CC BY
10
market and the possibility of placing short-term bonds in a simplified manner will be very effective.
In the Russian economy, further development of the situation will in most cases depend on changes in external economic conditions and the speed with which the domestic economy adapts to them. A reduction in debt burden, a gradual weakening of domestic financial conditions, and an improvement in business sentiment in the second half of 2018 can create prerequisites for restoring production and investment activity in 2019-2020.
References:
1. Alekseeva I.A. Russian corporate bond market: trends and development prospects // News of the Baikal State University. - 2017. - №3. - with. 1-9.
2. Antonov R.A. Problems and prospects of development of the corporate bonds market in the Russian Federation // Management of the reform of the socioeconomic development of enterprises. - 2017. - p. 15-18
3. Edunova PI State and development trends of the Russian corporate bond market // Managing the reform of the socio-economic development of enterprises. - 2017. - p. 1-5.
4. Kornienko M.N. Corporate bond market in the Russian Federation // IEAU Bulletin. - 2017. - №15. - with. 51-56.
5. Kryachkova L.I. Features of the functioning of the corporate bond market in Russia // European Studies. - 2017. - p. 7-8.
6. Morozenko N.D. Problems and prospects of development of the corporate bond market in Russia // New Science. - 2017. - p. 35-36.
UDC 51(09)
Aroev D.D.
Senior Lecturer of the department «Methods of Teaching Mathematics»
Kokand State Pedagogical Institute Uzbekistan, Kokan PYTHAGORAS AND HIS CONTRIBUTION TO MATHEMATICS
Annotation: This article discusses Pythagoras and his contribution to mathematics.
Keywords: mathematics, number, practice, theorem, geometry
Today, the student receives primary knowledge in mathematics. Even before school, children learn to count, and then in the classroom they get an idea of the unboundedness of the number series, of the elements of geometry, of fractional and irrational numbers, they study the beginning of algebra and mathematical analysis. This knowledge is absolutely necessary for every young man, regardless of who he becomes in the future: a worker, an engineer, a machine operator, a doctor, an officer or a scientist. The rudiments of counting are lost in the depths of the centuries and refer to the period of human history, when there was no written language yet. Man learned to write when he advanced quite far in his ability to count. Mathematical knowledge in the distant past was used to solve
everyday problems, and it was the practice that largely guided all further development of mathematics. And nowadays, as in the distant past, the practice puts forward complex tasks for mathematics. This is precisely the reason for the modern rapid development of mathematics, the emergence of its new branches, which make it possible to study the phenomena of the world around us more deeply and actively and to solve specific practical problems that inevitably arise in connection with the progress of engineering and science. To solve them, it is necessary not only to immaculately possess the knowledge that humanity acquired in the past, but also to find and discover new means of mathematical research. "You get satisfaction only when you overcome difficulties, when you manage to find a way that leads to solving a problem that seemed previously insoluble." It is clear to everyone that without modern mathematics with its developed logical and computing apparatus, progress in physics, engineering and production organization would be impossible, and many fundamental problems of aviation and cosmonautics, meteorology and radio engineering would remain unresolved. Nowadays, without preliminary calculations, the plant will not start the production of a single complex machine, they will not begin to modernize the technological process.
Space flights were made, and in their implementation, mathematics takes pride of place. Calculation of rocket designs, motion trajectories, construction of models of bombardment of rocket surfaces by meteorites and meteor dust is only a small part of those branches of natural science and technology where mathematics was widely and essentially used. The fact that it was possible to find out about the existence of a number of elementary particles not by experiment, but from the results of mathematical calculations, says quite a lot.
That is why a good mathematical education and the development of mathematical abilities are necessary not only for those who later will be engaged in scientific research in mathematics, physics, astronomy or engineering, but also for those who become economists, production managers, astronomers, skilled workers. Mathematical style of thinking, the ability to argue strictly, without logical leaps are also needed by future lawyers and historians, biologists and linguists, doctors.
The beginning of the new millennium makes us think about the millennia of the past. All people look back at the distance traveled. In a new way, they comprehend their lives, the lives of their ancestors, the course of history, including the history of science."
He who wants to confine himself to the present without knowing the past will never understand him. "Leibniz G.V. Many different stories and legends are connected with the name of Pythagoras. In some of them, merit is clearly attributed not to him. Thus, in one of the seventeenth-century Slavic manuscripts, it is stated that Pythagoras initiated the arithmetic. As for the facts from the life of Pythagoras, it is very difficult to separate truth from fiction here, especially since his students attributed much to him in order to elevate his teacher in the eyes of the people.
According to legend, Pythagoras was born on the island of Samos, which is located in the Aegean Sea near the coast of Asia Minor. In his youth, Pythagoras traveled a lot, traveled to Egypt and penetrated through Asia Minor by caravan routes to Babylon. As if everywhere and everywhere he bit by bit collected the knowledge of the most ancient peoples in mathematics, astronomy, technology and that, returning to his homeland, he was so amazed by the acquired knowledge of his compatriots that he was considered a demigod. Further information about the life of Pythagoras is becoming more reliable. Returning to the island of Samos, Pythagoras gathers around him young men from noble families and leads with them secret conversations. No one knows what he teaches them. Polycrat, the ruler of the island, fearing that under the cover of these secret conversations a conspiracy against him is brewing, orders his people to watch them. Pythagoras, outraged by this, leaves his native island forever and settles in one of the Greek cities of southern Italy - Crotone.
Here there is a struggle between the nobility and the people for power over the city. The nobility have a leader - the athlete Milon, but there is no person who could philosophically substantiate the need to transfer power over the city into the hands of the rich. And here comes Pythagoras. His fame reached the city of Croton. Pythagoras teaches: "Look around you. Everywhere in the world is order, everything is subject to harmony, to the least. Even the sounds and those are subject to numbers. Everywhere in nature there is a harmonious order established by the gods. Even the heavenly bodies and stars obey him. How can a man disobey him? Woe to that city where there is no reverence for the ancient order. "More and more students at Pythagoras. They unite in a union, a union of initiates, where ordinary people cannot penetrate. Alliance reigns discipline, obedience, the word of the teacher - everything. His teaching, contrary to popular religion, was kept secret. The pupils of Pythagoras were facing years of testing, while they were allowed to enter the coveted circle of initiates. For initiation, a long attentive teaching was not enough, but the whole way of life had to be consistent with the basic thought of Pythagoras.Pupils with their wives and children lived together with a mentor, they got up early at the first rays of the sun, with solemn songs and music, sent to meet a magnificent star. After that, the philosopher informed them about the most important subjects of human knowledge, and especially often occupied them with mathematics, in the field of which many very important theorems belong to Pythagoras. Mathematics, as a theory, was developed in the school of Pythagoras (571-479 years. BC. E.). The main merit of the Pythagoreans in the field of science is the substantial development of mathematics, both in content and in form. According to the content - the discovery of new mathematical facts. The form - the construction of arithmetic and geometry as theoretical, evidentiary sciences, studying the properties of abstract concepts of numbers and geometric forms.
The Pythagoreans called their own studies "mathema", which means "science" and divided them into 4 parts: arithmetic, geometry, astronomy, harmony (the study of music). The main thing was considered arithmetic - the
science of numbers. It was she who was the basis of both geometry, astronomy, and harmony. "The number is the law and the connection of the world, the power that reigns over the gods and mortals", "the essence of things is the number that brings unity and harmony to everything", "everything is number" - these were the provisions of the Pythagoreans.
Therefore, not without reason, many mathematicians left aphorisms devoted to mathematics. "Mathematics is the queen of sciences, arithmetic is the queen of mathematics. "K.F. Gauss "The number controls the whole world quantitatively, and the four rules of arithmetic can be considered as a complete equipment of mathematics."D.C. Maxwell "Arithmetic is one of the oldest, perhaps the oldest branch of human knowledge, and at the same time the deepest secrets are somewhere near its hackneyed truths. "H. D.S. Smith
Использованные источники:
1. Жмудь Л. Я. Пифагор и ранние пифагорейцы. — М., 2012. — 445 с. ISBN 978-5-91244-068-7
2. Жмудь Л. Я. Пифагор и его школа. — М.: Наука, 1990. — ISBN 5-02027292-2
3. Жмудь Л. Я. Наука, философия и религия в раннем пифагореизме. — СПб., 1994. — 376 с. — ISBN 5-86050-066-1
4. Колчинский И.Г., Корсунь А.А., Родригес М.Г. Астрономы: Биографический справочник. — 2-е изд., перераб. и доп.. — Киев: Наукова думка, 1986. — 512 с.
5. Фрагменты ранних греческих философов. Часть 1: От эпических теокосмогоний до возникновения атомистики, Изд. А. В. Лебедев. — М.: Наука, 1989. — с. 138—149.
6. Леонтьев А. В. Традиция о Пифагоре у Аристоксена и Дикеарха // Человек. Природа. Общество. Актуальные проблемы. Материалы 11-й международной конференции молодых учёных 27-30 декабря 2000 г. — СПб.: Издательство Санкт-Петербургского университета. 2000. — С. 298— 301.
7. Леонтьев А. В. К вопросу об образе Пифагора в античной традиции VI—V веков до н. э. // Мнемон. Исследования и публикации по истории античного мира. Под редакцией профессора Э. Д. Фролова. — Выпуск 3. — Санкт-Петербург, 2004.
8. Панченко Д. В. Парадокс Пифагора // Индоевропейское языкознание и классическая филология — XII: Материалы чтений, посвящённых памяти проф. И. М. Тронского. 23-25 июня 2008 г. — С. 355—363.
