In mathematics, a unit square is a square whose sides have length 1 . 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) .

Cartesian coordinates

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 . That is, a unit square is the Cartesian product I × I , where I denotes the closed unit interval.

Complex coordinates

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 .

Rational distance problem

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