XI Международная студенческая научная конференция Студенческий научный форум - 2019

Pythagoras of Samos (570 BC - 490 BC) ancient Greek philosopher, great dedicated to the Earth, political and religious figure, mathematician, founder of Pythagoreanism, mystic, philosopher, founded the religious and philosophical movement (Pythagoreanism). He was a politician who left the works as an inheritance to descendants. His main life concept is "Everything is a Number". It usually is stated in the encyclopedias and biographies.

Born on the island of Samos. The father of Pythagoras was a master in the handling of the Golden stones, in the family of present prosperity. In the childhood the boy showed curiosity about different Sciences, possessed unusual abilities. The first teacher of the future philosopher was Permodalan, he taught Pythagoras the basics of music, technology, beautiful art, reading, rhetoric, grammar. To help Pythagoras develop his memory, the teacher made Homer read "Odyssey" and "Iliad" and memorize songs from poems. Get good education.

According to legend, Pythagoras went to Egypt to get acquainted with the wisdom of Eastern scientists and as if he lived there for 22 years. Having mastered all the Sciences of the Egyptians, including mathematics, he moved to Babylon, where he lived for 12 years and got acquainted with the scientific knowledge of the Babylonian priests. Returning home Pythagoras tried to organize his philosophical school. However, for unknown reasons, he soon leaves Samos and settles in Crotone (Greek colony in Northern Italy). Here Pythagoras managed to organize his school, which operated for almost thirty years. The school of Pythagoras, or as it is called, the Pythagorean Union, was at the same time a philosophical school, a political party, and a religious brotherhood. The Statute of the Pythagorean Union was very severe

The system of knowledge in the school consisted of 4 sections:

Arithmetic - the study of numbers

Geometry - study of shapes

Astronomy-the doctrine of the structure of the world

Music-the doctrine of harmony and music theory

This system, founded by Pythagoras, existed for millennia…

The discovery of the fact that there is no common measure between the side and the diagonal of the square was the greatest merit of the Pythagoreans. This fact caused the first crisis in the history of mathematics. The Pythagorean doctrine of the integer basis of all existing could no longer be recognized as true. Therefore, the Pythagoreans tried to keep their discovery secret. Pythagoras is credited with a number of important discoveries at the time, namely: the theorem on the sum of the internal angles of a triangle; the problem of dividing the plane into regular polygons (triangles, squares and hexagons). There is evidence that Pythagoras built "cosmic" figures, i.e. five regular polyhedra. But it is more likely that he knew only three simple regular polyhedra: cube, tetrahedron, octahedron. The school of Pythagoras did a lot to give the nature of science to geometry. The main feature of his method was the Union of geometry with arithmetic.

Pythagoras did a lot of proportions and progressions and probably similarity of figures, as he is credited with solving the problem: "according to the two figures to build a third, equal to one of the data and a similar second." Pythagoras and his disciples introduced the concept of polygonal, friendly, perfect numbers and studied their properties. Pythagoras was not interested in arithmetic as a practice of calculations, and he proudly stated that "he put arithmetic above the interests of the merchant". Pythagoras was one of the first to believe that the Earth has the shape of a ball and is the center of the Universe, that the Sun, Moon and planets have their own motion, different from the daily movement of fixed stars.

Pythagoras of Samos – genius scientist, dedicated to the great philosopher, the sage, founder of the celebrated school of the Pythagoreans, the spiritual master of a number of prominent philosophers from around the world. Pythagoras became the ancestor of the teachings on Numbers, Music of celestial spheres and Space, created the basis of Monadology and quantum theory of the structure of matter. He made discoveries of great importance in such Sciences as mathematics, music, optics, geometry, astronomy, number theory, superstring theory, psychology, pedagogy, ethics.

For Pythagoras, the number is really an incredible amount of discoveries:

- Pythagoras created the doctrine of even and odd numbers. He gave definitions to these kinds of numbers and investigated their properties.

- In geometry: Pythagorean theorem, as well as the construction of individual polyhedra and polygons.

- In geography and astronomy: one of the first to Express the hypothesis that the Earth is round, and also believed that we are not alone in the Universe.

- Music: determined that the sound depends on the length of the flute or strings. Pythagoras discovered mathematical regularities in music.

- In numerology: in our time numerology has become known and quite popular, but it Pythagoras combined numbers with forecasts for the future.

Pythagoras taught that both the beginning and the end of all existing consists in a certain abstract value, the so-called Monad. It represents the unknowable absolute emptiness, chaos, the ancestral home of all the gods and at the same time accommodates the fullness of being in the form of divine Light. Monad, as ether, permeates all things, but is not in any one of them.

This is the sum of all numbers, which is always considered as an indivisible whole, as a unit. Pythagoreans portrayed the Monad figure, which consists of ten points – the so-called nodes. All ten of these nodes, called tetractys by the Pythagoreans, among themselves creates nine equilateral triangles, which represent the fullness of the universal emptiness and the life-giving Cross. It is also believed that Pythagoras created the foundations of planimetry, introduced a wide and mandatory use of evidence in geometry, created the doctrine of similarity.

Van der Waerden (Dutch mathematician) concluded: "the Merit of the first Greek mathematicians, such as Pythagoras and Pythagoreans, is not the discovery of mathematics, but its systematization and justification. In their hands, computational recipes based on vague concepts have become an exact science."

Pythagoras, proving his famous theorem, built a figure where squares are located on the sides of a right triangle. The figure was first constructed by Dutch mathematics teacher albert E. Bosman in 1942, during world war II, using a ruler. He named this fractal figure after the ancient Greek mathematician Pythagoras, because each triple touching squares covers a right triangle, these configurations are traditionally used to depict Pythagorean theorems.

One of the properties of the Pythagorean tree is that if the area of the first square is equal to one, then at each level the sum of the squares will also be equal to one. If the angle in the classical Pythagorean tree is 45 degrees, it is also possible to construct a generalized Pythagorean tree using other angles. This tree is often called the windswept Pythagorean tree. If you change the angles at the base of the triangle, you will get a slightly different shape of the tree. And at an angle of 60°, all three squares will be equal, and the tree will turn into a periodic pattern on the plane. If we draw only the segments connecting the selected "centers" of triangles in any way, we get a naked Pythagorean tree.

References:

1.https://multiurok.ru/files/pifaghor-samosskii-drievnieghriechieskii-filosof-i.html

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