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Buffon's needle is a classic experiment in the field of Geometric Probability Theory.<BR><BR> A needle of length 1 is thrown on a floor made of planks of width 2. The problem is to determine the probability p of the event that the needle will fall across a crack between planks. <BR><BR> Using the geometry, we can calculate p=1/<font face="Symbol">p</font>. We can also physically perform this experiment or simulate it on a computer (see picture). <p><center><img SRC="seminar_2.gif"></center> <BR>Suppose we throw the needle N=160 times. We count the number of times M that the needle falls across a crack between planks. In our computer simulation this event (red needle) happened M=49 times and did not happen (blue needle) 111 times. <BR><BR> Hence, M/N=p=1/<font face="Symbol">p</font> approximately. Now, to turn the mathematics around, <font face="Symbol">p</font>=N/M=160/49=3.26531 giving us an approximation for <font face="Symbol">p</font> ! <BR><BR> This approximation is an example of a general mathematical technique called the <I><font color="#CC0033">Monte Carlo Method</I></FONT>.
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Prof. Ashay Dharwadker