User:Hans G. Oberlack/FS Q

The square is one base element

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: $$0.0000000$$