Problem 21 - ECOR1606 Problem Solving and Computers Page 1...

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Page 1 of 3 Department of Systems and Computer Engineering, Carleton University Summer 2003 Assignment – Buffon’s Needle Suppose we have a row of lines that are spaced 1 inch apart and that we drop a 1 inch needle onto the row of lines that are spaced 1 inch apart (see Figure 1). What is probability that the needle crosses one of the lines? Figure 1 Although we can solve this probability analytically, this is actually a classic Monte Carlo method (estimation by performing statistical sampling via computer simulations) of estimating the value of π . We first assume that the position of the needle is totally random. In this case we can assume that needle tip always lands between the same two lines because all we care about is whether or not the needle crosses a line. When the needle is dropped, we can specify the needle’s position by specifying the location of the needle tip ([a,b]) and the needle orientation ( θ ). See Figure 2. Figure 2
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This note was uploaded on 02/27/2010 for the course ENG ECOR taught by Professor N/a during the Spring '10 term at Carleton CA.

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Problem 21 - ECOR1606 Problem Solving and Computers Page 1...

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