Buffon’s Needle is a wonderful probability experiment you can do with a class that has a most surprising result. Out of a seemingly ordinary, unspectacular experiment involving dropping a pencil between a pair of parallel lines, the relative frequency is related to pi! Here is a superb website that explains the experiment and gives a derivation of why the results tend towards pi.
I tried Buffon’s Needle with a class this week and they loved it. We did over 1500 trials and got 2.90 to 2 d.p., a slightly disappointing result but after showing them the Java applet simulation on the website, they were convinced. Being a top set they were able to follow an explanation of why the result is linked to pi, although they did have to take my word for the integration of 1/2 sin theta between zero and pi!
Buffon’s Needle is a great lesson if you want to show the magical, mysterious side to maths where seemingly unrelated topics such as random pencil drops and pi are shown to be intertwined!