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Thursday, July 13, 2017

San Francisco Exploratorium- Buffon's Needle





Today, I visited the Exploratorium in San Francisco. There were various exhibits in the Mathematics section from the parabola- powered calculator to models of various Archimedean solids to the square shaped wheel. One of the exhibits I found interesting was the “Pi(𝜋) Toss,” in which the value of pi would be estimated by tossing chips. I would be given chips and I would randomly toss any number of chips onto the table. According to the instructions, tossing all 22 would be preferable. Then, I had to count how many times the lines on the chips cross the lines on the table and using the calculator, I divided the total number of chips tossed by the number of crossings. This answer would yield an approximation of pi. This value was not very close to pi at first, but with several more rounds of tosses and averaging the results over time, I was able to obtain values closer to the actual value of pi.
    Pi is a famous mathematical constant relating the circumference of a circle to its diameter. More tosses would yield more accurate results; hence, if we were to have the patience to toss chips all day, all week, all year we would obtain an increasingly accurate estimate of pi. This method of calculating pi, also known as Buffon’s Needles, was discovered over 300 years ago by a French mathematician, Count Buffon. Buffon discovered this method in an accident as he had wanted to calculate the odds of winning in a then-popular game of chance, in which one would toss a coin onto a tiled floor and bet on whether it would land entirely within one of the tiles.


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