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).
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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 the unit interval from 0 to 1.
That is, the unit square is the Cartesian product I × I, where I denotes the unit interval.
Whether the interval used is open or closed, and at which ends, is at the discretion of the user of the term, who should make it clear which precise definition they are using; however, the term unit interval is most usually used to refer to the closed interval [0,1].
In the complex plane
In the complex plane, the corners of the unit square are at 0, 1, i, and 1 + i.
See also
References
- Weisstein, Eric W., "Unit square" from MathWorld.
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