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Unit square

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 $(1, 1)$ .

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 $1$ .

That is, the unit square is the Cartesian product $I \times I$ , where $I$ denotes the closed unit interval.

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 $1 + i$ .

It is not known whether any point in the plane is a rational distance from all four vertices of the unit square. However, no such point is on an edge of the square.

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