Riemann Hypothesis and Random Walk

Disclaimer: I am in no way a mathematician. I do want to become one but this is off-topic. Given that, please take everything below with a grain of salt. If you spot any mistakes in my story below, please do let me know and I will be happy to fix.

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Uniform point generation within circle

So this is a problem that was bugging me for some time now and I never found a chance to think about it thoroughly. The problem statement is simple: how to generate points within a circle in such a way that points’ distribution be uniform? One can assume that a rand() function is provided and that it returns a number between $0$ and $1$ with a uniform distribution. Once I investigated the problem in turned out being so fascinating I decided to write a blog post about it. Here it is.