Comments by "Jasper Mooren" (@jaspermooren5883) on "Numberphile2" channel.

  1. I would actually pick 2 random points with coordinates between (-1/2,-1/2) and (1/2,1/2) and then see which of them cover the circle and of those see how many fit the criteria. Doing it this way seems to be the most 'honest' uniform distribution, because you're not using any information of the circle itself to come to find the answer. This problem makes me think of the problem of a uniform distribution of points in a circle and that Cartesian coordinates give a uniform distribution while polar coordinates don't. By using angles, the far away points are less densly populated than the points nearby, so using Cartesian coordinates here seems to be the safe bet. I haven't calculated the probably of that yet, but that seems to be the best answer.
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