Buffon's needle

A needle of length ℓ\ell is dropped onto a floor of parallel lines spaced ℓ\ell apart. What is the probability it crosses a line? (to 2 decimals)

Show hints (2)+
  1. Parametrize by the center's distance to the nearest line and the angle.
  2. Integrate the crossing condition over θ.

Answer

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0.64 (± 0.01)

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