Celebrating pi - our favourite non-whole number

There's more to pi than meets the eye, writes Alex Bellos. 

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Pi is an irrational number, its decimal expansion will never repeat in a periodic pattern. This unpredictability has captured the imagination of mathematicians, artists, writers and musicians.

He’s a nerd, I guess!

You may not have noticed, but the sentence above is written in “pilish”, a style of constrained writing in which word length is determined by the digits in the mathematical constant pi. As every student knows, pi – the ratio of a circle’s circumference to its diameter – is 3.1415 to four decimal places. “He’s” has three letters, “a” has one and the remaining words have lengths four, one and five.

Many poems have been written in pilish – “piems”, of course – and there’s even a pilish novel 10,000 words long. As such, pi is the only mathematical constant to have inspired a literary genre. In fact, no other non-whole number has been garlanded by so much cultural attention. Pi is the name of a song by Kate Bush, a film by Darren Aronofsky and a perfume by Givenchy. Memorisation of pi’s decimal expansion is a competitive sport, with the record of 100,000 digits held by retired Japanese engineer Akira Haraguchi. You can buy a treasure trove of pi merchandise online such as T-shirts, jewellery, stationery and poster art.

On the 14th of March, the world celebrates Pi Day.

The date was chosen because it writes out 3/14. Well, it does if you are American, which is annoying for the rest of us, but in fairness it was originally an American idea. We should probably be grateful since there are only 30 days in April, ruling out what would be our Pi Day, 31/4.

The 2015 Pi Day was the most eagerly anticipated of our lifetime, since for the first time in a century the date shows pi for five digits: 3/14/15

I know – the thrill is almost unbearable. Imagine the feeling at 9:26:53am.

Ancient Greek mathematician Archimedes, the first person to arrive at an approximate value of pi. – Getty Images

Fascination with the ratio of a circle’s circumference to its diameter is thousands of years old, even though it only gained the symbol of the Greek letter π in 1706, when the Welsh mathematician William Jones suggested it as an abbreviation of either “periphery” or “perimeter”.

The circle is the simplest two-dimensional shape there is. It is visible in an eyeball, a planet and the cross-section of an egg, and you can draw one easily with a piece of string or a pair of compasses. The fact that the two simplest measurable quantities of a circle – around it and across it – produce a ratio that is so messy to express has led to one of the epic narratives of mathematics: the race to find better approximations. Archimedes was the first to two decimal places in the third century BCE, German-Dutch mathematician Ludolph van Ceulen got to 20 in 1596, English astronomer John Machin reached 100 in 1717 and the record stands at 13.3 trillion decimal places, announced last October by an anonymous programmer known online as “houkouonchi”.

Pi is a metaphor for the unexplained; a link between the beautifully simple and the infinitely complex.

The race will go on forever since pi is an irrational number, meaning that the digits in its decimal expansion will never repeat in a periodic pattern. It is also likely that pi is “normal”, meaning that each of the digits from 0 to 9 will appear in the expansion exactly one tenth of the time. Pi’s digits seem to mimic randomness exceptionally well, meaning that – theoretically, at least – it should be possible to find any number string somewhere in pi.

Its unpredictable cacophony of digits, arising from such a simple definition, is one reason why pi has captured the imagination not only of mathematicians but also of artists, writers and musicians. Pi is a metaphor for the unexplained; a link between the beautifully simple and the infinitely complex.

Pi is also interesting to mathematicians because it crops up frequently in areas with no obvious connection to geometry or circles. For example, if you toss a coin 2n times, and n is very large, the probability of getting equal numbers of heads and tails is 1/√(nπ).

Albert Einstein whose birthday, March 14, appropriately falls on Pi Day. – Getty Images

Pi Day’s status as an annual international celebration of science is reinforced because March 14 is also Albert Einstein’s birthday. To be born on such an appropriate date is surely further evidence of his genius. At Princeton, where Einstein lived for two decades, Pi Day is now one of the biggest outdoor events of the academic year, with many activities based around the eating and throwing of pies.

It was on the West Coast, however, where Pi Day was born. The earliest official incarnation took place at the Exploratorium, a science museum in San Francisco, in 1988. Since then Pi Day has grown to be celebrated all over the world, including in those countries where they write the date correctly. Schools use it as an excuse to have fun with mathematics, and grown-ups don’t like to be left out.

Pi Day has turned into Christmas for maths lovers (Christmaths?), a day to celebrate not only the geometry of circles but everything about the subject. Pi has long outgrown its origins as a mere ratio to become a cultural icon in the wider world.

The π fest: a blast!

More on mathematics from Cosmos: Seduced by calculus

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Alex Bellos is the author of Alex’s Adventures in Numberland and Alex Through the Looking Glass. He writes a maths blog for The Guardian.
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