# Definition:Quadrilateral/Square

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## Definition

A **square** is a regular quadrilateral.

That is, a regular polygon with $4$ sides.

That is, a **square** is a plane figure with four sides all the same length and whose angles are all equal.

## Euclid's Definition

In the words of Euclid:

*Of quadrilateral figures, a***square**is that which is both equilateral and right-angled; an**oblong**that which is right-angled but not equilateral; a**rhombus**that which is equilateral but not right-angled; and a**rhomboid**that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called**trapezia**.

(*The Elements*: Book $\text{I}$: Definition $22$)

## Also known as

Writers of popular mathematical literature, appealing to the non-mathematically inclined, can be seen using the term **perfect square**.

However, as there is no such thing as an "imperfect square", this sort of usage not welcome on $\mathsf{Pr} \infty \mathsf{fWiki}$.

## Also see

- Internal Angles of Square: the angles of a
**square**are all right angles

## Sources

- 1968: M.N. Aref and William Wernick:
*Problems & Solutions in Euclidean Geometry*... (previous) ... (next): Chapter $1$: Triangles and Polygons: Theorems and Corollaries $1.22$: Corollary $3$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $4$ - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**parallelogram** - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $4$ - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**square**