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Buffons needle variation

  1. Dec 20, 2006 #1

    daniel_i_l

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    In the "buffons needle" riddle you have a paper with horizontal lines in it all 1 unit apart and you drop a needle 1 unit long - you have to calculate the chance that the needle will hit a line. but i remembered the riddle wrong so instead i tried to solve the same question with both horizontal and vertical lines (graph paper). all of the cells are 1X1 unit. i got that the chance of hitting a line is:
    3/pi which is about 95%
    is that right?
    Thanks.
     
  2. jcsd
  3. Dec 20, 2006 #2

    StatusX

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    Homework Helper

    I get the same answer. Also, note the result proves pi>3, and since it's obviously pretty likely the needle will hit a line, it shows pi is pretty close to 3. Maybe you can get other approximations for pi using a similar method, which is ironic considering the point of the original problem was to empirically approximate pi.
     
    Last edited: Dec 20, 2006
  4. Dec 21, 2006 #3

    daniel_i_l

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    I wrote a program that simulates a needle falling 10000000 times and counts the times that it hits a line. using that i got that
    3/pi = 0.95521 or pi = 3.14067 - ok but i guess that this method of calculating pi doesn't converge very fast.
     
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