Shows the largest circle within a square.

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

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

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

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

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: ${\displaystyle x_{1}=0\quad y_{1}=0}$

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

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

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

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

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: ${\displaystyle x_{1}=0\quad y_{1}=0}$

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: ${\displaystyle 1.1415927}$

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