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), a pi recitation contest (naturally), a giant Pi Day display, and an opportunity to find your birthday in the digits of pi.
In the fall, the Department of Mathematics celebrates Integral Day on October 29.
On this page, you'll find more about Pi Day at 缅北强奸 and more about the fascinating number pi.
Pi Background
Pi is defined to be the ratio between the circumference C of a circle and its diameter d. Thus, 蟺 = 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 hundred trillion digits (see Pi Facts, below). The digits of pi do not appear to have any pattern whatsoever---they seem to be random. It's remarkable that from such simplicity (蟺 = 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 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 . 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 Facts
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The largest number of decimal digits of pi ever computed is two hundred two trillion, one hundred twelve billion, two hundred ninety million (202,112,290,000,000). This was completed on June 28, 2024 by Jordan Ranous, Kevin O鈥橞rien and Brian Beeler using a computer assembled from commercially available parts. The total time of the computation was 104 days. The last ten decimal digits of the result are 3622511852.
The digits were never printed out, but if they were, what would over 200 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 over 400 Friedsam Libraries to hold all of the books required to contain the digits from the Ranous-O鈥橞rien-Beeler computation*.
* We assume that the 缅北强奸 library contains 360,000 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 with an error less than the diameter of a , 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. (This application of the number will please fans of .) Thus, in the mountains of known digits of pi, all digits beyond the 42nd have no practical value.
Here are all the digits of pi you'll ever need:
3.141592653589793238462643383279502884197169.
** We assume that the diameter of the known universe is 93 billion light years and that the diameter of a proton is 1.6鈭10-15 meters. |
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In 2020 : an Earth-sized planet that briskly orbits its star every 3.14 days. |
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The 2018 Pi Day marked the 30th anniversary of the event. The first Pi Day celebration was organized by physicist Larry Shaw at the San Francisco Exploratorium in 1988.
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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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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. |
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The symbol 蟺, 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.
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March 14 is Albert Einstein's birthday. Pi appears in Einstein's field equation for general relativity: G = 8蟺T. |
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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鈭1783) discovered a remarkable equation involving the five most important constants and no others:
e蟺颈 + 1 = 0.
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 鈥渨rong鈥, at least according to Bob Palais and Michael Hartl. By 鈥渨rong鈥, 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 2蟺. Palais calls this constant 鈥渙ne turn鈥 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, 1 Hartl subsequently took up the cause with . Are they right? Is pi 鈥渨rong鈥? Decide for yourself.
We at 缅北强奸 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. 鈥溝 Is Wrong!鈥, The Mathematical Intelligencer, Volume 23, Number 3, 2001, pp. 7鈥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. |
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Pi 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.
- For when "3.14" just won't do. Organized in blocks of fifty digits.
- 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.)
- 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.
- Once this page loads, it sings the digits of pi to you. Unlike pi itself, the song eventually repeats.
- Part of Eve Andersson's , this game tests your knowledge of pi.
- sells numerous pi-related tee-shirts, mugs, and other items. Just search the site for or
Pi Books
- , by David Blatner. ISBN: 0802775624. Blatner maintains a website for his book at . Intended audience: general.
- , by Petr Beckmann. ISBN: 0312381859.
- , by Pierre Eymard and Jean-Pierre Lafon. ISBN: 0821832468. Intended audience: mathematics majors through university professors.
- , 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.
- , 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. Sadly, this book is out of print, presumably due to the fact that a million digits of pi is now available at no cost on numerous web pages. ISBN: 1460976215.
Pi Songs
Happy Pi Day (By LaVern Christianson. Sung to the tune of 鈥淗appy Birthday.鈥)
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 鈥淥h Christmas Tree.鈥)
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.
(All rights reserved, lyric 漏 1997--2007 Lawrence Mark Lesser. Sung to the tune of Don McClean's "American Pie."
Pi to 1000 digits
Each row contains 50 digits (ignoring the initial "3"). One curious feature of this segment of pi is the appearance of , beginning at digit 762. The author Douglas Hofstadter once remarked that he'd like to memorize the digits of pi out to this spot so that he could recite them, concluding with "nine, nine, nine, nine, nine, nine, and so on," giving the impression that the digits continued to repeat.
3.14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999837297804995105973173281609631859
50244594553469083026425223082533446850352619311881
71010003137838752886587533208381420617177669147303
59825349042875546873115956286388235378759375195778
18577805321712268066130019278766111959092164201989