User:Hans G. Oberlack/FS C



The circle as base element.

Segments in the general case
The radius of the circle $$ = r_0$$

Perimeters in the general case
Perimeter of base circle: $$ P_0= 2 \cdot \pi \cdot r_0$$

Areas in the general case
Area of the base circle: $$A_0 = \pi \cdot r_0^2$$

Centroids in the general case
Centroid positions are measured relative to the centroid point of the base element. Centroid positions of the base circle: $$x_0=0 \quad   y_0=0$$

Normalised case
In the normalised case the area of the base circle is set to 1. So $$A =\pi \cdot r_0^2=1 \quad \Rightarrow r_0^2=\frac {1} {\pi} \quad \Rightarrow r_0=\frac {1} {\sqrt \pi}$$

Segments in the normalised case
Segment of the base circle $$ r_0=\frac {1} {\sqrt \pi} = 0.5641895... $$

Perimeters in the normalised case
Perimeter of base circle$$ = 2 \cdot \pi \cdot r_0 = 2 \cdot \pi \cdot \frac {1} {\sqrt \pi} = 2 \cdot \frac {\pi} {\sqrt \pi} = 2 \cdot \sqrt \pi = 3.5449077... $$

Areas in the normalised case
Area of the base circle is by definition $$ A_0= 1$$

Centroids in the normalised case
Centroid positions of the base circle: $$x_0=0 \quad   y_0= 0.$$

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. $$decimalpart (3.5449077...+0)=decimalpart(3.5449077...)=.5449077...$$ So the identifying number is: $$0.5449077$$