Squares are preferred because that is the same as minimizing Euclidean Distance, which is defined as sqrt((x2-x1)^2).
sqrt((x2-x1)^2) == x2-x1
I think you meant sqrt(x^2+y^2)
alt Hacker News
sqrt((x2-x1)^2) == x2-x1
I think you meant sqrt(x^2+y^2)