Salopians celebrate World Pi Day with interesting experiments

To celebrate World Pi Day last week, the Lower Sixth Further Mathematicians recreated an experiment known as Buffon’s Needle to estimate the value of the mathematical constant, pi.   

The equipment required was very simple – a box of cocktail sticks and a piece of lined paper.  The pupils dropped the sticks at random onto the paper and recorded the proportion of sticks that landed across one of the lines.  By repeating this a large number of times it was possible to derive an estimate for pi by comparing their results to the theory.  For this they had to consider the position and orientation of a stick as it landed, and then do some seriously challenging bivariate probability calculations.

One of the groups achieved an estimate for pi of 3.156, which is less than half a percent away from the true value (3.14159…).   

Overall results varied due to experimental randomness, but the pupils found this a stimulating and thought-provoking experience, encompassing trigonometry, calculus, and theoretical and experimental probability.  And, most of all, it was serious fun! 

Martin Johnson 
Head of Mathematics