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geometry

 square
 define a square

 Calling Sequence square(Sq, [A, B, E, F] )

Parameters

 Sq - the name of the square A, B, E, F - four points

Description

 • 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:

 form(Sq) returns the form of the geometric object (i.e., square2d if Sq is a square). DefinedAs(Sq) the list of four vertices of Sq. diagonal(Sq) the distance of the diagonal of Sq. detail(Sq) returns a detailed description of the object Sq.

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

Examples

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

define four points A(0,0), B(1,0), C(1,1) and F(0,1)

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

define the square Sq that have A, B, C, F as its vertices

 > $\mathrm{square}\left(\mathrm{Sq},\left[A,B,C,F\right]\right)$
 ${\mathrm{Sq}}$ (1)
 > $\mathrm{form}\left(\mathrm{Sq}\right)$
 ${\mathrm{square2d}}$ (2)
 > $\mathrm{map}\left(\mathrm{coordinates},\mathrm{DefinedAs}\left(\mathrm{Sq}\right)\right)$
 $\left[\left[{0}{,}{0}\right]{,}\left[{1}{,}{0}\right]{,}\left[{1}{,}{1}\right]{,}\left[{0}{,}{1}\right]\right]$ (3)
 > $\mathrm{diagonal}\left(\mathrm{Sq}\right)$
 $\sqrt{{2}}$ (4)
 > $\mathrm{detail}\left(\mathrm{Sq}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{Sq}}\\ {\text{form of the object}}& {\mathrm{square2d}}\\ {\text{the four vertices of the square}}& \left[\left[{0}{,}{0}\right]{,}\left[{1}{,}{0}\right]{,}\left[{1}{,}{1}\right]{,}\left[{0}{,}{1}\right]\right]\\ {\text{the length of the diagonal}}& \sqrt{{2}}\end{array}$ (5)
 > $\mathrm{area}\left(\mathrm{Sq}\right)$
 ${1}$ (6)