Unit square
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In mathematics, a unit square is a square whose sides have length Template:Math. Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points Template:Math), Template:Math, Template:Math, and Template:Math.<ref>Template:Citation</ref>
Cartesian coordinates
In a Cartesian coordinate system with coordinates Template:Math, a unit square is defined as a square consisting of the points where both Template:Mvar and Template:Mvar lie in a closed unit interval from Template:Math to Template:Math.
That is, a unit square is the Cartesian product Template:Math, where Template:Mvar 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 Template:Math, Template:Math, Template:Mvar, and Template:Math.
Rational distance problem
Template:Unsolved It is not known whether any point in the plane is a rational distance from all four vertices of the unit square.<ref>Template:Citation</ref>