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Buffon's Needle problem (Geo Prob)

  1. Oct 16, 2005 #1

    can someone explain problem "A" for me please. this isn't for school or hw but just something that i dont understand and would like to know where i'm going wrong.

    how would i go about solving question "A"?

  2. jcsd
  3. Oct 16, 2005 #2


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    There is no question A. Did you mean q.1?
  4. Oct 16, 2005 #3
    yes thats what i mean
  5. Oct 17, 2005 #4


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    It seems to me that q.1 is asking you to assume 1,000 needle drops with thetas distributed evenly between 0 and pi.

    First, renormalize by multiplying all areas by 2/pi. After renormalization the area of the large rectangle is 1 and the shaded area is 2/pi. Prob{hit} = (2/pi)/1 = 2/pi as before.

    Now you are to approximate the shaded area by calculating the area for 1,000 little rectangles. The 1st little rectangle has area 0. The 2nd has area = base x height x renormalization = (pi/1000) x sin(pi/1000)/2 x 2/pi = sin(pi/1000)/1000. The 3rd has area = (pi/1000) x sin(2pi/1000)/2 x 2/pi = sin(2pi/1000)/1000. The Nth has area = (pi/1000) x sin((N-1)pi/1000)/2 x 2/pi = sin((N-1)pi/1000)/1000.

    Sum area = [tex]\right.\sum_{N=1}^{1000}\sin\left(\frac{(N-1)\pi}{1000}\right)\left/1000[/tex]

    It seems to me like this sum area is the approximate 2/pi that the question is after. (This still doesn't make a whole lot of sense to me because pi is parametric in the formula itself; so one must already assume an exact value for it before one can approximate it.)
  6. Apr 6, 2007 #5
    I am working on a practical application of Buffon's Needle for when the length of the needle is greater than the distance between the lines.

    I am looking for an EXCEL model to calculate the probability.

    Thanking You in Advance.
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