or purse (or cell phone or BlackBerry). If we count the initial "3," the number of digits becomes 42---a fact that will please fans of Douglas Adams.
 

** We assume that the diameter of the universe is 20 billion light years and that the diameter of a proton is 10^-15 meters.

March 14 is Albert Einstein's birthday. Pi appears in Einstein's field equation for general relativity:

G = 8πT.

Europeans cannot have a Pi Day whose date is derived from the initial digits of pi. In Europe, dates are written with the format day/month, which is the opposite of the format used in the United States. Since there's no 14th month and April does not have 31 days, we can't create a sensible European date from the first three digits of pi. However, Europeans can celebrate Pi Approximation Day: June 22. In day/month format, this date is 22 June, corresponding to the fraction 22/7, which is a common rational approximation for pi.

Pi is one of the five most important constants in mathematics. The other four are 0, 1, e, and i. 0 is the additive identity, 1 is the multiplicative identity, e is the base of the natural logarithm, and i is the square root of -1. Leonard Euler (1707−1783) discovered a remarkable equation involving the five most important constants and no others:

Pi is “wrong”, at least according to Bob Palais and Michael Hartl. By “wrong”, Palais and Hartl don't mean factually incorrect; they mean that C/d is a confusing and unnatural choice for the circle constant. They propose that a much better choice would be C/r, which numerically equals 2π. Palais calls this constant “one turn” and Hartl denotes it with the Greek letter tau: 1 turn = tau = C/r. Palais initiated this movement with his persuasive article in The Mathematical Intelligencer, π Is Wrong!¹ Hartl subsequently took up the cause with The Tau Manifesto. Are they right? Is pi “wrong”? Decide for yourself. (We at SBU will continue to celebrate Pi Day for a simple, practical reason. Since tau is about 6.28, Tau Day falls late in June, when most of our students are away.)

1. Palais, Robert. “π Is Wrong!”, The Mathematical Intelligencer, Volume 23, Number 3, 2001, pp. 7–8.