User:Hans G. Oberlack/FS C

The circle as base element.

General case

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: $0.5449077$