Java Program Algorithm for Pi (Monte Carlo Technique)

by Collin Harry

Submitted : Fall 2014

In this project, the statistical Monte Carlo technique was utilized as the primary algorithm for determining the approximate value of pi. The Monte Carlo technique is basically an experiment with a random outcome with a certain probability of success. That success, in a dartboard situation, is defined as the number of darts that land inside the inscribed circle. The probability of success of the Monte Carlo technique is difficult to compute so an approximation is better suited to solve the situation. The simulation of Monte Carlo’s method is the ratio of the area of the circle to the total area, or the number of darts landing in the circle to the total number of darts thrown. The probability of success of the Monte Carlo technique can also be defined as the number of times an outcome was successful to the number of times the experiment was performed. In this project, Monte Carlo’s Method was utilized through a personally-created computer program simulation. The estimation algorithm for pi was equated to the number of darts landing inside the circle divided by the total number of darts thrown, and then this whole quantity multiplied by 4.

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