Unit Square - in The Real Plane

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 I × I, where I 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. However, no such point is on an edge of the square.

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