Myth and Heresy

SQUARING THE CIRCLE USING ONLY A COM­PASS AND A STRAIGHTEDGE not only is it not impossible, but it is a process inherent in the same 'figurative' geometry in a natural way, since the π it is the cornerstone of the laws of harmony and balance that regulate it.

In spite of what F. Lin­demann ex­hibited a­bout the un­solv­ability of the prob­lem, his suc­cess was and still is due sole­ly to the fact that the cur­rent cal­cu­la­tion of π it has al­ways been en­trusted to het­er­o­ge­ne­ous cri­te­ria to the laws ­/ na­ture of the cir­cle.

The in­sti­tut­ed π de­rives in fact in the most ad­vanced of cas­es, from re­con­di­tioning the cir­cle to a pol­y­gon, di­lat­ing with­in the cir­cum­fer­ence pro­gres­sive po­lyg­o­nal ac­cen­tu­a­tions, se­quenced by for­mu­las that do not make it ge­o­met­ri­cal­ly de­duc­i­ble.

If the π has far ex­ceeded the boast of ce­leb­ri­ty, this is not so much due to its un­dis­put­ed sci­en­tif­ic pri­or­i­ty, as to the fact that it still con­sti­tutes the great­est chal­lenge, i­de­al­ly un­re­solved but there­fore elected as a ban­ner that flaunts end­less dec­i­mals for the sole pur­pose, more or less con­scious, of con­cealing the in­ev­i­ta­ble com­pro­mise.

This paper will outline the fundamentals of such statements, in­ves­ti­gat­ing pos­si­ble gaps and yet introducing the radical and intrinsic solution of the π enigma.

Preliminary observations

Even if the squaring of the circle has risen to the proverbial limelight as a met­a­phor of the impossible, as it is now a must to believe and make believe, the in­i­tial goal was not to be the direct conversion of circumference and circle into the corresponding squares perimeter and area.
If at the beginning of this unlikely research I wondered, questioning the op­por­tu­ni­ty of such a claim at the various cultures, over the course of this ex­pe­ri­ence I realize how natural the cause was: anyone who has advanced in the search for the solution formula of the calculation of a circle, which imposes a π, it is in fact un­beat­en in the need for a verification, to be carried out only through the in­ter­me­di­ary of a square shape, flat, symmetrical and free from irrational in­ter­ven­tions.
When we say area =, we aim at a number of squares with a unitary side, as the only matrix capable of expressing it with indisputable conceptual precision; even when the basic unit carried an irrational value.
The actual aim has always been to be able to define that constant – hereinafter referred to as pi-greek from the first letter of the Greek word 'perimeter', or another ad personam – that would enable the calculation of circumference and area; a problem that has always been too uncomfortable to emphasize as such.

Putting the spotlight on squaring the circle, which would have had only a re­port­ing and verification purpose and that has never found a solution, would have in­stead strengthened the pedestal of the research in place, to the point of putting its dictates out of the question; a typical reaction in the face of all sorts of riddles not entirely unraveled.

After the first historical attempts, squaring the circle had in fact become the challenge that would have gripped illustrious scholars in vain in the centuries to come, giving impetus to the most disparate experiments and formulas not exempt from unusual expedients, with no other outcome than to be mocked and crumbled shortly, albeit in the shadow of a compromise of transcendence claimed as such; but as I said, this is only a human component, not properly scientific.