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Unit square
 
 
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The unit square is a square with all of the side lengths equalling 1.

Cartesian coordinate system with coordinates (x , y) the unit square is defined as the square
Square (geometry)

In Euclidean geometry, a square is a regular polygon with four equal sides and four equal angles . A square with vertices ABCD would be denoted ....
 consisting of the points where both x and y lie in the unit interval
Unit interval

In mathematics, the unit interval is the interval [0,1], that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1....
 from 0 to 1.

Whether the interval used is open or closed, and at which ends, is at the discretion of the user of the term, who should make it clear which precise definition they are using; however, the term unit interval is most usually used to refer to the closed interval [0,1].






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The unit square is a square with all of the side lengths equalling 1.

In the real plane

In a Cartesian coordinate system with coordinates (x , y) the unit square is defined as the square
Square (geometry)

In Euclidean geometry, a square is a regular polygon with four equal sides and four equal angles . A square with vertices ABCD would be denoted ....
 consisting of the points where both x and y lie in the unit interval
Unit interval

In mathematics, the unit interval is the interval [0,1], that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1....
 from 0 to 1.

Whether the interval used is open or closed, and at which ends, is at the discretion of the user of the term, who should make it clear which precise definition they are using; however, the term unit interval is most usually used to refer to the closed interval [0,1]. The unit square is a square with all of the side lengths equalling 1.

In the complex plane

In the complex plane
Complex plane

In mathematics, the complex plane is a geometric representation of the complex numbersestablished by the real axis and the orthogonal imaginary axis....
, the unit square contains the points (0,0), (1,0), (0,i), and (1,i).

See also

  • Unit circle
    Unit circle

    In mathematics, a unit circle is a circle with a 1 radius, i.e., a circle whose radius is 1. Frequently, especially in trigonometry, "the" unit circle is the circle of radius 1 centered at the origin in the Cartesian coordinate system in the Euclidean plane....
  • Unit sphere
  • Unit cube
    Unit cube

    A unit cube is a cube all of whose sides are 1 unit long. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units....