File:FS QC.png

Summary[edit]

Shows the largest circle within a square.

General case[edit]

Base is the square ${\displaystyle [ABCD]}$ of side length s.
The radius r of the inscribed circle has the length ${\displaystyle {\frac {s}{2}}}$

Segments in the general case[edit]

0) The side length of the base square ${\displaystyle =s}$
1) Radius of the inscribed circle ${\displaystyle r_{1}={\frac {s}{2}}}$

Perimeters in the general case[edit]

0) Perimeter of base square ${\displaystyle P_{0}=4\cdot s}$
1) Perimeter of the circle ${\displaystyle P_{1}=2\cdot \pi \cdot r_{1}=\pi \cdot s}$

Areas in the general case[edit]

0) Area of the base square ${\displaystyle A_{0}=s^{2}}$
1) Area of the inscribed circle ${\displaystyle A_{1}=\pi \cdot r_{1}^{2}=\pi \cdot ({\frac {s}{2}})^{2}=\pi \cdot {\frac {s^{2}}{4}}={\frac {\pi }{4}}\cdot s^{2}={\frac {\pi }{4}}\cdot A_{0}}$

Centroids in the general case[edit]

Centroid positions are measured from centroid point of the base shape
0) Centroid positions of the base square: ${\displaystyle x_{0}=0\quad y_{0}=0}$
1) Centroid positions of the inscribed circle: ${\displaystyle x_{1}=0\quad y_{1}=0}$

Normalised case[edit]

In the normalised case the area of the base is set to 1.
${\displaystyle ||ABCD||=1\Rightarrow s^{2}=1\Rightarrow s=1}$

Segments in the normalised case[edit]

0) Segment of the base square ${\displaystyle s=1}$
1) Segment of the inscribed circle ${\displaystyle r_{1}={\frac {1}{2}}=0.5}$

Perimeters in the normalised case[edit]

0) Perimeter of base square ${\displaystyle P_{0}=4}$
1) Perimeter of the inscribed circle ${\displaystyle P_{1}=2\cdot \pi \cdot r_{1}=2\cdot \pi \cdot {\frac {1}{2}}=\pi =3.1415926...}$

Areas in the normalised case[edit]

0) Area of the base square ${\displaystyle A_{0}=1}$
1) Area of the inscribed circle ${\displaystyle A_{1}=\pi \cdot r_{1}^{2}=\pi \cdot ({\frac {1}{2}})^{2}={\frac {\pi }{4}}=0.785398...}$

Centroids in the normalised case[edit]

Centroid positions are measured from the centroid point of the base shape
0) Centroid positions of the base square: ${\displaystyle x_{0}=0\quad y_{0}=0}$
1) Centroid positions of the inscribed circle: ${\displaystyle x_{1}=0\quad y_{1}=0}$

Identifying number[edit]

Apart of the base element there is only one other shape allocated. Therefore the integer part of the identifying number is 1.
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.

${\displaystyle decimalpart(3.1415927...+0)=decimalpart(3.1415927...)=0.1415927...}$

So the identifying number is: ${\displaystyle 1.1415927}$

Licensing[edit]

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