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Q. A needle is dropped on a paper, keeping it parallel to the plane of paper. Find the probability that the needle cuts one of the parallel lines on the ruled sheet of paper, given that needle is of length 1 unit and distance between 2 parallel lines is one unit. The method I adopted- I assumed the needle to cut a length x units of a parallel line, then, I rotated it in a circle of radius 1/2, and I calculated the angle when the needle just touches the line. I found the arcsin of this value, dividing it by pi, integrated it from x=0 to x=1/2, and multiplied my answer by 2. I hope this is correct. If yes, please tell me a shorter method, if possible. Thanks.
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(Original post by Muttley79)
This is Buffon's needle problem ...
This is Buffon's needle problem ...
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#4
Yes - I set the experiment to Year 7s that have learned about pi (and think they know everything about it) at primary school.
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(Original post by Spandy)
Q. A needle is dropped on a paper, keeping it parallel to the plane of paper. Find the probability that the needle cuts one of the parallel lines on the ruled sheet of paper, given that needle is of length 1 unit and distance between 2 parallel lines is one unit. The method I adopted- I assumed the needle to cut a length x units of a parallel line, then, I rotated it in a circle of radius 1/2, and I calculated the angle when the needle just touches the line. I found the arcsin of this value, dividing it by pi, integrated it from x=0 to x=1/2, and multiplied my answer by 2. I hope this is correct. If yes, please tell me a shorter method, if possible. Thanks.
Q. A needle is dropped on a paper, keeping it parallel to the plane of paper. Find the probability that the needle cuts one of the parallel lines on the ruled sheet of paper, given that needle is of length 1 unit and distance between 2 parallel lines is one unit. The method I adopted- I assumed the needle to cut a length x units of a parallel line, then, I rotated it in a circle of radius 1/2, and I calculated the angle when the needle just touches the line. I found the arcsin of this value, dividing it by pi, integrated it from x=0 to x=1/2, and multiplied my answer by 2. I hope this is correct. If yes, please tell me a shorter method, if possible. Thanks.
http://www.madasmaths.com/archive/pr.../pi_boufon.ppt
need powerpoint to view it
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(Original post by TeeEm)
look at the link
http://www.madasmaths.com/archive/pr.../pi_boufon.ppt
need powerpoint to view it
look at the link
http://www.madasmaths.com/archive/pr.../pi_boufon.ppt
need powerpoint to view it
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