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 .
Cartesian coordinates
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.
Complex coordinates
The unit square can also be thought of as a subset of the
complex plane, the topological space formed by the
.
In this view, the four corners of the unit square are at the four complex numbers , , , and .
Rational distance problem
It is not known whether any point in the plane is a
Rational number distance from all four vertices of the unit square.
See also
External links
