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!
A great field day activity for end of the year HS math — probability AND geometry (Pi): Use up those last, past-their-safe date, frozen food-service hot dogs instead of throwing them away (donations from supermarkets help too). The idea is to use hot dogs that are NO LONGER EDIBLE — don’t waste! –
Mark off the football field or basketball court with parallel lines. Distance apart:the length of an average hot dog. Then toss outdated, frozen hot dogs from the top of the bleachers onto the marked-off field. Hot dogs hitting a parallel line are HITS and hot dogs NOT hitting a line are MISSES. Use the scoreboard to keep track of HITS(home team) vs. MISSES (visitors). This is basically a giant, fun Buffon’s Needle and the mysterious outcome, so close to Pi, is fun. You need at least 1,000 hot dogs. To keep the math simpler, try a multiple of 213 (like 2,130 hot dogs or 1,065). Other possible objects would be pens out of ink, or stale breadsticks, or Have fun!