The Buffon Needle Experiment. Thefollow ing experiment was devised byComte Georges-Louis

Chapter 4, Problem P4.27

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The Buffon Needle Experiment. Thefollow ing experiment was devised byComte Georges-Louis Leclerc deBuffon (17071788), a Frenchnaturalist. A needle of length 1 inch isdropped onto paper that is ruled withlines 2 inches apart. If the needle dropsonto a line, we count it as a hit. (SeeFigure 8.) Buffon conjectured that thequotient tries/hits approximates p. For the Buffon needle experiment, you must generate two random numbers: one todescribe the starting position and one to describe the angle of the needle with thex-axis. Then you need to test whether the needle touches a grid line.Generate the lower point of the needle. Its x-coordinate is irrelevant, and you mayassume its y-coordi nate ylow to be any random number between 0 and 2. The angle between the needle and the x-axis can be any value between 0 degrees and 180degrees (p radians). The upper end of the needle has y-coordinatey y high low = + sinThe needle is a hit if yhigh is at least 2, as shown in Figure 9.Stop after 10,000 tries and print the quotient tries/hits. (This program is not suitablefor computing the value of p. You need p in the computation of the angle.)

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