What happens when I try to demonstrate ‘funny’ side of math to an innocent soul who loves surprises? It is always to rewarding to start with a simple question that triggers the curiosity. Would you like to play a game? Let’s go…
Can there a be a deep relationship between a pure chance event and the most famous constant, ?? A very simple question asked by the 18th century naturalist Comte de Buffon, which is now famously known as Buffon’s needle led to a very entertaining way of estimating ?. The actual solution to the problem takes a little bit calculus but the take-home message is that you just throw a short stick or match on to the paper with some parallel lines on it, count the number of throws, and how many times the stick / match crossed one of the lines and then you do a a simple division. The more you repeat your action, note down your numbers and do the calculation the more you start to irresistibly get close ?. Where is the mystery? Of course there is nothing in the X-Files sense here, the limit, the calculations, etc. are clear but nevertheless the re-interpretation of end result is just striking. Striking in that sense (click to see the animation):
Buffon's needle visual simulation for estimating PI
It is always a great reward to see the smile and having more and more questions to explore with enhusiasm. As I was trying to find a good animation (you know, playing this throw the needle stuff is not very sustainable for a human after 9-10 throws), I have found a nice explanation of the problem that includes warnings to programmers who wish to implement this ‘simple’ idea, an even nicer animation created by R, and another good explanation that includes a simpler animation.
And finally, yes, of course you can find a Lisp implementation of Buffon’s needle (if you don’t mind the Turkish text surrounding it).
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