Unit square should not be confused with Square (unit).
In mathematics, a unit square is a square whose sides have length . Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points),,, and .
In a Cartesian coordinate system with coordinates, a unit square is defined as a square consisting of the points where both and lie in a closed unit interval from to .
That is, a unit square is the Cartesian product, where denotes the closed unit interval.
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,,, and .
It is not known whether any point in the plane is a rational distance from all four vertices of the unit square.