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mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a unit square is a square whose sides have length . Often, ''the'' unit square refers specifically to the square in the Cartesian plane with corners at the four points ), , , and .


Cartesian coordinates

In a Cartesian coordinate system with coordinates , a unit square is defined as a square consisting of the points where both and lie in a closed
unit interval In mathematics, the unit interval is the closed interval , that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted ' (capital letter ). In addition to its role in real analysis ...
from to . That is, a unit square is the Cartesian product , where 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 number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the fo ...
s. In this view, the four corners of the unit square are at the four complex numbers , , , and .


Rational distance problem

It is not known whether any point in the plane is a rational distance from all four vertices of the unit square..


See also

* Unit circle * Unit cube * Unit sphere


References


External links

* {{mathworld , urlname = UnitSquare , title = Unit square 1 (number) Types of quadrilaterals Squares in number theory