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).^{[1]}

That is, a unit square is the Cartesian productI × 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

Unsolved problem in mathematics:

Is there a point in the plane at a rational distance from all four corners of a unit square?