(Approximating 7) A classic method of approximating the value of pi is to relate the area inside a circle to the area of a square just encompassing it. In particular, consider the portion of the unit circle which is in the first quadrant (whose area is ) and the square [0, 1] × [0, 1] (whose area is 1). If we throw darts randomly at this square and count up the proportion of darts which land inside the unit circle compared to the total number of darts thrown, this proportion should approach the ratio of areas, from which we can solve for pi. For this problem, we will continue throwing darts until a given number of darts land inside the circle. A graphical representation of this for 100 darts inside the circle and a total of 127 darts thrown is: Feel free to try and reproduce this type of a figure to practice with MATLAB's graphics capabilities. mc_pi Function: Input variables: • a scalar representing the desired number of darts landing inside the circle Output variables: • a scalar representing the approximate value of 7 • a scalar representing the total number of darts thrown to achieve the given approximation A possible sample case is: » [approx_pi, tot_darts] = mc_pi(100) approx_pi = 3.1496 tot_darts = 127 %3D

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