A square is an equilateral and equiangular parallelogram.

A square Sq is defined by a list of four given points in the correct order. For a list of four points $A,B,E,F$, the condition is that the segments AB, BE, EF, and FA must make a square.

To access the information relating to a square Sq, use the following function calls:

The command with(geometry,square) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{point}\left(A\,0\,0\right),\mathrm{point}\left(B\,1\,0\right),\mathrm{point}\left(C\,1\,1\right),\mathrm{point}\left(F\,0\,1\right)\:$

$\mathrm{square}\left(\mathrm{Sq}\,\left[A\,B\,C\,F\right]\right)$

$\mathrm{Sq}$

$\mathrm{form}\left(\mathrm{Sq}\right)$

$\mathrm{square2d}$

$\mathrm{map}\left(\mathrm{coordinates}\,\mathrm{DefinedAs}\left(\mathrm{Sq}\right)\right)$

$\left[\left[0\,0\right]\,\left[1\,0\right]\,\left[1\,1\right]\,\left[0\,1\right]\right]$

$\mathrm{diagonal}\left(\mathrm{Sq}\right)$

$\sqrt{2}$

$\mathrm{detail}\left(\mathrm{Sq}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{Sq}\\ \text{form of the object}& \mathrm{square2d}\\ \text{the four vertices of the square}& \left[\left[0\,0\right]\,\left[1\,0\right]\,\left[1\,1\right]\,\left[0\,1\right]\right]\\ \text{the length of the diagonal}& \sqrt{2}\end{array}$

$\mathrm{area}\left(\mathrm{Sq}\right)$

$1$