In a maths class in Educating Essex, a girl asked this question, and didn't get an answer. In one sense, no-one knows. **π**, or pi, is the circumference of a circle divided by its diameter. It is a constant figure, but one that cannot be precisely described in terms of a number. People have calculated it to an almost infinite number of decimal places, and will no doubt continue to do so.

A history of **π** , from David Wilson of Rutgers University Maths department is here, including the speculation that it was first discovered by ancient Babylonians using lengths of rope. This could usefully be repeated using a hula hoop, taping string carefully round the outside, and comparing its length with a string stretched across the diameter. The outside string will probably be a little over three times as long as the string stretched across the diameter.

The next stage in the demonstration is to draw a line on a piece of squared paper, of a reasonable length. We don't need to measure it, and we can call it r. We can then draw a square with r as its base, and we know that the area of the square is r^{2}. Draw another square beside it, using the side of the first square as one of its sides, and the area of the two squares is 2r. Do the same below, so that we have four squares the same size, a little like a block of four postage stamps, and we have four squares with the same central point, and so 4 lots of the original area - 4r^{2}.

Set a pair of compasses, carefully, to the same length as r, and draw a circle on the mid point of the squares. The circle will touch the edge of the square once at each side, and cut off the corners. It's easy to see that the area cut off from the corner is the same each time, so multiplying r^{2} by four is going to give an area that is too big. How much are we cutting off? We know that it's the same amount each time - not only can we see it, but the compass is set to the same length all the way round the circle (or it wouldn't be a circle). We also know that it's less then 4.

We might repeat our experiment with the hula hoop to putting string round other large-ish discs and coins, and find that the longer string is always a little over three times the length of the shorter one. Again, this corresponds to what we can see in the circle - the area is always that much smaller than the area of the squares. But how long is a piece of string, and how accurate are we in measuring it? **π** provides the answer. We might not know what the ratio is exactly, but we know that it is the same for any circle. Multiplying r^{2}, the are of one of our squares, by **π**, or, for the figure used for GCSE foundation, 3.14, will give us the same reduction from the area of the squares to that of the circle.

This explanation has been helpful to students taking GCSE (and some parents), who remembered the formula, but did not know how to apply it, for example calculating (**π**r)^{2} and not seeing how this produced an error. There may be clearer explanations available, and I'd be pleased to hear of them.