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Buffon's Needle Problem
In probability theory, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: :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 for the sought probability , in the case where the needle length is not greater than the width of the strips, is :p=\frac \cdot \frac. This can be used to design a Monte Carlo method for approximating the number , although that was not the original motivation for de Buffon's question. The seemingly unusual appearance of in this expression occurs because the underlying probability distribution function for the needle orientation is rotationally symmetric. Solution The problem in more mathematical terms is: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buffon Needle
In probability theory, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: :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 for the sought probability , in the case where the needle length is not greater than the width of the strips, is :p=\frac \cdot \frac. This can be used to design a Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ... for approximating the number pi, , although that was not the original motivation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
