Editing Square (section)

===Compass and straightedge===
The construction of a square with a given side, using a [[Compass and straightedge constructions|compass and straightedge]], is given in [[Euclid's Elements|Euclid's ''Elements'']] I.46.<ref>[[Euclid's Elements|Euclid's ''Elements'']], Book I, Proposition 46. [http://aleph0.clarku.edu/~djoyce/elements/bookI/propI46.html Online English version] by [[David E. Joyce]].</ref> The existence of this construction means that squares are [[constructible polygon]]s. A regular {{nowrap|<math>n</math>-gon}} is constructible exactly when the odd [[prime factor]]s of <math>n</math> are distinct [[Fermat prime]]s,<ref>{{cite book |last= Martin |first= George E. |date= 1998 |title= Geometric Constructions |title-link= Geometric Constructions |publisher= Springer-Verlag, New York |series= Undergraduate Texts in Mathematics |isbn= 0-387-98276-0|page=46}}</ref> and in the case of a square <math>n=4</math> has no odd prime factors so this condition is [[vacuously true]].

''Elements'' IV.6–7 also give constructions for a square inscribed in a circle and circumscribed about a circle, respectively.<ref>[[Euclid's Elements|Euclid's ''Elements'']], Book IV, [http://aleph0.clarku.edu/~djoyce/elements/bookIV/propIV6.html Proposition 6], [http://aleph0.clarku.edu/~djoyce/elements/bookIV/propIV7.html Proposition 7]. Online English version by [[David E. Joyce]].</ref>
<gallery widths=180 heights=180>
Straight Square Inscribed in a Circle 240px.gif|Square with a given circumcircle
01-Quadrat-Seite-gegeben.gif|Square with a given side length, using [[Thales' theorem]]
01-Quadrat-Diagonale-gegeben.gif|Square with a given diagonal
</gallery>