python

The idea of using a probabilistic (random) simulation to model a physical pro- cess is called a Monte Carlo simulation. We can simulate a physical process to create an estimate of 7. The physical process in question is that of throwing darts at a target. Imagine a square board of side 2 units, with a circular target of radius 1 unit drawn in the centre (0,0) of the board: The idea: Throw a large (known) number of darts at the board. The fraction of the darts that fall within the circle will be proportional to the area of the circle. Assume all darts thrown hit the board: Area of Circle Area of Square 7 (1) (2) Num. darts in circle Total num. darts The mechanics of doing the simulation simplify considerably if we conduct the simulation in the first quadrant of the target: The part of the square has corners (0, 0) (1,0) (1,1) (0,1). The quarter circle has radius 1 unit. If we throw darts at the quarter square then, following the calculation above: Area of 1/4 Circle Area of 1/4 Square 7 (1)2/4 (1) Num. darts in 1/4 circle Total num. darts thrown From this, we obtain an estimate of a: 4 x Num darts in 1/4 circle Test = Total num. Darts thrown Throwing a dart: A thrown dart falls (randomly) on the 1/4 board. The coordinates of the dart hits are: 0