Unit square: Difference between revisions
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==Rational distance problem== |
==Rational distance problem== |
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{{unsolved|mathematics|Is there a point in the plane at a rational distance from all four corners of a unit square?}} |
{{unsolved|mathematics|Is there a point in the plane at a rational distance from all four corners of a unit square?}} |
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It is not known whether any point in the plane is a [[Rational number|rational]] distance from all four vertices of the unit square.<ref>{{citation|last=Guy|first=Richard K.|authorlink=Richard K. Guy|title=Unsolved Problems in Number Theory |
It is not known whether any point in the plane is a [[Rational number|rational]] distance from all four vertices of the unit square.<ref>{{citation |
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| last = Guy | first = Richard K. |authorlink = Richard K. Guy |
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| title = Unsolved Problems in Number Theory |
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| volume = 1 |
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| publisher = Springer-Verlag |
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| edition = 2nd |
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| year = 1991 |
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| pages = 181–185 |
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| doi = 10.1007/978-1-4899-3585-4 |
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}}</ref> |
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== See also == |
== See also == |
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Revision as of 01:45, 13 October 2023
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).
Cartesian coordinates
In a Cartesian coordinate system with coordinates (x, y), a unit square is defined as a square consisting of the points where both x and y lie in a closed unit interval from 0 to 1.
That is, a unit square is the Cartesian product I × I, where I 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 0, 1, i, and 1 + i.
Rational distance problem
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.[1]
See also
References
- ^ Guy, Richard K. (1991), Unsolved Problems in Number Theory, vol. 1 (2nd ed.), Springer-Verlag, pp. 181–185, doi:10.1007/978-1-4899-3585-4