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 (0, 0), (1, 0), (0, 1), and (1, 1).
In the real plane
In a Cartesian coordinate system with coordinates (x, y) the unit square is defined as the square consisting of the points where both x and y lie in a closed unit interval from 0 to 1 on their respective axes.
That is, the unit square is the Cartesian product I × I, where I denotes the closed unit interval.
In the complex plane
In the complex plane, the corners of the unit square are at 0, 1, , and 1 + .
- Guy, Richard K. Unsolved Problems in Number Theory, Vol. 1, Springer-Verlag, 2nd ed. 1991, 181-185.
- Barbara, Roy. "The rational distance problem", Mathematical Gazette 95, March 2011, 59-61.