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.
In
algebra, the
square of
x is written
x^{2} and is defined as the product of
x with itself:
x ×
x.
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square was a person who failed to appreciate the medium, i.e. one who was out of date or out of touch.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".
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