Monday, 4 March 2013

A slice of π

March 14th is denoted π day. Why? Because our American brethren write the date with the month first, producing a date of 3/14, which are the first three digits in the decimal expansion of π.

To celebrate this most holy of mathematical days the Continuing Education Department of the University of Oxford are hosting π day, which is going to be presented by none other than Professor Marcus du Sautoy. And what's more you can join in the discussion.

The project is an ambitious attempt to simultaneously run an online lecture (in which you can take part) as well as stream the presentation live on YouTube. Not only will you get a nice lecture on the properties and history of π, but you'll also get a chance to be part in a huge experiment estimating π.

Using computers can calculate π to any accuracy we would like. But because π is irrational it never repeats. The goal of the experiment is to see how well we can estimate π through physical experimentation. After all, that is how it was first found; as the constant ratio of diameter to circumference of all circles.

Left: initial set up. Right: The rain drops and calculation for π.
Many potential methods of approximating π are possible, many of which are described here. However, I thought I'd suggest one more for all of you stuck here in rainy ol' England.
  1. Draw a large square, the larger the better.
  2. Connect two of the corners by a circular arc.
  3. Wait for the rain. A drizzle is better than a down pour.
  4. As best you can, mark the point where each drop hits the paper.
  5. Catch a cold from being out in the rain. Step 5 is optional.
Call the length of the square's side L. The area of the square is then L2 and the area of the quarter circle is πL2/4. The probability of being inside the circle (having hit the square) is then,
Area of circle/Area of square=π/4.
This can also be estimated through the rain drop data as,
Number of raindrops in the circle/Total number of rain drops inside the square.
Equating these two we find that: four times the above fraction (gained from the data) is an estimate of π.

Good luck with your estimations and I look forward to seeing the results.