Надуманную "Проблему" Квадратуры Круга пора признать решенной в 2026г. И утвердить новую инженерную константу AV=3,144655011 в замен "худой" ПИ.

Author: Krapukhin Avenir Mikhailovich

26 February 2026

The problem of squaring the circle — constructing a square with an area exactly equal to that of a given circle — has occupied the minds of mathematicians for over 2,000 years [1,4,9]. Along with the Delian problem (doubling the cube) and the trisection of an angle, it is one of the classical problems of ancient mathematics [6].

The great mathematician of antiquity, Archimedes (3rd century BC), was the first to put the problem on a scientific footing. He proved that a circle is equal in area to a right triangle, one leg of which is the radius of the circle, and the other is the straightened circumference [1]. Archimedes himself provided an estimate for the number π: 3 + 10/71 < π < 3 + 1/7 [1].

The problem seemed so alluring that the search for its solution was compared to the quest for the elixir of life, the search for the philosopher's stone, and the invention of a perpetual motion machine [4]. However, in 1882, Ferdinand Lindemann proved the transcendence of the number π, which finally established the impossibility of an exact solution to squaring the circle using only a compass and straightedge within the framework of classical mathematics [6,9]. Since then, the problem was considered "finally unsolvable" [1].

Despite Lindemann's proof, the search for approximate solutions and alternative approaches continued. Ramanujan (1913-1914), Olds (1963), Gardner (1966), and others provided geometric constructions for approximate values [9]. Dixon (1991) presented constructions for π ≈ 3.1416 and π ≈ 3.142 (Kochanski's approximation) [9].

However, all these constructions remained within the old paradigm. A fundamentally new view of the nature of fundamental constants was required.

An important step was research in the field of chemistry. In 2025, a group of scientists led by Igor Nikovsky (INEOS RAS) discovered that the universally accepted Hammett constants, which chemists have used for almost a century to predict molecular properties, contained systematic errors [3,7,10]. The corrected constants made it possible to explain previously puzzling chemical anomalies and opened the way to creating new materials for quantum technologies, sensors, and smart coatings [3,7]. This demonstrated that even well-established constants may need revision.

Concurrently, the work of A.A. Korneev explored connections between Fibonacci numbers, the golden ratio φ ≈ 1.6180339, and new constants termed the "golden fret" [2]. These investigations showed that the golden ratio could serve as a fundamental basis for new numerical constants [2].

In 2026, the author of this article introduced two new fundamental constants:

The Constant A_v (from the Latin Area vera — true area):

A_v = 4 / √φ ≈ 3.1446055110

where φ = (1+√5)/2 ≈ 1.6180339887 — the golden ratio.

The Constant KR (from the German Kraプhin Reelle — Kradukhin's real constant):

KR = φ^φ ≈ 2.1784575679

These constants satisfy a fundamental relationship (the Kradukhin Identity):

φ × (A_v)² = 16

The new constant A_v provides an exact solution to the problem of squaring the circle. For a circle of radius 1, the side of the equal-area square is given by the formula:

x = √A_v ≈ 1.773

For a circle with diameter √5 (the classic illustration from the Wikipedia article "Golden Ratio"), the side of the square is:

x = √5 × φ^(-1/4) ≈ 1.982660

Thus, the two-thousand-year-old problem of squaring the circle receives a precise analytical solution within a new paradigm.

Current research shows that standard formulas for estimating plasma pressure in tokamaks work reliably only in a narrow range of parameters, with errors potentially reaching tens of percent at high pressures [5]. Russian scientists, using the SPIDER computational code, created a "virtual tokamak" and discovered that the accuracy of the old approach depends not only on plasma pressure but also on the current profile — a factor previously largely ignored [5].

Introducing the constant A_v into calculations of magnetic surfaces and plasma confinement could allow us to:

In radio engineering, calculations of resonant frequencies traditionally use the number π. The deviation of the classical π from the true constant A_v is about 0.096% — a value that accumulates in complex systems and creates parasitic resonances, false harmonics, and noise. Using A_v will make it possible to:

The 2025 discovery regarding the need to correct the Hammett constants [3,7,10] shows that chemistry is ripe for revising its fundamental foundations. Introducing the constants A_v and KR will allow us to:

In synchronous generators, the rotation frequency is linked to π through angular velocity. Replacing classical π with A_v will change the calculated frequency by 0.096%, which will allow for:

The two-thousand-year history of the search for squaring the circle [1,4,6] culminated in 2026 with a fundamental discovery — the introduction of new constants A_v and KR, linked to the golden ratio φ. These constants not only provide an exact solution to the ancient problem but also open the way to revising many established scientific concepts.

Simultaneous discoveries in chemistry, where correction of the Hammett constants proved necessary [3,7,10], and in plasma physics, where the inadequacy of old formulas for tokamaks became evident [5], point to a pressing need for a transition to a new system of fundamental constants.

The adoption of A_v and KR will enable the design of truly calibrated (aligned) technology — tokamaks with stable plasma confinement, resonators free from parasitic modes, radars without false targets, and catalysts with predictable properties. This is not merely a change of numbers; it is a paradigm shift, opening the path to a new level of precision and harmony.

Author: Krapukhin Avenir Mikhailovich

Date: February 26, 2026 ;

Rossia , Sankt-Peterburg, Kolomjagy kr921@mail.ru