Pi is the circumference of the circle.C.B. wrote: Mon Aug 18, 2025 7:51 pm if we cannot equal 4b=π then we can’t establish any equality anymore btw geometric figures. Geometry would be dead.
4b=pi means you assume a circumference of a circle = perimeter of a square.
So you just miss you said "let suppose we can square the circle".
> You have to differentiate. There is a nominal value “π” and there is its numerical value. I may use very well its nominal value to find an equation to obtain the numerical value.
Its a trick to get the result you wanted.
> Nothing of circular reasoning.
You want to know the value of pi and you use it as a term of your hypothesis.
If its not a circular reasoning i don't know what it is.
By doing this, you are denying yourself the discovery of pi.
So you created 2 definitions of pi, a trick, (the variable, the value) to avoid this circular reasoning.
> We have two expressions of the same value b and b^2, in a form that we can construct a right triangle with it.
« Let there be a semicircle on segment AB. If the vertex C of triangle ABC lies on the semicircle, the triangle at C has a right angle. » Thales's theorem.
They are all right triangle.
There are countless of right triangle inscribed in this semicircle.
So you chose this triangle (1, b^2, b) in a way to get the result you want.
There is no logic o choose this one and not another.