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词汇 Buffon needle problem
分类 英语词汇 英语翻译词典
释义

Buffon needle problem

中文百科

布丰投针问题 Buffon's needle

（重定向自Buffon needle problem）
The red and blue needles are both centered at x. The red one falls within the gray area, contained by an angle of 2θ on each side, so it crosses the vertical line; the blue one does not. The proportion of the circle that is gray is what we integrate as the center x goes from 0 to 1
A quick experiment to estimate π, yielding the value of 34/11≈3.1 based on 17 throws.

18世纪，布丰提出以下问题：设我们有一个以平行且等距木纹舖成的地板（如右图），现在随意抛一支长度比木纹之间距离小的针，求针和其中一条木纹相交的概率。这就是布丰投针问题（又译“蒲丰投针问题”）。

使用积分几何能找到此题的解，并得出一个求π的蒙特·卡罗方法。

英语百科

Buffon's needle 布丰投针问题

（重定向自Buffon needle problem）
The red and blue needles are both centered at x. The red one falls within the gray area, contained by an angle of 2θ on each side, so it crosses the vertical line; the blue one does not. The proportion of the circle that is gray is what we integrate as the center x goes from 0 to 1
A quick experiment to estimate π, yielding the value of 34/11≈3.1 based on 17 throws.

In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:

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.
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