THE BINARY GOLDBACH CONJECTURE

<p>The Goldbach Conjecture, one of the oldest problems in mathematics, has fascinated and inspired many mathematicians for ages. In 1742 German mathematician Christian Goldbach, in a letter addressed to Leonhard Euler, proposed a conjecture. The modern-day version of the Binary/Strong Goldbach conjecture asserts that: Every even integer greater than 2 can be written as the sum of two primes. The conjecture had been verified empirically up to 4 × 1018, its proof however remains elusive, which seems to confirm that:</p><p><em>Some problems in mathematics remain buried deep in the catacombs of slow progress ... mind stretching mysteries await to be discovered beyond the boundaries of former thought. Avery Carr (2013) </em></p><p>The research was aimed at exposition, of the intricate structure of the fabric of the Goldbach Conjecture problem. The research methodology explores several topics, before the definite proof of the Goldbach Conjecture can be presented. The Ternary Goldbach Conjecture Corollary follows the proof of the Binary Goldbach Conjecture as well as the representation of even numbers by the difference of two primes Corollary. The research demonstrates that the Goldbach Conjecture is a genuine arithmetical question.</p>

Tradução do Texto “Réflexions et Eclaircissemens sur les Nouvelles Vibrations des Cordes Exposées dans les Mémoires de L’Académie de 1747 & 1748”, de Daniel Bernoulli

Este artigo apresenta uma tradução do texto Réflexions et Eclaircissemens sur les Nouvelles Vibrations des Cordes Exposées dans les Mémoires de l’Académie de 1747 & 1748 do estudioso Daniel Bernoulli (1700–1782), publicado nas Mémoires de l’Académie Royale des Sciences et Belles-Lettres em Berlim. Este texto fora escrito em resposta às memórias De vibratione chordarum exercitatio (1748) de Leonhard Euler (1707–1783) e Recherches sur la courbe que forme une corde tendue, mise en vibration (1747), de Jean le Rond d’Alembert (1717–1783), trabalhos que também foram publicados nas Mémoires da academia mencionada. Em contrapartida ao tratamento matemático apresentado por Euler e d’Alembert, Bernoulli procura construir uma justificativa para a percepção dos sons ouvidos simultaneamente ao som principal de uma corda vibrante, por meio da sobreposição dos modos de vibração de uma corda qualquer, dando continuidade a uma acirrada disputa sobre a questão. Em tal abordagem, é fundamental ressaltar que Bernoulli mantém continuamente um sentido físico para as teorizações dos sons simultâneos por ele estabelecidos e inferências delas decorrentes.

“Sobre as Somas das Séries de Recíprocos”, de L. Euler

Esta é uma tradução do artigo De summis serierum reciprocarum (Sobre a soma das séries de recíprocos), de Leonhard Euler (1707–1783), em que ele resolve o famoso problema de Basileia.

Role of zero-divisor graph in power set ring

The first article about graph theory was written by Leonhard Euler the famous Swiss mathematician which was published in 1736. Primarily, the idea of graph was not important as point of mathematics because it mostly deals with recreational puzzles. But the recent improvement in mathematics specially, its application brought a strong revolution in graph theory. Therefore, this article is written under the title of (Role of Zero-divisor graph in power set ring). This study clarifies the role of the zero-fraction graph in the strength ring and the library research method was used for the collection of information from the past research. This study first introduces the zero-divisor graph set of alternatives in R ring. Then presents the Role of Zero-divisor graph in power set ring. Whereas the vertex is denoted with K1 and the elements of an optional ring which are not zero-divisors they are the vertices without edges of that ring in zero-divisor graph. Next, we will study when a graph is planar in power set ring. The research found out that if the element numbers of set X  is less than 4, the graph of zero-divisor graph ring of P X( ) is planar and if the element numbers of set X is greater than or equals to 4, the zero-divisor graph ring is not planar.

An Abridged Review of Buckling Analysis of Compression Members in Construction

The column buckling problem was first investigated by Leonhard Euler in 1757. Since then, numerous efforts have been made to enhance the buckling capacity of slender columns, because of their importance in structural, mechanical, aeronautical, biomedical, and several other engineering fields. Buckling analysis has become a critical aspect, especially in the safety engineering design since, at the time of failure, the actual stress at the point of failure is significantly lower than the material capability to withstand the imposed loads. With the recent advancement in materials and composites, the load-carrying capacity of columns has been remarkably increased, without any significant increase in their size, thus resulting in even more slender compressive members that can be susceptible to buckling collapse. Thus, nonuniformity in columns can be achieved in two ways— either by varying the material properties or by varying the cross section (i.e., shape and size). Both these methods are preferred because they actually inherited the advantage of the reduction in the dead load of the column. Hence, an attempt is made herein to present an abridged review on the buckling analysis of the columns with major emphasis on the buckling of nonuniform and functionally graded columns. Moreover, the paper provides a concise discussion on references that could be helpful for researchers and designers to understand and address the relevant buckling parameters.

The Binary Goldbach Conjecture

The Goldbach conjecture, one of the oldest problems in mathematics, has fascinated and inspired many mathematicians for ages. In 1742 a German mathematician Christian Goldbach, in a letter addressed to Leonhard Euler proposed a conjecture. The modern day version of the Binary/Strong Goldbach conjecture asserts that: Every even integer greater than 2 can be written as the sum of two primes. The conjecture had been empirically verified up to 4× 10 18​​​​​, its proof however remains elusive, which seems to confirm that: Some problems in mathematics remain buried deep in the catacombs of slow progress ... mind stretching mysteries await to be discovered beyond the boundaries of former thought. Avery Carr (2013) The research was aimed at exposition, of the intricate structure of the fabric of the Goldbach Conjecture problem. The research methodogy explores a number of topics, before the definite proof of the Goldbach Conjecture can be presented. The Ternary Goldbach Conjecture Corollary follows the proof of the Binary Goldbach Conjecture as well as the Representation of even numbers by the difference of two primes Corollary. The research demonstrates that the Goldbach Conjecture is a genuine arithmetical question. ​​​

TOKOH-TOKOH (MATEMATIKAWAN), ALIRAN, DAN PENGARUHNYA

Adapun beberapa tokoh-tokoh (Matematikawan) dunia yang juga merupakan ahli filsuf yang diuraikan dalam makalah ini antara lain : Thales (Yunani, 624-646 SM), Phytagoras (582-493 SM), Aristoteles (Yunani, 384-322 SM), Plato (Athena, 427-347 SM), Socrates (427-347 SM), Leonhard Euler (1707-1783 M), Rene Descartes (France, 1.596-1.650 M), dan Blaise Pascal (Prancis, 1.623-1.662 M).Thales merupakan filosof pertama yang mengilhami tentang asal usul alam dan menganut aliran fisafat Monisme. Dia membangun sebuah pandangan filosofi penciptaan alam yang terbuat dari air. Pemikiran tersebut dijadikan Aristoteles sebagai dasar pemikirannya selanjutnya. Phytagoras menganut paham aliran Relativisme. Bagi “Pythagoras” manusia itu adalah ukuran bagi segalanya, baik yang ada karena adanya. Bagi yang tidak ada karena tidaknya. Dikenal sebagai "Bapak Bilangan", dia memberikan sumbangan yang penting terhadap filsafat dan ajaran keagamaan pada akhir abad ke-6 SM. Aristoteles menganut paham aliran Realisme. Aristoteles memiliki pemikiran bahwa materi tidak mungkin tanpa bentuk karena ia ada (eksis) dan pemikiran Aristoteles sangat berpengaruh pada pemikiran Barat dan pemikiran keagamaan lain pada umumnya.Plato dan Socrates menganut paham aliran Idealisme. Pemikiran Plato memisahkan kenyataan yang terlihat dalam alam lahir dengan jiwa yang abstrak (idea). Sementara pemikiran filsafat Socrates ditujukan untuk menentang ajaran relatifisme sophis. Ia ingin menegakkan sains dengan agama. Sekalipun Socrates telah tiada ajarannya tersebar justru dengan cepat karena kematiannya itu. Orang mulai mempercayai adanya kebenaran umum.Rene Descartes dan Blaise Pascal menganut paham aliran Rasionalisme. Descartes memisahkan fenomena ke dalam eksistensi dan esensi sementara. Sementara karya-karya Pascal yang telah disatukan oleh para muridnya dalam buku Pensees de Pascal (Pemikiran Pascal) menjadi satu kekayaan tersendiri bagi dunia hingga kini yaitu pemikiran tentang hati (Le Coeur) dan pertaruhan (Le Pari).

Considerations for Goldbach's Strong Conjecture

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.