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Code Listing by Zach Pace

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I saw something like this in C++ as an introduction to Monte Carlo, so I decided to make something similar in Python. My original code used for loops, but I vectorized it with no small amount of effort, and it now runs orders of magnitude faster. For example, I can calculate pi to .002% error with 100,000,000 randomized coordinates in approximately 15 seconds. Careful to start small, because memory fills up quickly, and the computer will...