Unit square

Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points (0, 0), (1, 0), (0, 1), and (1, 1).

[1] In a Cartesian coordinate system with coordinates (x, y), a unit square is defined as a square consisting of the points where both x and y lie in a closed unit interval from 0 to 1.

The unit square can also be thought of as a subset of the complex plane, the topological space formed by the complex numbers.

In this view, the four corners of the unit square are at the four complex numbers 0, 1, i, and 1 + i.

It is not known whether any point in the plane is a rational distance from all four vertices of the unit square.