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A floor is ruled with equally spaced parallel lines a distance

Dapart. A needle of lengthLis dropped at random on the floor. It is assumed thatL no more than D. What is the probability that the needle will intersect

one of the lines? This problem is known as Buffon’s needle problem.

In summary, I think I spent on this problem a few month, trying to solve it, but suddenly without much of success. For now I have no sleep at night, and I have found some solution, unfortunately this solution is seems to be wrong, I have checked it with a book solution, and me is very sad and crying about that :sad:

So I need hint with this cursed problem, to be more preciously with my solution, why my solution sux. My solution can give a good approximation with small numbers of, andDL

Actually solution:

I have draw a few coordinate Axis, Theta is perpendicular to lines on the floor, Eta is parallel to them. The endpoints of a Needle, have its own coordinates.

Then I have represented all possible values of coordinates of this endpoints as side of the rectangle. This coordinates of endpoints must be no more than. From this stuff I have build the equation for the line in the Cartesian Coords. Then I have calculate the total area of my shape, and then I have calculated the area of triangle in which the endpoints in the different "sides" of the line, which is mean the line must be crossed.L

Then I have divide this triangle are by the total area, and multiplied by factor two, because there is a two line that can be crossed, and I have obtain the probability that the frigging needle will cross the frigging line.. In case ofp(U), andD = 16, my formula gives probability approx.L = 12, and formula which has been discovered by this mr Buffon, gives to us0,45.0,477

Perhaps I need little bit correct my stuff, and then it will sux no more? :( .

Thanx for the answers.

P.S. My solution is actually on the images so I hope, this forum will show ma' images, if not - https://s25.postimg.org/bcx5x9ifj/Buffon_stick.jpg, this is a direct link. And sorry for ma' english level.

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# I Mathematical problem about Buffon's Needle

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