Can you calculate Pi using a Solver?

12142019, 12:34 AM
Post: #27




RE: Can you calculate Pi using a Solver?
(12132019 11:30 PM)Valentin Albillo Wrote: The comprehensive list given in a previous post doesn't include MonteCarlo methods to compute Pi if I'm not mistaken (cursory read), and there are some really pretty, though very slowconverging (typically like the square root, i.e.: 100 tries give 2 digits, 10,000 tries give 4, a million tries give 6, and so on.) Π Unleashed, Springer, © 2000, ISBN 3540665722, page 39 3.4 Π and chance (Monte Carlo methods) The needle problem of the Comte de Buffon During the American Civil War, Captain C.0. Fox was recovering from a wound in a military hospital. To pass the time, he threw a number of identical needles in random fashion onto a board on which he had previously drawn a series of parallel lines each a needle's length apart. He counted the number of throws and the number of hits, i.e. instances in which a needle touched or intersected a line. After 1100 throws, the Captain had determined Π to two decimal places. How come? First of all it seems to have been the Comte de Buffon (17071788), who examined this kind of experiment and in whose honour it is now known as the Buffon needle problem. In 1777, Buffon showed that the ratio of hits to throws was 2:Π, or, stated otherwise, that the probability of a needle thrown at random onto the area coming to rest across one of the lines was, ²/Π ≈ 63.7%. With this knowledge, Fox was able to calculate Π by doubling the number of throws and dividing by the number of hits. The interesting thing about the needle problem is that it forges a link between the "geometric" Π and the quite different area of probabilities. There are other similar relationships between Π and chance, from which other methods of calculating Π are derived. They are informatively called Monte Carlo methods. emphasis mine BEST! SlideRule 

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