Putting on a spread for Pi day (Image: Steph Goralnick/Getty)

On March 14, mathematics enthusiasts celebrate Pi day, in honour of the famous ratio’s first few digits, 3.14. You probably know that pi is the circumference of a circle divided by its diameter, but here are some less familiar facts about the mathematical constant. We did consider giving you 3.14 facts but alas we had five…

Pi really is in the sky…

The stars overhead inspired the ancient Greeks, but they probably never used them to calculate pi. Robert Matthews of the University of Aston in Birmingham, UK, combined astronomical data with number theory to do just that.


Matthews used the fact that for any large collection of random numbers, the probability that any two have no common factor is 6/pi2. Numbers have a common factor if they are divisible by the same number, not including 1. For example, 4 and 15 have no common factors, but 12 and 15 have the common factor 3.

Matthews calculated the angular distance between the 100 brightest stars in the sky and turned them into 1 million pairs of random numbers, around 61 per cent of which had no common factors. He got a value for pi of 3.12772, which is about 99.6 per cent correct.

… as well as the rivers back on Earth

Back on Earth, pi controls the path of winding rivers from the Amazon to the Thames. A river’s meandering is described by its sinuosity – the length along its winding path divided by the distance from source to ocean as the crow flies. It turns out the average river has a sinuosity of about 3.14.

Pi is the only number to have inspired a literary genre

In his book Alex’s Adventures in Numberland, journalist Alex Bellos describes how pi has inspired a particularly tricky form of creative “constrained” writing called Pilish. These are poems – or “piems” – where the number of letters of successive words is determined by pi.

One of the most ambitious piems is the Cadaeic Cadenza by Mike Keith. It begins with the lines: One/A poem/A raven, corresponding to 3.1415, and continues for 3835 word-digits. Keith has also written a 10,000-word book using the technique.

You can find pi in your front room

The current record for finding the value of pi stands at just under 2700 billion digits, set by Fabrice Bellard late last year. He used a computer, but you can also calculate pi at home with some needles and a sheet of lined paper.

Drop the needles on the paper and calculate the percentage that fall on a line. With enough attempts, the answer should be the needle length divided by the width between lines, all multiplied by 2/pi.

This is known as Buffon’s needle problem, after the French mathematician Georges-Louis Leclerc, Comte de Buffon, who first proposed it in 1733. The theory was put to the test in 1901 by Mario Lazzarini, a mathematician who dropped 3408 needles to get a value of 3.1415929…, correct to the first six decimal places. Subsequent examination of his results suggests he might have fiddled the numbers, as Lazzarini just happened to choose numbers for the needle length and line width that gave the answer 355/113, a well-known approximation to pi.

Your bank details can be found in pi

Pi is an irrational number, which means its decimal representation goes on forever. This means that potentially every possible number you can think of is hidden somewhere in pi – your date of birth, phone number, or even your bank details. What’s more, using a code that converts numbers into letters would let us find the Bible, the complete works of Shakespeare, or indeed every book ever written, if we looked at enough digits.

There’s one catch: for this to be true, pi would have to be a “normal” number, and we don’t yet know if it is. If it’s normal, the numbers 0 to 9 will appear equally often in its decimal representation. That means any single-digit number occurs one-tenth of the time, any two-digit number one-hundredth of the time, and so on.

The probabilities get vanishingly small when you start looking for the huge numbers of digits corresponding to the Bard, but just like those infinite monkeys and their typewriters, you’d get there in the end.

Until mathematicians figure out whether pi is normal or not, why not try searching the first 200 million digits yourself?