Unit square

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File:Unit Square.svg
The unit square in the real plane

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.[1]

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

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Unsolved problem in mathematics
Is there a point in the plane at a rational distance from all four corners of a unit square?

It is not known whether any point in the plane is a rational distance from all four vertices of the unit square.[2]

See also

References

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External links

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