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Needle on parallel lines, problem

  1. Mar 7, 2007 #1
    Hi, I was given a problem by the professor, and I feel like I do not know where to begin. Well, here is the problem:
    Endless, parallel East-to-West lines are spaced 2 inches apart on the ground, and a needle of length 1 inch is randomly tossed on the ground.
    Compute the probability that the needle touches a line.

    I have tried attempting it, but I really don't have anywhere to start. Would anyone perhaps nudge me in the right direction? Thanks in advance.

  2. jcsd
  3. Mar 7, 2007 #2
    This is a classical problem with a very interesting solution. There's a couple ways of doing it. Think about circles that spinning the needle generates...
  4. Mar 7, 2007 #3


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    One thing you will need to decide is: what is your random variable and what probability distribution will you use? It is probably simplest to assume a uniform distribution but what variable? The position of the center of the needle or one end point? The angle the needle makes with the horizontal? A combination of those?
  5. Mar 7, 2007 #4
    ah thx guys. :wink:
  6. Mar 7, 2007 #5
    oh yeah nice problem, a classic one too...... I won't spoil the fun but just do some geometry. In fact... I remember that there is like this one guy that does this experiment over and over and over... and over again to estimate a certain mathematical constant. :wink:
  7. Mar 7, 2007 #6
    And then fudged his results before publishing them, of course.

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