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In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:〔''Histoire de l'Acad. Roy. des. Sciences'' (1733), 43–45; ''Histoire naturelle, générale et particulière'' Supplément 4 (1777), p. 46.〕 :Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips? Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry. The solution, in the case where the needle length is not greater than the width of the strips, can be used to design a Monte Carlo method for approximating the number π, although that was not the original motivation for de Buffon's question. == Solution == The problem in more mathematical terms is: Given a needle of length dropped on a plane ruled with parallel lines ''t'' units apart, what is the probability that the needle will cross a line? Let ''x'' be the distance from the center of the needle to the closest line, let ''θ'' be the acute angle between the needle and the lines. The uniform probability density function of ''x'' between 0 and ''t'' /2 is : The uniform probability density function of θ between 0 and π/2 is : The two random variables, ''x'' and ''θ'', are independent, so the joint probability density function is the product : The needle crosses a line if : Now there are two cases. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Buffon's needle」の詳細全文を読む スポンサード リンク
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