There are many ways to approximate Pi. The most basic one which has a nice geometrical interpretation is shown below. It is a Monte Carlo style of approximation, such that we randomly throw points in a unit square which contains quarter of a circle. Then, the value of Pi is simply the ratio between the points inside the quarter circle and all generated points multiplied by 4. We can observe one such simulation below:
Although this has a nice geometrical interpretation, it is not an effective method to approximate Pi. The source code related this visualization can be found in this GitHub Gist. For more information, please follow me on Twitter.
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