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Buffon's needle is a classic experiment in the field of Geometric Probability Theory.
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.
Using the geometry, we can calculate p=1/
. We can also physically perform this experiment or simulate it on a computer (see picture).
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.
approximately. Now, to turn the mathematics around,
=N/M=160/49=3.26531 giving us an approximation for
This approximation is an example of a general mathematical technique called the
Monte Carlo Method
Prof. Ashay Dharwadker