Unit square
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In mathematics, a unit square is a square whose sides have length 1Script error: No such module "Check for unknown parameters".. Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points (0, 0Script error: No such module "Check for unknown parameters".), (1, 0)Script error: No such module "Check for unknown parameters"., (0, 1)Script error: No such module "Check for unknown parameters"., and (1, 1)Script error: No such module "Check for unknown parameters"..[1]
Cartesian coordinates
In a Cartesian coordinate system with coordinates (x, y)Script error: No such module "Check for unknown parameters"., 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 0Script error: No such module "Check for unknown parameters". to 1Script error: No such module "Check for unknown parameters"..
That is, a unit square is the Cartesian product I × IScript error: No such module "Check for unknown parameters"., 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 0Script error: No such module "Check for unknown parameters"., 1Script error: No such module "Check for unknown parameters"., Template:Mvar, and 1 + iScript error: No such module "Check for unknown parameters"..
Rational distance problem
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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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