Bet you didn’t know this about Pi

Happy Pi Day (3/14)!

Pi shows up everywhere. Here’s one place: Did you know that Buffon’s Needle Problem, one of the oldest problems in Geometric probability, was posed by Count Buffon, who was inspired by a popular game of chance of his time? In that game, you would toss coins onto a tiled floor and bet on whether the coin would land entirely inside one tile. Count Buffon modified the problem to look at the probability that a needle (or stick) dropped on a grid of parallel lines would cross a line. Counting the number of stick crossings using multiple tosses, you can approximate Pi:

See the Science Friday article (where this image is from) for more: https://www.sciencefriday.com/articles/estimate-pi-by-dropping-sticks/
Try simulating stick-dropping yourself here, and see how close you can get to Pi:
Bonus: we know that random number generators aren’t perfect (and are not really “random”). Some generators are not that good, but others do a pretty good job.  If you write your own Buffon’s Needle simulator, you could use it to test how good different underlying random number simulators are. (More on randomness here: https://www.random.org/analysis/ )
Find some history of Pi here:
Enjoy Pi Day!
(Source: L. de Pillis, chair of the mathematics department at Harvey Mudd)


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