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- W842009 abstract "If a needle of length I is dropped onto a floor con structed of evenly spaced wooden planks of width k, what is the probability that the needle crosses a crack between planks? This question is Buffon's needle problem.* Schroeder (1974), in an article in the Mathematics Teacher, considers this problem and shows that for the case I where / < k. He also asks what is the probability that the needle will cross a crack in the floor. To solve this problem, it is necessary to repre sent the possible positions in which the needle could land, relative to the cracks in the floor, by a set of independent variables. How many such vari ables would be needed? Two variables?an jc coordinate and ay-coordinate?are required to spec ify the position of one point on the needle. But the needle could fall in infinitely many positions that have this point in the same position, relative to the cracks in the floor, but different slopes. To deter mine a unique position of the needle, in addition to specifying the position of a particular point, we could specify the slope of the needle. This process would require a third variable. Thus we see that three independent variables are required to deter mine the result of a needle toss. In solving his vari ation of the needle problem, Schroeder mistakenly uses two variables to represent the set of all possi ble needle tosses and obtains an incorrect answer, P = 21V2 kn" @default.
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- W842009 date "1995-03-01" @default.
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- W842009 title "Buffon’s Needle Problem for a Rectangular Grid" @default.
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- W842009 doi "https://doi.org/10.5951/mt.88.3.0205" @default.
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