The Squaring of the Circle, part I. and part II.
© Dr. Eick Sternhagen 2016 first edition, 2019 second edition.

I. The squaring of the circle and its purpose

From another perspective:
When dimensioned as shown in the graph (see 1st photo below), proportionally increasing distances are definable, e.g. distances of (micro)waves, expansion of the universe (due to the Big Bang), circular wave extensions caused by earthquakes, i.e. circular extensions, as with a stone, which is thrown into a pond, circular waves are being formed relatively proportionally.

Description of the mathematical process:
The square is considered the basis of the calculation, because the squaring as 'terminus technicus' cannot be transferred to other geometrical figures, like e.g. on the triangle, since there is no "triangling".

a = π × r ^ 2
π × r ^ 2 - a ^ 2 = x
a ^ 2 - π × r ^ 2 = y

[x + a ^ 2 = area of the circle
y + π × r ^ 2 = area of the square]

x + a ^ 2 ≙ π × r ^ 2

Conclusion:
a (1) ^ 2 ≙ a (2) ^ 2 - y ≙ a (3) ^ 2 + x ≙ a (4) ^ 2 - y = ∞

II. The squaring of the circle

seen this way (2nd photo below):
A1 ^ 2 = A2
:D