Alex's Adventures in Numberland - Alex Bellos [66]
With regard to pi, Buffon is remembered for having devised an equation that led to a new method for calculating pi, though Buffon did not himself make the connection. Buffon arrived at his equation by studying an eighteenth-century gambling game called ‘clean tile’, in which you throw a coin on to a tiled surface and bet on whether it will touch the cracks between tiles or rest cleanly. Buffon came up with the following alternative scenario: imagine that a floor is marked with parallel lines spaced evenly apart and that a needle is thrown on it. He then correctly calculated that if the length of the needle is l and the distance between lines is d, then the following equation holds:
Probability of the needle touching the line =
A few years after Buffon died, Pierre Simon Laplace realized that this equation could be used to estimate a value for pi. If you throw lots and lots of needles on the floor, then the ratio of the number of times that the needle hits the line to the total number of throws will be approximately equal to the mathematical probability of the needle touching the line. In other words, after many throws
or:
(The symbol means ‘is approximately equal to’.)
Even though Laplace was the first to write about how pi could be estimated this way, his work followed from Buffon’s equation, so Buffon is the person remembered for it. His achievement put him in esteemed company as a member of the club of mathematicians, including Archimedes and Leibniz, who each found a new way to calculate pi.
The more throws of the needle that are taken, the better the approximation, and aiming needles at boards has become a standard diversion for mathematicians unable to think of more creative ways to pass the time. You need, however, to keep on going a fair while before any interesting result is achieved. An early adopter is said to have been a certain Captain Fox in the American Civil War, who, while recovering from battle wounds, threw a piece of wire eleven hundred times on a board of parallel lines and managed to derive pi to 2 decimal places.
Pi’s mathematical properties have made it a celebrity among numbers, and also a more general cultural icon. Because pi’s digits never repeat, they are perfect for feats of memorization. If remembering numbers is your thing, the ne plus ultra of digits is the digits in pi. This has been a pastime since at least 1838, when The Scotsman reported that a 12-year-old Dutch boy recited all the 155 digits that were known at the time to an audience of scientists and royals. Akira Haraguchi, a 60-year-old retired engineer, holds the current world record. In 2006 he was filmed in a public hall near Tokyo reciting pi to 100,000 decimal places. The performance took him 16 hours and 28 minutes, including five-minute breaks every two hours to eat rice balls. He explained to a journalist that pi symbolized life since its digits never repeated and followed no pattern. Memorizing pi, he added, was ‘the religion of the universe’.
Pi memorization gets a little dull, but pi memorization while juggling, now there’s a competitive sport! The record is held by Mats Bergsten, an actuary in Sweden in his late fifties, who has recited 9778 digits while juggling with three balls. He told me, however, that he is proudest of his achievements in the ‘erest test’, in which the first 10,000 digits of pi’s expansion are divided into 2000 groups of five, beginning with 14159. In the test 50 groups are randomly read out, and the contestant has