Benutzer:Hans G. Oberlack/C 0.5449077

The circle as base element.

General case

Segments in the general case

The radius of the circle $=r$

Perimeters in the general case

Perimeter of base circle$=2\cdot \pi \cdot r$

Areas in the general case

Area of the base circle $=\pi \cdot r^{2}$

Centroids in the general case

Centroid positions are measured from the lower left point of the surrounding square.
Centroid positions of the base circle: $x_{c}=r\quad y_{c}=r$

Normalised case

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

Segments in the normalised case

Segment of the base circle $r={\frac {1}{\sqrt {\pi }}}=0.5641895...$

Perimeters in the normalised case

Perimeter of base circle$=2\cdot \pi \cdot r=2\cdot \pi \cdot {\frac {1}{\sqrt {\pi }}}=2\cdot {\frac {\pi }{\sqrt {\pi }}}=2\cdot {\sqrt {\pi }}=3.5449077...$

Areas in the normalised case

Area of the base circle is by definition $=1$

Centroids in the normalised case

Centroid positions of the base circle: $x_{c}=r={\frac {1}{\sqrt {\pi }}}=0.5641895...\quad y_{c}=0.5641895...$