04/32

I could even make some mathematicians horrified by having turned the subject upside down, but so be it: that aforesaid π – exquisitely geometric in the reality – it cannot be the object of instrumental geometry, it invalidates its absolute or in­dis­put­a­ble validity.
Why can't a number that is part and function of natural intelligence - not artificial or resulting from mathematical devices - be geometrically representable? is it not geometry itself that claims the distinctive criterion of classification?
However, I am confident that at the end of the reading they may have reviewed this reaction.

In other words, if that artificial π cannot result from, or belong to any algebraic equation with rational coefficients, this does not prove that [the true] π is tran­scen­dent to the point that it cannot be reproduced by the correct geometric for­ma­tion or path, such as the golden section is equally irrational, and is also con­sid­ered tran­scen­dent by some scholars. It would remain to find the way.

Whether the formulas in force are right or wrong, it must in any case be rec­og­nized that the proof of F. von Lindemann is a child of itself - even if it is re­warded by the Mathematische Annalen and generally agreed; since a π ‘DOC’ has un­doubt­ed­ly always existed, may be it is not transcendent and as for ge­om­e­try it­self, it only needs instrumental competence. It does not require cal­cu­la­tions and numbers, on the contrary it defines them better than a calculator, generating ab­so­lute accuracy thanks to logical figurations obtained objectively, from a co­-or­di­nated process of executive movements; the lines will intersect in points and with measures that in many cases we will never be able to define with numerical ex­act­i­tude. And there is nothing complicated about drawing a circle.

It has always been clear to everyone that a straightedge or ruler simply indicates a rod rightly suited to drawing straight lines, not millimetre-marked – nor should it be depicted that way, as almost all articles on the Web illustrate! – since it is not in­tend­ed, nor enabled by practice to measure lines or distances, but only to produce them, as does the compass, which does not function as a protractor.

Was that already universalized a theoretical impossibility or a rhe­tor­i­cal im­pos­si­bil­i­ty? although exasperated in the most varied ways, in these inexperienced pages it risks collapsing unexpectedly.

The question haunted me: will not so much transcendence – that not even the Golden Section can officially boast – be derived from the fact that it was nec­es­sary to resort to terribly cumbersome procedures, which by now are pleased only to add useless millions of decimal digits, as last bastion of our skill?

It was convenient to make it a myth, relieving schools and academies of every country from the common inability to deal with it, the absolute certainty that it will never be possible to square the circle with a ruler and compass, as well as per­form any geometric figure belonging to a transcendent number.
On the other hand, it cannot be scientifically excluded that the research ap­proach developed to date may not be 100% exhaustive or substantial, even if it has been indispensable; since indeed it encloses and itself flaunts its ge­o­met­ric im­prac­ti­ca­bil­i­ty so sought after and ideally necessary.

A circle is not to be thought of as the limit of
a sequence of regular polygons with an ever-increasing number of sides.
Because it isn't.
Thanks to its transcendent nature, by no stretch a polygon can become circle.