Fix r1 = 1. Find the value of r2 that maximizes the ratio of the geometric mean to the arithmetic mean.
The geometry behind the geometric mean is based on the following argument. If a random variable R takes on each of the values r1 and r2 with probability 0.5, a rectangle with sides of length r1 and r2 has area equal to that of a square with sides with length equal to the geometric mean.