File:FS C dia.png

Summary[edit]

Licensing[edit]

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The circle as base element.

General case[edit]

Segments in the general case[edit]

The radius of the circle: ${\displaystyle r_{0}}$

Perimeters in the general case[edit]

Perimeter of base circle: ${\displaystyle P_{0}=2\cdot \pi \cdot r_{0}}$

Areas in the general case[edit]

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

Centroids in the general case[edit]

Centroid position of a base shape is: ${\displaystyle S_{0}=0+0i}$

Normalised case[edit]

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

Segments in the normalised case[edit]

Segment of the base circle: ${\displaystyle r_{0}={\frac {1}{\sqrt {\pi }}}\quad \approx 0.564}$

Perimeters in the normalised case[edit]

Perimeter of base circle: ${\displaystyle P_{0}=2\cdot \pi \cdot r_{0}=2\cdot \pi \cdot {\frac {1}{\sqrt {\pi }}}=2\cdot {\frac {\pi }{\sqrt {\pi }}}=2\cdot {\sqrt {\pi }}\quad \approx 3.544}$

Areas in the normalised case[edit]

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

Centroids in the normalised case[edit]

Centroid positions of the base circle: ${\displaystyle S_{0}=0+0i}$