Inmathematics, aunit square is asquare whose sides have length1. Often,the unit square refers specifically to the square in theCartesian plane with corners at the four points(0, 0),(1, 0),(0, 1), and(1, 1).[1]
In aCartesian coordinate system with coordinates(x,y), a unit square is defined as asquare consisting of the points where bothx andy lie in a closedunit interval from0 to1.
That is, a unit square is theCartesian productI ×I, whereI denotes the closed unit interval.
The unit square can also be thought of as a subset of thecomplex plane, the topological space formed by thecomplex numbers.In this view, the four corners of the unit square are at the four complex numbers0,1,i, and1 +i.
It is not known whether any point in the plane is arational distance from all four vertices of the unit square.[2]