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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 (0, 0), (1, 0), (0, 1), and (1, 1).
==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 a closed unit interval from 0 to 1 on their respective axes.
That is, the unit square is the Cartesian product × , where denotes the closed unit interval.
It is not known whether any point in the plane is a rational distance from all four vertices of the unit square.〔Guy, Richard K. ''Unsolved Problems in Number Theory'', Vol. 1, Springer-Verlag, 2nd ed. 1991, 181-185.〕 However, no such point is on an edge of the square.〔Barbara, Roy. "The rational distance problem", ''Mathematical Gazette'' 95, March 2011, 59-61.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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