# 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 Mathematical Association of America. 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 3.141592653589793238462643383279502884197169 Background

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 twelve 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!

On this page, the following (common but not universal) convention is used: when counting digits of pi, the initial "3" is skipped. For example, pi to eight digits is 3.14159265.

### Pi 3.141592653589793238462643383279502884197169 Facts

The 2015 Pi Day was called the "Pi Day of the Century," because its date in the day-month-year format was 3-14-15, which gives the first four digits of pi. This splendid event occurs but once it a century. However, one could argue that the 2016 Pi Day is the Pi Day of the Century, because its date is 3-14-16, which gives pi rounded to four digits. |
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The largest number of decimal digits of pi ever computed is 12,100,000,000,050, that is, twelve trillion, one hundred billion, fifty. This staggering achievement was completed in 2013 by Alexander Yee and Shigeru Kondo using a custom-built PC. The total time of the computation was 94 days. The digits were never printed out, but if they were, what would twelve trillion, one hundred billion, fifty digits look like? If every book in the Friedsam Memorial Library were replaced by a book containing only digits of pi, we would need 41 Friedsam Libraries to hold all of the books required to contain the digits from Yee & Kondo's computation*. What is the twelve trillion, one hundred billion, fiftieth 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. |
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The largest number of digits of pi that you will ever need is 42, at least for computing circumferences of circles. To compute the circumference of the known universe with an error less than the diameter of a proton, you need 42 digits of pi**. It seems safe to conclude that 42 digits is sufficient accuracy in pi for any circle measurement problem you're likely to encounter. Thus, in the over twelve trillion digits of pi computed in 2013, all digits beyond the 42nd have no practical value. The gold pi approximation in the middle of each section header on this page has exactly 42 digits of accuracy. Tuck that number away in your wallet or purse or smartphone. This appearance of the number 42 will no doubt please fans of Douglas Adams.** We assume that the diameter of the known universe is 93 billion light years and that the diameter of a proton is 1.6 ∙10^{-15} meters. |
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Based on the digits computed thus far, the digits of pi appear to be random. That is, the digits of pi have the same appearance as an unending list of digits created by repeatedly rolling a fair ten-sided die with the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 on its sides. Is is not known whether the digits of pi continue to have the appearance of randomness. It is not even known whether each of the ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 appears infinitely many times in pi. For all we know, from some point on in the decimal expansion for pi, the digits are just zeroes and ones. This possibility seems extraordinarily unlikely, but we cannot yet prove that it does not happen. You can see the random appearance of the digits of pi for yourself in the thousand digits of pi provided at the bottom of this page. | ||

The symbol π, which is the lowercase Greek letter pi, was first used to represent the ratio of the circumference of a circle to its diameter by William Jones in 1706. Thus, 2006 marked the 300th anniversary of the symbol for pi. | ||

March 14 is Albert Einstein's birthday. Pi appears in Einstein's field equation for general relativity: G = 8πT. |
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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. |
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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:
Some mathematicians (including the one who maintains this webpage) regard Euler's equation as the most beautiful equation in mathematics. Euler's equation can be proved using the techniques of second-semester calculus. |
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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. |
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You can't spell "happiness" without "pi." Well, you could, but who wants "Life, liberty, and the pursuit of hapness"? Not me, man, not me. |

### Pi 3.141592653589793238462643383279502884197169 Sites

At the following pi-related web sites, you can learn more about pi, gaze at the digits of pi, search the digits of pi, listen to pi, match wits with pi, or buy cool stuff celebrating pi.

- The Pi Pages A celebration of and information about mathematics' greatest constant.
- A Million Digits of Pi Provided by the San Francisco Exploratorium (see Pi Background, above), the digits are helpfully arranged in blocks of ten and rows of one hundred.
- http://3.141592653589793238462643383279502884197169399375105820974944592.com/index314159.html The URL of this website is as cool as its contents, which are the first one million digits of pi. The digits are not formatted as nicely as those in the San Francisco Exploratorium's page (see above), but the photo of Dr. Evil makes up for this shortcoming. The person who maintains this page changes its URL slightly (specifically, the "index" portion) from time to time to prevent excessive traffic from crashing his server. The above URL is accurate as of Pi Day 2015.
- The Pi-Search Page Search for any string of digits (up to 120 of them) in the first 200 million digits of pi. For example, you can search the digits of pi for your birthday. (If your birthday were, say, February 26, 1984, you would search for the string 022684 or the string 02261984.)
- Irrational Numbers Search Engine Search the first two billion digits of pi. Not as fast as the Pi Search Page, but it offers ten times the number of digits of pi. Additionally, the Irrational Numbers Search Engine allows you to search the first two billion digits of
*e,*the first two billion digits of the square root of 2, and the first 500 million digits of the golden ratio phi. - Singing Pi Once this page loads, it sings the digits of pi to you. Unlike pi itself, the song eventually repeats.
- Pi Trivia Game Part of Eve Andersson's Pi Land, this game tests your knowledge of pi.
- MathematiciansPictures.com An online gift shop for people who love math, offering high-quality t-shirts, posters, mugs, greeting cards and more, all with mathematical themes. The "Pi Department" is devoted to "everything pi," including Pi Day.

### Pi 3.141592653589793238462643383279502884197169 Books

- The Joy of Pi, by David Blatner. ISBN: 0802775624. Blatner maintains a website for his book at joyofpi.com. Intended audience: general.
- A History of Pi, by Petr Beckmann. ISBN: 0312381859.
- The Number Pi, by Pierre Eymard and Jean-Pierre Lafon. ISBN: 0821832468. Intended audience: mathematics majors through university professors.
- Pi: A Source Book, 3rd edition, edited by Lennart Berggren, Jonathan Borwein, and Peter Borwein. ISBN: 0387205713. This is a large and diverse collection of articles about pi, ranging from the first known written reference to pi (the Egyptian Rhind Mathematical Papyrus, circa 1650 B.C.) to a method for computing the ten billionth hexadecimal digit of pi without computing any of the previous digits (by Bailey, Borwein, and Plouffe, 1997). Intended audience: for buying the book, teachers; for reading portions of the book, anyone with an interest in pi.
- Pi Reference: A Table of One Million Digits, by David Dubowski. The digits are arranged in columns with a place counter, so that you know where you are in the digits at any place in the book. ISBN: 1460976215.

### Pi 3.141592653589793238462643383279502884197169 Songs

**Happy Pi Day** (By LaVern Christianson. Sung to the tune of “Happy Birthday.”)

Happy Pi Day to you,

Happy Pi Day to you,

Happy Pi Day everybody,

Happy Pi Day to you.

**Oh Number Pi **(By LaVern Christianson. Sung to the tune of “Oh Christmas Tree.”)

Oh, number pi

Oh, number pi

Your digits are unending,

Oh, number pi

Oh, number pi

No pattern are you sending.

You're three point one four one five nine,

And even more if we had time.

Oh, number pi

Oh, number pi

For circle lengths unbending.

Oh, number pi

Oh, number pi

You are a number very sweet,

Oh, number pi

Oh, number pi

Your uses are so very neat.

There's 2 pi r and pi r squared,

Four-thirds pi r cubed---don't be scared.

Oh, number pi

Oh, number pi

We know that pi's a tasty treat.

**American Pi** (All rights reserved, lyric © 1997--2007 Lawrence Mark Lesser. Sung to the tune of Don McClean's "American Pie."

### Pi to 3.141592653589793238462643383279502884197169 1000 digits

Each row contains 50 digits (ignoring the initial "3"). One curious feature of this segment of pi is the appearance of six consecutive nines, beginning at digit 762. This sequence of nines is called the *Feynman point*, after physicist Richard Feynman.

3.14159265358979323846264338327950288419716939937510

58209749445923078164062862089986280348253421170679

82148086513282306647093844609550582231725359408128

48111745028410270193852110555964462294895493038196

44288109756659334461284756482337867831652712019091

45648566923460348610454326648213393607260249141273

72458700660631558817488152092096282925409171536436

78925903600113305305488204665213841469519415116094

33057270365759591953092186117381932611793105118548

07446237996274956735188575272489122793818301194912

98336733624406566430860213949463952247371907021798

60943702770539217176293176752384674818467669405132

00056812714526356082778577134275778960917363717872

14684409012249534301465495853710507922796892589235

42019956112129021960864034418159813629774771309960

51870721134999999837297804995105973173281609631859

50244594553469083026425223082533446850352619311881

71010003137838752886587533208381420617177669147303

59825349042875546873115956286388235378759375195778

18577805321712268066130019278766111959092164201989