The reason this satisfies formula_21, while the analogous procedure fails for most other quadratic integer rings, is as follows. A fundamental domain for the ideal formula_22, acting by translations on the complex plane, is the 60°-120° rhombus with vertices formula_23. Any Eisenstein integer "α" lies inside one of the translates of this parallelogram, and the quotient formula_13 is one of its vertices. The remainder is the square distance from "α" to this vertex, but the maximum possible distance in our algorithm is only formula_25, so formula_26. (The size of "ρ" could be slightly decreased by taking formula_13 to be the closest corner.)