Submitted by Clarice Pelczarski on

Every year on March 14^{th} we celebrate Pi day in honor of everybody’s favorite mathematical constant. Pi, represented by the symbol above, is the ratio of a circle’s circumference to its diameter.

In other words, no matter what the size of the circle, dividing its circumference by its diameter will always result in the same number. Pi is represented by a symbol because it is an irrational number that cannot be written as an integer ratio, which means that the numbers that follow the decimal point go on forever with no discernible repetitive pattern.

For the sake of practical applications, just a few decimal places is sufficient for relatively accurate calculations. For instance, according to 19^{th} century mathematician Simon Newcomb, just ten decimals of pi would provide enough accuracy to calculate the circumference of the Earth within a fraction of an inch. Most scientific calculators, which often include a pi button, contain a finite estimation of pi only calculated to a limited number of decimal places.

In 1897, a bill reached the Indiana General assembly that proposed to indirectly legally change the definition of pi to the dubious value of 3.2, in an effort to “solve” the age-old mathematical problem of “squaring the circle.” If passed, the Indiana education system would have henceforth used this approximation in schools across the state. Squaring the circle, suspected but never proven to be impossible by ancient mathematicians, is the problem of whether or not one could construct a square with the same area of a given circle using nothing but a compass and a straightedge for tools. In 1882, this was finally proven to be impossible by the Lindemann**–**Weierstrass Theorem, which among other things proved that the nature of pi prohibits one from “squaring a circle” without using an approximation (hence the proposal to make 3.2 the “official” value of pi). Luckily, a scrupulous mathematician happened to be present on the day that the bill would have come to pass, and it never came into law.

Calculating the infinite digits of pi has become something of a favorite pastime in the world of mathematics. Although once one could only calculate these digits by applying a formula by hand (and there are several different formulae that work), the age of computers has vastly changed the game. In 2010, a Japanese systems engineer named Shigeru Kondo and an American computer science student named Alexander Yee teamed up to set a new world record for calculating the digits of pi. Using computer hardware with sufficient memory capacity provided by Kondo and software with the ability to efficiently calculate pi written by Yee, the pair managed to calculate the mathematical constant to five trillion digits! According to their website, as of December 28, 2013, they have now calculated pi to 12.1 trillion digits.

Another approach to Pi-related record breaking is to memorize the non-repeating digits of the decimal. According to the *Guinness Book of World Records*, the record for most pi places memorized belongs to Chao Lu. In 2005, he successfully recited an astonishing 67,890 digits of pi out of a planned 93,000 (he made a mistake at digit 67,891). The feat was accomplished without any food or bathroom breaks. There is some contention, however, as Akira Haraguchi also claims to hold the record. He has allegedly recited 100,000 digits of pi over a 16-hour period. The entire feat was filmed in a public hall for legitimacy, including his food and bathroom breaks, yet the Guiness Book of World Records association has yet to recognize it.

There are some (often mathematicians) who believe that ratios like pi are the key to understanding the language of the Universe---that something so constant and yet so unknowable can help us unravel the patterns in nature and unlock existential secrets. Whether or not this is true is up for philosophical debate, but whatever your opinion, there is no denying that pi is all around us.

Happy Pi Day!

To learn more about pi and other mathematical marvels, here are few books for both children and adults that you can check out at our library today:

Pi in the Sky by Wendy Mass

The Joy of [pi] by David Blatner

Sir Cumference and the Dragon of Pi: A Math Adventure by Cindy Neuschwander

Here’s Looking at Euclid: A Surprising Excursion through the Astounding World of Math by Alex Bellos

Visions of Infinity: The Great Mathematical Problems by Ian Stewart

Also, acclaimed director Darren Aronofsky wrote and directed a film in 1998 called [Pi] that explores the metaphysical implications of the number.

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