p: Easier than you think?

In Statistics, when an experiment is conducted, the results are analysed for any patterns or trends present. Graphs are usually made and examined to see if the results fit any special distribution e.g. the Normal distribution; or to see if there is any correlation in the results.

One of the best known mathematical constants is p (The Greek letter, pi). It crops up in numerous mathematical relationships such as V = (4/3)pr³ to find the volume of a sphere of radius r. The basic definition of p is the ratio of the circumference of a circle to its diameter. But it is difficult to evaluate p because it is impossible to express both the diameter and circumference of a circle as either whole numbers or fractions.

For thousands of years, great Mathematicians and Scientists have attempted to calculate p. Archimedes (287-121 B.C.) estimated p to be between 3(10/71) and 36, while in 1717, Abraham Sharp used the following series to calculate p to 72 decimal places:

The latest values of p, calculated by modern-day super computers, run into thousands of decimal places.

Bearing in mind all of the above, it might be surprising to know that a simple experiment allows us to calculate an approximate value for p. Mark off on a large sheet of paper a series of parallel lines two inches apart. Cut ten sticks, each one inch long; toothpicks will do. Now hold the ten sticks about a foot above the ruled paper and drop them.

Now count the number of sticks that either touch or cross a line. If you repeat this 100 times, you will have dropped 1000 sticks altogether. Total the number of sticks that have crossed or touched a line and divide this total into 1000, the total number of sticks thrown. The division, theoretically, according to the laws or probability, should give the value of p. Of course in reality you won't get the exact value of p (just as in coin tossing you can't expect an exact distribution of heads and tails), but it would be interesting to see just how close we could get to the real value.