$\pi$ is, by definition, $\frac{C}{d}$. It's not an approximation.
Of course if you use a computer of some kind it has to be an approximation $\pi$ is irrational, but in theory it's exactly $C$.
π is irrational, i agree.
The logic behind c/d is what I understand as a quantity produced by the division of two variables, giving an irrational value that we call π.
By definition an irrational number implies that the value is without reasoning being conducted or assessed according to strict principles of validity. mainly in this case the set of principles underlying the arrangements of its elements. This arrangement is linear. A linear function has two variables. one independent and one dependent. They graph straight lines.
If a regular polygon has more sides, it becomes more "
like" a circle. Because the perimeter of a polygon is equal to the sum of all it's sides, when there are more sides, the perimeter becomes more "
like" the circumference of a circle. This process will continue on forever, and never give an accurate valid answer as it is still straight lines between points.
Let the diameter of the polygon be d and the side of the polygon be a.
The area of the Triangle=T
Then the area of the triangle is
T=1/2×a×d/2=ad/4
The perimeter P of the polygon is
P=na,P=na,
while the area of the polygon is
A=nT=nad/4.
Hence, we get that
A=Pd/4
Letting the number of sides n tend to infinity, the polygon
"tends" to a circle and we get that
Area of the circle=Circumference × diameter/4
or to put it the other way around
Circumference=4×Area of the circle /diameter
As you see from this, there is no need for π anywhere.
The reality is that the curvature will end, the circle will meet. This has yet to be shown.
"What we call the beginning is often the end. And to make an end is to make a beginning. The end is where we start from."
T. S. Eliot