A generalization of Buffon's needle problem

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  • ビュフォンの針の高次元化と指導
  • ビュフォン ノ ハリ ノ コウジゲンカ ト シドウ

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Suppose that we drop a needle of length l at random onto the plane with a set of parallel lines a distance d apart. Buffon's needle problem is to calculate the probability that the needle lands crossing one of the lines. We generalize the problem into a higher dimension as follows. Suppose that we put a needle of length l at random in the space with a set of parallel planes a distance d apart. Then we calculate the probability that the needle is crossing one of the planes.

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