File:FS V dia.png

The quarter circle as base element.

The radius of the quarter circle ${\displaystyle S_{1}=r_{0}}$

Perimeter of base quarter circle: ${\displaystyle P_{0}=2\cdot r_{0}+{\frac {\pi \cdot r_{0}}{2}}=(2+{\frac {\pi }{2}})\cdot r_{0}}$

Area of the base quarter circle ${\displaystyle A_{0}={\frac {\pi \cdot r_{0}^{2}}{4}}}$

Centroid positions of the quarter circle: ${\displaystyle x_{0}=0\quad y_{0}=0}$
Positions of the point A: ${\displaystyle x_{A}=-{\frac {4\cdot r_{0}}{3\cdot \pi }}\quad y_{A}=-{\frac {4\cdot r_{0}}{3\cdot \pi }}}$

In the normalised case the area of the base quarter circle is set to 1.
So ${\displaystyle A={\frac {\pi \cdot r_{0}^{2}}{4}}=1\quad \Rightarrow r_{0}^{2}={\frac {4}{\pi }}\quad \Rightarrow r_{0}={\sqrt {\frac {4}{\pi }}}={\frac {2}{\sqrt {\pi }}}}$

Segment of the base quarter circle ${\displaystyle r_{0}={\frac {2}{\sqrt {\pi }}}=1.128379...}$

Perimeter of base quarter circle${\displaystyle P_{0}=(2+{\frac {\pi }{2}})\cdot r_{0}=(2+{\frac {\pi }{2}})\cdot {\frac {2}{\sqrt {\pi }}}=4.029212...}$

Area of the base quarter circle is by definition ${\displaystyle A_{0}=1}$

Centroid positions of the quarter circle: ${\displaystyle x_{0}=0\quad y_{0}=0}$
Positions of point A: ${\displaystyle x_{A}=-{\frac {4\cdot r}{3\cdot \pi }}=-{\frac {4}{3\cdot \pi }}\cdot {\sqrt {\frac {4}{\pi }}}=-{\sqrt {\frac {64}{9\cdot \pi ^{3}}}}=-0.479...\quad y_{A}=x_{A}=-0.479...}$

Apart of the base element there is no 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.

${\displaystyle decimalpart(4.0292122...+0.0)=decimalpart(4.0292122...)=.0292122}$

So the identifying number is: ${\displaystyle 0.0292122}$

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