Pi Day: What Is Pi and Why Is It so Important?

Today is Pi Day, an annual celebration of the famous mathematical concept that has fascinated people for millenia. But what exactly is π (pronounced like the word "pie"), and where did the concept originate?

Ostensibly, π is the 16th letter of the Greek alphabet, but in mathematics it is used to represent a special number—the ratio of a circle's circumference (the distance around the edge of circle) to its diameter (the distance from one edge to another measuring straight through the center).

Pi—which can be found in nearly all areas of mathematics and physics—is a so-called mathematical constant, meaning however big or small the circle is, its value will always be the same—roughly 3.14159.

But pi is also what's called an irrational number—a "non-repeating" number with infinite value, or in other words, the numbers after the decimal place go on forever. Non-repeating in this sense means that no single sequence of digits—let's take '546' as an example—will ever be repeated forever. The sequence 546 may be repeated many times in a row—this is likely at some point given that pi is infinite—but eventually this repetition will stop.

Despite this, countless enthusiasts around the world have been inspired to try their luck at memorizing and reciting pi to as many digits as possible. Japanese memory master Akira Haraguchi is the unofficial pi memorization record-holder: in 2006, he recited 111,700 digits of the constant, although Guinness World Records have not validated this attempt. Their top honor goes to Rajveer Meena, from India, who recited 70,000 digits over the course of 10 hours in 2015.

This fascination with pi is not just a modern phenomenon. The concept has been studied for thousands of years—with mathematicians gradually becoming more adept at approximating its true value.

A brief history of pi

The earliest written estimates for pi—which are within one percent of the true value— come from ancient Egypt and Babylonia, and date back nearly 4,000 years. One Babylonian clay tablet from around 1900 BC, for example, demonstrated pi to be 3.125, while the Egyptian Rhind Papyrus from 1650 BC placed the number at 3.1605.

Later, around 250 BC, the great Ancient Greek mathematician Archimedes pioneered a new geometry-based approach using an algorithm—or an ordered set of rules—to approximate pi to within a certain range of numbers, finding that the constant could be used to calculate the surface area and volume of a sphere.

Similarly, around 480 AD, the brilliant Chinese mathematician Zu Chonghzi—who was not familiar with Archimedes' method—managed to calculate pi to 3.141592920, also using an algorithm-based approach. This figure was the most accurate estimate for the next 800 years.

Then, in the 16th and 17th centuries, so-called infinite series techniques revolutionized the calculation of pi allowing the number of decimals to be accurately worked out into triple figures.

Pi is an important mathematical constant. J.Gabás Esteban/Flickr

And in 1706, self-taught British mathematics teacher William Jones introduced the use of the Greek letter to represent the constant in his book A New Introduction to the Mathematics. Before this, approximations such as 22/7 and 355/113 were typically used to express the ratio.

In more recent times, the advent of computers has allowed pi aficionados to calculate the number to astronomically high levels of accuracy, far beyond anything Archimedes and his ilk could ever have imagined.

For example, in November 2011, Peter Trueb successfully calculated the constant to a world-record 22,459,157,718,361 (twenty-two trillion, four hundred fifty-nine billion, one hundred fifty-seven million, seven hundred eighteen thousand, three hundred sixty-one) figures using a special program called y-cruncher.

The computer he used to run the program contained 24 hard drives and 6 terabytes of memory to store the huge quantity of data required to process the numbers.

Calculating pi to this level of accuracy has few practical uses, though—other than for testing supercomputers and high-tech algorithms—as most scientific applications require only hundreds of digits or fewer.

For example, NASA uses a maximum of 15 digits in its calculations for sending spacecraft to other planets. And with 39 digits, you would be able to calculate the circumference of the known universe to within the width of a single hydrogen atom, according to mathematician James Grime.

Despite this, pi itself is incredibly useful because it relates to the circle and so is found in many formulae in fields such as trigonometry (a branch of mathematics which examines the relationship between the lengths and angles of triangles) and geometry (the field of mathematics concerned with shapes, size, relative positions and the properties of space)—which are essential to sectors like architecture and robotics, among others.

But pi also has countless applications beyond geometry and trigonometry. For example, it can help scientists to understand objects and phenomena in nature which contain circular shapes, such as the orbit of the planets or the concentric waves created by a stone falling into a pond.

In fact, pi is useful for describing everything from the way light and sound waves ripple to the 'bendiness' of rivers, and it even crops up in calculations where circles are nowhere to be seen, such as Euler's Identity—a probability formula that has been described as the "most beautiful" in mathematics.

Pi Day was first organized by physicist Larry Shaw of the San Francisco Exploratorium in 1988, with the initial celebrations involving the consumption of pie—a tradition that continues to this day. March 14 or 3/14 was chosen as a reference to the first series of numbers in the constant and the date was officially recognised by the U.S. House of Representatives in 2009.

And in case you're wondering, here are the first 1,000 digits of pi:

3.1415926535897932384626433832795028841971693993751058209749445923 0781640628620899862803482534211706798214808651328230664709384460 9550582231725359408128481117450284102701938521105559644622948954 9303819644288109756659334461284756482337867831652712019091456485 6692346034861045432664821339360726024914127372458700660631558817 4881520920962829254091715364367892590360011330530548820466521384 1469519415116094330572703657595919530921861173819326117931051185 4807446237996274956735188575272489122793818301194912983367336244 0656643086021394946395224737190702179860943702770539217176293176 7523846748184676694051320005681271452635608277857713427577896091 7363717872146844090122495343014654958537105079227968925892354201 9956112129021960864034418159813629774771309960518707211349999998 3729780499510597317328160963185950244594553469083026425223082533 4468503526193118817101000313783875288658753320838142061717766914 7303598253490428755468731159562863882353787593751957781857780532 171226806613001927876611195909216420198