[marcodiego]

A friend of mine made this mistake a long time ago when sampling points in a circle. He was baffled and couldn't understand why there was concentration of points around some areas of the circle. My explanation: draw a square around this circle; trace a horizontal line passing along its center; now, draw a diagonal line; can you see it is more likely that a randomly sampled point is closer to the diagonal than to horizontal line? He said "sure!" and I asked "why?" to what he promptly answered "because its longer.". He then asked what he should do about it, I simply said: "just ignore the points that are too far". He immediately understood that points inside the square but outside the disk were the reason for the concentration of the points.