In plane geometry, a **square** is a polygon with four equal sides and equal angles. Those angles are then necessarily right angles. Squares are regular quadrilaterals.

The coordinates for the vertices of a square centered at the origin and with side length 2 are (±1, ±1), while the interior of the same consists of all points (x_{0}, x_{1}) with -1 < x_{i} < 1.

See also:

In algebra, the

**square**of

*x*is written

*x*

^{2}and is defined as the product of

*x*with itself:

*x*×

*x*. Taking the square is exponentiation with exponent two. If

*x*is a positive real number, the value of

*x*

^{2}is equal to the area of a (geometric) square of edge length

*x*. If

*y*=

*x*

^{2}and

*x*≥0, then

*x*is the square root of

*y*.

A positive integer that is the square of some other integer is known as a square number, or more simply a square.

In urban planning, a

**square**is a planned open area in a city, usually or originally square in shape. See Red Square, Tiananmen Square, Times Square and Trafalgar Square for examples. Some are permanently or on certain days of the week used for an open market.

In carpentry, a

**square**is a guide for establishing right angles (ninety-degree angles), usually made of metal and in the shape of a right triangle.

In the geometry narrative Flatland,

**A Square**is the name of the main narrator of the story.

In video games,

**Square**is short for Squaresoft.

In the parlance of jazz, a

**square**was a person who failed to appreciate the medium, i.e. one who was out of date or out of touch. The term has persisted and permeated into mainstream cultures, as exemplified in Elvis Costello's hit

*Hip to be square*, which, in ultimate self-reference, was used by Sesame Street to illustrate the geometrical meaning of "square".