How I wish I could calculate pi

By Burkard Polster and Marty Ross

The Age, 17 March 2008

Did you all enjoy March 14? That was Pi Day, when we celebrate the mathematical constant π. Why March 14? Because the Americans who came up with the idea write this date as 3.14. And π has a second birthday, in July, on 22/7.

You know that π is equal to the circumference of a circle divided by its diameter. But here are some surprising π facts to impress your friends on the next Pi Day.

π is not exactly 3.14 or ²²/₇ - it is an irrational number, a number that cannot be written exactly as a fraction. So, how can we calculate it? Here is a beautiful formula for π, without a circle in sight:

^π/₄ = ¹/₁ - ¹/₃ + ¹/₅ - ¹/₇ + ¹/₉ - ¹/₁₁ + ...

The formula allows you to estimate π, by adding up more and more terms of the infinite sum. There are much better methods to estimate π, but we're interested in a much stranger method; we'll use car number plates.

Suppose you pick two whole numbers at random. What is the probability P that the two numbers have no common factor? Amazingly, the answer involves π: the probability is P = ⁶/_π².

Now, to the number plates. Sit down by a busy road and watch the cars go by. When you see two cars together, write down the 3-digit numbers on their number plates and see if they have a common factor. When you've had enough, count how many number plate pairs did not have a common factor, and divide this by the total number of pairs. This fraction will approximate P in the above equation. And then you can solve the equation to give you an approximation for π.

This is indeed a strange way to calculate π, but a very similar method was reported in the prestigious science journal Nature. There, π was estimated to a high degree of accuracy using random astronomical data. Truly, π in the sky.

How did we celebrate Pi Day? With pie, of course. And, we sang the first 100 digits of π with Kate Bush in her song Pi. Then we watched the 1998 cult movie π. Alas, Kate actually only gets the first 53 decimals correct. And, in the thousands of digits in the opening credits for the movie π, only the first 8 are correct.

Finally, how can you remember π, more accurately than just 3.14 or ²²/₇? Simple! Just remember the title of this column.