If I throw 1000 10centimeterlong needles on to a tiled floor, where each tile is a 10 cm x 30 cm rectangle, approximately how many needles will end up lying across a crack?
You may assume that the widths of both the needles and the cracks are negligible.
(In reply to
re(2): Simulation supports by Charlie)
Charlie, here's why I posted the MathWorld reference.
When I saw your solution, I thought that it was counerintuitive that the likeliness, that a needle crossing the 1 unit away lines also crossed the 3 units away lines, was the same as the other way around.
Next day, I started thinking on it in the car, visiting customers and when returning home, I wanted to post a question on it. Then I saw your comment "second thoughts" and there was no need for a further posting. I also remembered there was something on this on MathWorld, I searched for the formula and as it was in agreement with your result, I didn't feel I had tot post it. After your simulation test, it posted the link just to show that they arrived at the same result.
Now when you make the remark that their formula doesn't work for l > a or b, I think your formula has the same problem: in your integration you do not take into account the length either (Although I may have missed it)

Posted by Hugo
on 20050121 19:35:00 