Buffon's Needle A floor is ruled with equally spaced parallel lines a distance D apart. A needle of length L is dropped at random on the floor. It is assumed that L 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 D, and L 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 L. 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. 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. p(U). In case of D = 16, and L = 12, my formula gives probability approx. 0,45, and formula which has been discovered by this mr Buffon, gives to us 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.