Gaussian Technologies Department of Mathematics x=cose 6 we see that this inequality describes the shaded region under the graph hence, we conclude that the probability of the needle falling across a crack equals to the following ratio of areas cos 8de area under curve area of rectange 兀/2 兀/22 which is slightly less than 3 Who would have thought that a question starting out on probability could have used the integral calculus to solve it Here is an experimental procedures to think about. say that i decided to carry out the experiment of tossing and recording the amount of times it falls across the crack. i toss the needle n times and record when it falls k times. I happen to be very free to the point where I performed this experiment an infinite amount of times. Mathematically then we have k 2 n→n兀 which reduces to MISCELLANEOUS CALCULUS RELATED PUZZLESGaussian Technologies Department of Mathematics MISCELLANEOUS > CALCULUS RELATED PUZZLES we see that this inequality describes the shaded region under the graph. hence, we conclude that the probability of the needle falling across a crack equals to the following ratio of areas: area under curve area of rectange = cos! 0 " /2 # d! " 2 = 1 " 2 = " 2 which is slightly less than 2 3 . Who would have thought that a question starting out on probability could have used the integral calculus to solve it. Here is an experimental procedures to think about. Say that I decided to carry out the experiment of tossing and recording the amount of times it falls across the crack. I toss the needle n times and record when it falls k times. I happen to be very free to the point where I performed this experiment an infinite amount of times. Mathematically then, we have limn!" k n = 2 # which reduces to ! 2 x ! 1 x = cos!