User:Hans G. Oberlack/FS Q

The square is one base element

General case

Segments in the general case

The side length of the square $=s$

Perimeters in the general case

Perimeter of base square$P_{0}=4\cdot s$

Areas in the general case

Area of the base square $A_{0}=s^{2}$

Centroids in the general case

By definition the centroid points of a base shape are $x_{0}=0\quad y_{0}=0$. Relatively is the lower left point of the base of the square is at:
$\quad x_{L}=-{\frac {s}{2}}\quad y_{L}=-{\frac {s}{2}}$

Normalised case

In the normalised case the area of the base is set to 1.
$||ABCD||=1\Rightarrow s^{2}=1\Rightarrow s=1$

Segments in the normalised case

Segment of the base square $s=1$

Perimeters in the normalised case

Perimeter of base square: $P_{0}=4$

Areas in the normalised case

Area of the base square $A_{0}=1$

Centroids in the normalised case

The position of the lower left point of the base of the square: $x_{L}=-{\frac {1}{2}}\quad y_{L}=-{\frac {1}{2}}$

Identifying number

Apart of the base element there is no other shape allocated. Therefore the integer part of the identifying number is 0.
The decimal part of the identifying number is the decimal part of the sum of the perimeters and the distances of the centroids in the normalised case.

$decimalpart(4.0000000...+0)=decimalpart(4.0000000...)=.0000000...$

So the identifying number is: $0.0000000$