Cortically Magnified

Disk point picking is an elementary problem in geometry. To evenly distribute points on a disk, an intuitive idea is to sample pairs of numbers in polar coordinate (radius and angle) randomly from uniform distributions. After all, “uniformly” is just another word for “evenly”, isn’t it? But it doesn’t work. When the points are sampled this way, the density of the dots fall off linearly with the distance to the origin.