List of publications on a keyword: «symmetry»

The ABC conjecture states that for three mutually prime numbers A, B, and C satisfying the relation A + B = C, the product of the prime divisors A, B, and C is usually not much less than C. The theorem is very simple to formulate, but extremely difficult to prove. Some five hundred pages have been spent by some of the most eminent mathematicians in the Western world trying to find a proof - but the result is anything but ambiguous and difficult to verify. Meanwhile, any student with advanced training in the exact sciences can understand and prove the ABC hypothesis, relying on creative imagination based on the synthesis of school knowledge, including physics and chemistry. Prime numbers have a huge research potential, they play a unifying role in understanding the world around us. And this is important for education.

In 1637, Pierre de Fermat wrote at the margins of Diophantus’ Arithmetica that he had found a truly wonderful proof of the insolvability of the Diophantine equation a^n + b^n = c^n, where n > 2, but the narrow margins of the books did not allow him to give the full proof. Is there a short and easy way to prove Fermat's Last Theorem? The following ABC conjecture states that for three co-prime numbers A, B, and C which satisfy A + B = C, the product of the prime factors of ABC is usually not much less than C. Both theorems are formulated very simply, but are extremely difficult to prove. Hundreds of pages have been spent by eminent mathematicians of Western world searching for proofs, and the search for proofs continues. The author found new methods of proof that are generally understandable, even to schoolchildren on the basis of a synthesis of several sciences, including physics. Number theory plays an interesting role in pedagogy.

In 1637, Pierre de Fermat wrote at the margins of Diophantus’ Arithmetica that he had found a truly wonderful proof of the insolvability of the Diophantine equation a^n + b^n = c^n, where n > 2, but the narrow margins of the books did not allow him to give the full proof. Is there a short and easy way to prove Fermat's Last Theorem? The following ABC conjecture states that for three co-prime numbers A, B, and C which satisfy A + B = C, the product of the prime factors of ABC is usually not much less than C. Both theorems are formulated very simply, but are extremely difficult to prove. Hundreds of pages have been spent by eminent mathematicians of Western world searching for proofs, and the search for proofs continues. The author found new methods of proof that are generally understandable, even to schoolchildren on the basis of a synthesis of several sciences, including physics. Number theory plays an interesting role in pedagogy.

In 1637, Pierre de Fermat wrote at the margins of Diophantus’ Arithmetica that he had found a truly wonderful proof of the insolvability of the Diophantine equation a^n + b^n = c^n, where n > 2, but the narrow margins of the books did not allow him to give the full proof. Is there a short and easy way to prove Fermat's Last Theorem? The following ABC conjecture states that for three co-prime numbers A, B, and C which satisfy A + B = C, the product of the prime factors of ABC is usually not much less than C. Both theorems are formulated very simply, but are extremely difficult to prove. Hundreds of pages have been spent by eminent mathematicians of Western world searching for proofs, and the search for proofs continues. The author found new methods of proof that are generally understandable, even to schoolchildren on the basis of a synthesis of several sciences, including physics. Number theory plays an interesting role in pedagogy.

In this publication, the author proposes to find an elementary proof of Fermat's Last Theorem from the point of view of an engineering approach. As a model, a construction of three concentrically nested n-cubes or spheres with a common centre and integer edges or radii, a, b, c, is studied, provided that each point/unit cube of a small sphere corresponds to another point/unit cube of this subset of layers between the middle and the large sphere enclosed spheres. An insoluble conflict between the symmetric form and the content of the construction is studied for the case when n is greater than two. The proposed proof forces us to make broader generalisations concerning the necessity of the asymmetry of the universe as a condition for the emergence of matter and the origin of life. The proof of Fermat's Last Theorem, known as the "mathematical pearl", has an important symbolic, historical and educational significance.

The article is about the fact that the extraordinary beauty and conciseness of the formulation of Fermat's Last Theorem make us look for its visual solution. Let's try to consider Fermat's theorem from the eyes of physicist. Perhaps from this positions Pierre de Fermat found a solution whose main ideas would fit schematically in the fairly wide margins of the book, in a few drawings. Skeptics continue to believe that Pierre de Fermat was probably mistaken. Meanwhile, consistent application of the basic principles of physics, geometry, and engineering make us think differently.

The article analyzes and summarizes the principles of architectural bionics applied to various construction and technical structures. The analysis was carried out in the course of studying the scientific literature on the topic “Bionics. Architectural structures». The purpose of this work is to study the principles of architectural bionics, to study the possibility and effectiveness of their application for solving engineering and technical problems. The main task of the work was to study the directions and principles of development of architectural bionics, to assess the effectiveness of their application for solving technical problems, to find the correspondence of biological systems to construction and technical structures and facilities, to analyze known architectural structures from the point of view of architectural bionics.

Fermat's Last Theorem has been proved on the basis of school Physics, Mathematics, analytical Geometry. The main conceptions of the proof one can write on a math toy in the form of a wooden cube for children. Six faces of the cube are enough to deliver the main ideas of proof.

В статье анализируется моделирование профессионального будущего студента в современном мире. Задача моделирования находится в зависимости от самоопределения индивида на всех стадиях своего профессионального становления и определяет уникальную линию развития профессиональной карьеры человека. Главная роль моделирования профессионального будущего – создание желанной карьеры через понимание и оценку настоящего. В работе рассматриваются отличительные черты моделирования уникальных линий развития профессионального будущего и психологические методы минимизации его асимметрии.

The changes of biochemical asymmetry of rats with different motor phenotype (left-handed, right-handed and ambidexters) during their adaptation to hypokinesia have been studied. It is shown that the development of hypokinetic stress in rats owing to restriction of their mobility leads to sharp activation of the processes of lipids peroxidation and to decrease of tiol-disulphate metabolism in brain cortex of animals with different phenotype of motor hemispheric asymmetry. The degree of studied parameters asymmetry changes in hypokinesia. There is a significant reduction of asymmetry coefficient till the inversion of its sign that testifies about decreasing stress resistance of an organism and adaptive possibilities to external influences.

В статье излагается взгляд автора на проблему симметричности/асимметричности в языке в диахроническом плане. Исследователь использует материал архаичного кетского языка, сохранившего следы всех прошлых этапов развития, и сравнивает его с данными индоевропейских языков. В результате делается вывод о зигзагообразном развитии языка от асимметрии к симметрии и наоборот.

Calculation of the exact parameters of complex curves is required for many engineering problems, but to execute it in modern geometry is very difficult. On the basis of the previously developed method of straight voluntary linear transformations and symmetries theory a new solution for the four groups was obtained. However, incorrect estimates were obtained for certain transformations. Applying the methods of geometric modeling, a new feature of linear transformations was revealed.