The most famous of the discoveries of Pythagoras. Life of Pythagoras

DISCOVERIES OF PYTHAGORAS

Pythagoras of Samos, ancient Greek philosopher, great initiate of the Earth, political and religious figure, mathematician, founder of Pythagoreanism. His main life concept is "Everything is Number". This is usually indicated in encyclopedias and his biographies.

But who Pythagoras was, who is now, and who Pythagoras will be in the future remains a cosmic Mystery...

He is a most brilliant scientist, a great dedicated philosopher, a sage, the founder of the illustrious school of Pythagoreans and the spiritual teacher of a number of outstanding philosophers of world renown. Pythagoras became the founder of the teachings about Numbers, the Music of the celestial spheres and the Cosmos, created the basis of monadology and the quantum theory of the structure of matter. He made discoveries of great importance in the field of such sciences as mathematics, music, optics, geometry, astronomy, number theory, superstring theory (Earth monochord), psychology, pedagogy, ethics.

Pythagoras developed his philosophy on the basis of knowledge of the laws of the interconnections of the visible and invisible world, the unity of spirit and matter, on the concept of the immortality of the soul and its gradual purification through migration (the theory of incarnation). Many legends are associated with the name of Pythagoras, and his students were able to win fame for themselves and became outstanding people, thanks to whose works we became aware of the foundations of the teachings of Pythagoras, his sayings, practical and ethical advice, as well as theoretical postulates and spiritual tales of Pythagoras.

Perhaps not each of us will be able to remember the Pythagorean theorem, but everyone knows the saying “Pythagorean pants are equal on all sides”. Pythagoras, among other things, was quite cunning man. The great scientist taught all his students, the Pythagoreans, a simple tactic that was very beneficial for him: he made discoveries - attribute them to your teacher. Maybe this is a rather controversial proposition, but it is thanks to his students that Pythagoras has a truly incredible number of discoveries:

In geometry: the famous and beloved 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.

In music: determined that the sound depends on the length of the flute or string.

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

Pythagoras taught that both the beginning and the end of everything that exists is contained in a certain abstract quantity, the so-called Monad. It represents the unknowable absolute emptiness, chaos, the ancestral home of all gods, and at the same time contains the fullness of being in the form of divine Light. Monad, like ether, permeates all things, but is not located in any one of them. This is the sum of all numbers, which is always considered as an indivisible whole, as a unit.

The Pythagoreans depicted the Monad as a figure, which consists of ten points - the so-called knots. All these ten knots, called tetractys by the Pythagoreans, create nine equilateral triangles among themselves, which personify the fullness of the universal emptiness and the Life-Giving Cross.

It is also believed that Pythagoras created the foundations of planimetry, introduced the widespread and mandatory use of proofs in geometry, and created the doctrine of similarity.

Pythagoras made all these discoveries more than two and a half millennia ago! The discoveries of Pythagoras, like those of his faithful disciples, live and will live in the future.

History of the Pythagorean Theorem

The great discoveries of Pythagoras the mathematician found their application in different times and around the world. This is especially true for the Pythagorean theorem.

For example, in China, special attention in this regard should be paid to the mathematical book of Chu-pei, which says this about the well-known Pythagorean triangle, having sides 3, 4, 5: “If we decompose a right angle into its component parts, then the line connecting the ends of all its sides will be 5, while the base will be 3 and the height will be 4.” The same book shows a drawing that is similar to one of the drawings in the Hindu geometry of Bashara.

An outstanding German researcher in the history of mathematics Kantor believes that the Pythagorean equality 3?+4?=5? already known in Egypt around 2300 BC. e., during the reign of King Amenemhat I (according to papyrus 6619 of the Berlin Museum). According to Kantor, harpedonapts, or the so-called "string pullers", built right angles using right-angled triangles, the sides of which were - 3, 4, 5. Their method of construction is quite easily reproduced. If you take a piece of rope 12 m long, tie colored stripes to it - one at a three-meter distance from one end, and the other 4 meters from the other, then a right angle will be made between the two sides - 3 and 4 meters. It can be objected to the Harpedonapts that this method of construction would be superfluous if we take, for example, a wooden triangle, which is used by all carpenters. Indeed, there are Egyptian drawings, for example, depicting a carpentry workshop, in which such a tool is found. But nevertheless, the fact remains and the Pythagorean triangle was used in ancient Egypt.

There is little more information about the Pythagorean theorem used by the Babylonians. In the found text, which refers to the times of Hammurabi, and this is 2000 BC. e., there is an approximate definition of the hypotenuse right triangle. Therefore, this confirms that in Mesopotamia, calculations were already made with the sides of right-angled triangles, at least in some cases. The mathematician Van der Waerden from Holland, on the one hand, using the current level of knowledge of Babylonian and Egyptian mathematics, and on the other hand, based on a thorough study of Greek sources, came to the following conclusions: “The merit of the first Greek mathematicians: Thales, Pythagoras and the Pythagoreans - not the discovery of mathematics, but its substantiation and systematization. They were able to turn computational recipes based on vague ideas into an exact science.

Among the Hindus, along with the Babylonians and Egyptians, geometry was closely associated with the cult. It is quite possible that the Pythagorean theorem was already known in India in the 18th century BC. e.

The "list of mathematicians", which Eudemus allegedly compiled, speaks of Pythagoras as follows: "As reported, Pythagoras turned the occupation of this branch of knowledge (geometry) into a real science, analyzing its foundations with highest point vision and exploring its theories in a more mental and less material way."

Tree of Pythagoras

The Pythagorean tree is a type of fractal that is based on a figure known as the Pythagorean Pants.

Proving his famous theorem, Pythagoras built a figure in which squares were located on each side of a right triangle. After a while, this figure of Pythagoras turned into a whole tree. The first tree of Pythagoras was built during the Second World War by A. Bosman, using a conventional drawing ruler.

One of the main properties of the Pythagorean tree is that when the area of ​​the first square is one, then at each level the sum of the areas of the squares will also be equal to one. The classical Pythagorean tree has an angle of 45 degrees, but it is also possible to construct a generalized Pythagorean tree using other angles. Such a tree is called the wind-blown tree of Pythagoras. If you draw only segments that connect in any way certain "centers" of triangles, then you get a naked Pythagorean tree.

The Pythagorean tree is a fractal generated like this:

Start with a single square. Then, choosing one of its sides as the base (in the animation, the bottom side is the base):

Construct a right triangle on the opposite side of the base with the hypotenuse coinciding with this side and the ratio of sides 3:4:5. Note that the smaller leg should be to the right of the base (see animation).

On each leg of a right triangle, construct a square with a side that coincides with this leg.

Repeat this procedure for both squares, counting as their bases the sides touching the triangle.

The figure obtained after an infinite number of iterations is a Pythagorean tree.

Education of Pythagoras

As you know, Pythagoras received a good education. To do this, at a very young age, he went to Egypt, enlisting the support of the Samian ruler Polycart. There he spent 22 years, comprehending the wisdom of the ancient Egyptians and adopting their scientific experience accumulated over the years. Then, according to legend, he moves to ancient Babylon, where for 12 years he studies the wisdom of local priests and scientists. Also, Pythagoras, according to some sources, is credited with visiting India. The return to the homeland of the great thinker took place in 530 BC. But his native Samos did not take him into his arms, and Pythagoras moved to a Greek colony in Italy, a place called Coroton. Here he organizes his own school, which has existed for 30 years. This institution combined three different directions, philosophical, political and religious, and was called the Pythagorean Union. The school had its own strict rules. So, when joining it, it was necessary to give up all your property in favor of the school. Members of this union did not have the right to eat meat, shed anyone's blood and sacredly keep the secret of their mentor. Also they couldn't be engaged scientific activity on a paid basis.

Philosophical views of Pythagoras

In his philosophy, Pythagoras adhered to idealism. He was an adherent of the slave system and stood up for the defense of the aristocracy. Most likely, because of these principles, he was forced to leave his native island, since the overwhelming majority of the rulers of Samos were inclined towards the democratic foundation of social relations.

His school held the same views. Pythagoras taught that the aristocracy should be at the head of the order, and he strictly condemned all manifestations of the democratic system.

Pythagoras was the first to give a name to such a subject as philosophy. He interpreted it as space. Such his teaching provided for the knowledge of the world through a scientific approach and a religious way of life. He argued that for a complete knowledge of the world, a person needs to study such sciences as geometry, algebra, astronomy and music.

Activities of Pythagoras

Pythagoras a large number of time devoted to the study of medicine, politics, ethics, mathematics and other sciences. Great public, political and scientific figures came out from under his wing. He also did various kinds of research.

Pythagoras as a preacher

In the ancient world, Pythagoras occupied the niche of a popular preacher. Mostly he promoted his own vision of the world to the masses and had a large number of very high-ranking followers. The essence of his sermons was reincarnation, that is, the immortality of the human soul. After the death of the body, the soul is able to move into another shell for existence. Will move, the soul is capable even in the body of an animal. Therefore, Pythagoras and his disciples completely rejected the use of meat for food. In his opinion, the endless process of reincarnation can be interrupted only by the method of complete purification of the soul and body. Purification occurs by abstaining from all kinds of excesses, such as drunkenness, foul language, observance of the rules of conduct and etiquette. The highest form of purification was considered to be the comprehension of the inner philosophy of the world. Adherents of his sermons, inspired by the teacher's speeches, managed to organize their own order. This religious cell grew throughout Coroton and practically ruled the island. It included a huge number of followers. All the followers of Pythagoras paid great attention to such a concept as friendship. With their friends the Pythagoreans, they shared all their wealth.

Musical activities

In this direction, the great figure developed his own theory of acoustics and music. He studied musical tones and their numerical expression in mathematics. Also the first guess about the form earth's surface were expressed in his school.

Pythagoras and geometry

The scientific activity of Pythagoras is invaluable for the development of geometry as a science. One of the theorems he proved was called the Pythagorean theorem. The thinker also paid great attention to mathematics and especially to various ratios of numbers. He tried to know the essence of being with their help.

His school taught that all surrounding a person the world consists of the smallest particles called units of being. These particles in certain combinations form various geometric figures and are determined by a numerical expression. By number, Pythagoras also explained the essence of the appearance of matter and the universe. Later, the adherents of his school, thanks to their work, laid knowledge at the basis of the emergence of such a branch of mathematics as number theory.

With the growth of the democratic movement throughout Greece, the school of Pythagoras falls into disfavor with the people. As a result of this, the philosopher is forced to leave Coroton and settle in Metapontus.

Personal life of Pythagoras

Pythagoras, like most Greek citizens, had a family consisting of his wife Theana and two children, a daughter and a son.

Death of Pythagoras

As a result of the democratic movement, an uprising took place in the place where the scientist lived. Skirmishes swept all over Metapont. In one of them, Pythagoras died, according to some sources, at the age of ninety. His death ended the existence of the school he had formed.

After his death, the great philosopher left a huge amount of knowledge, which later formed the basis of some scientific achievements and works. So, for example, Euclid used the developments of Pythagoras in his writings. His works were also used by Socrates and his famous followers Plato and Aristotle. Also, many works of Pythagoras turned out to be erroneous, which once again confirms his ability to develop thoughts and assumptions, and therefore, in the ability to justify any manifestation of nature and human activity.

Sage Pythagoras

The name of Pythagoras, the great ancient Greek scientist, is associated, first of all, with mathematical discoveries. Pythagoras is credited with studying the properties of integers and proportions, proving a theorem, etc. He was also a talented political and religious figure, astronomer, brilliant philosopher and sage who had his own idea of ​​the world, the structure of the Universe. Many sciences owe their successful development to him.

Biography of Pythagoras and his teachings

In the 6th century BC, Ionia, a group of islands, became the center of Greek science and art. Aegean Sea located off the coast of Asia Minor. There, a son was born in the family of a goldsmith, seal cutter and engraver Mnesarchus. According to legend, in Delphi, where Mnesarchus and his wife Parthenisa arrived, either on business or on a honeymoon trip, an oracle predicted the birth of a son, who would become famous for centuries for his wisdom, deeds and beauty.

God Apollo, through the mouth of an oracle, advises them to sail to Syria. The prophecy miraculously comes true - in Sidon, Parthenisa gave birth to a boy. And then by ancient tradition Parthenis takes the name Pythiades, in honor of the Pythian Apollo, and names his son Pythagoras, that is, predicted by the Pythia.

The legend does not say anything about the year of birth of Pythagoras, historical studies date his birth to about 580 BC. Returning from a trip happy father erects an altar to Apollo and surrounds the young Pythagoras with cares that could contribute to the fulfillment of divine prophecy.

Biography of a brilliant ancient Greek scientist

There is very little exact information about the life of Pythagoras, most of the data is based on legends. Years of life - approx. 570 (580) - ca. 495 (500) BC. Place of birth - the Greek island of Samos, located in the northeastern part of the Aegean Sea at an altitude of up to 1434 m, spread over an area of ​​476 square kilometers with hanging evergreen forests and numerous remains of ancient buildings with ghostly shadows of prominent personalities who glorified their homeland for centuries.

He was lucky enough to be born in Ionia in the family of a stone carver, who was quite famous, in an area that was at that time the center of science and culture.

Mother and father

The philosopher's mother's name was Parthenia (Partenida, Pythiades), and his father's name was Mnesarchus. According to legend, once a young couple visited the city of Delphi as honeymoon trip. There, the newlyweds met an oracle who prophesied to the lovers that their son would soon appear. The legend said that the child would become a difficult person, famous for his wisdom, appearance, great deeds.

Some sources also say that two more boys were brought up in the family - the older brothers of the Greek philosopher: Evnost and Tyrrhenus.

Little is reliably known about the youthful life of Pythagoras.

Pythagoras was a very inquisitive child, so he asked sailors who came in about other countries. When he grew up a little, he became cramped on small island, which he climbed far and wide, and Pythagoras left Samos.

The birth of a talented son to his father, a goldsmith, was predicted by an oracle. Thanks to the wealth in the family, the boy was able to get a good education, teachers worked with him individually, who instilled a love for nature, its secrets.

Pythagoras was from a rich and noble family, which follows from the opportunities for him to receive a unique education for ancient times.

The main stages of education

The first teacher of the future philosopher was Germodamant. He taught Pythagoras the basics of music, the technologies of painting, reading, rhetoric, and grammar. To help Pythagoras develop his memory, the teacher made him read Homer's Odyssey and Iliad and memorize songs from poems.

On the advice of a mentor, Pythagoras goes to study with the Egyptian priests. But before that, he gets acquainted with the philosopher Ferekid, his teachings on astrology, medicine, and the secrets of numbers. Big influence The lectures of the philosopher Thales, which he listened to in Miletus, also had a great impact on the future brilliant scientist.

Improving his knowledge in Egypt, with the Memphis elders, Pythagoras becomes one of the most educated people, not only Ancient Greece but also other countries. He even used his captivity by the Persians to meet Persian magicians, to gain new knowledge about eastern astrology and mysticism. The teachings of the magicians later affected the nature of the works of Pythagoras, because even his mathematical treatises have a mystical sound.

Ten can be expressed as the sum of the first four numbers (1+2+3+4=10), where one is the expression of a point, two is a line and a one-dimensional image, three is a plane and a two-dimensional image, four is a pyramid, that is, a three-dimensional image. Why not the four-dimensional universe of Einstein?

The idea that numbers rule the world came to Pythagoras by accident.

He had a delicate ear and, passing by a forge one day, he noticed that the coinciding blows of hammers differing in weight produce different harmonious harmonies. The weight of the hammers could be measured, and Pythagoras came to the conclusion that the qualitative phenomenon is precisely determined through the quantity, "that the number owns ... things." The Samian philosopher decided that everything in the world is determined by numbers or their ratios. His observations were also confirmed in music: it turned out that if the lengths of the strings in musical instrument relate to each other as 1:2, 2:3, 3:4, then the ratio of sounds in terms of vibration frequency corresponds to an octave, fifth, fourth.

After sixty, a scientist who already has quite famous name, returns to Greece, to the city of Croton. There he founds philosophical school. He devoted the rest of his life to education in matters of medicine, politics, mathematics, and astronomy. His school produced many well-known statesmen and scientists.

The philosopher quickly gained wide popularity among the inhabitants. Even women who were forbidden to attend mass gatherings came to hear him speak. At one of these events, Pythagoras met his future wife.

Discoveries of Pythagoras

Perhaps not each of us will be able to remember the Pythagorean theorem, but everyone knows the saying “Pythagorean pants are equal on all sides”. Pythagoras, among other things, was a rather cunning person. The great scientist taught all his students, the Pythagoreans, a simple tactic that was very beneficial for him: he made discoveries - attribute them to your teacher.

It is difficult to single out the most important discoveries of a brilliant scientist, because he did a lot for the development of many sciences.

• One of the main theorems in geometry is the famous Pythagorean theorem. Also, the scientist is the author of the rules for the construction of polyhedra, polygons. (developed the theory of even and odd numbers, and in general became the founder of theoretical arithmetic; developed the theory of proportions, found a numerical expression for harmonious intervals (quarts, fifths and octaves)
• Pythagoras and his students were among the first to suggest that the Earth has a spherical shape.
• Thanks to Pythagoras, who extols the meaning of numbers, figures, numerology also acquired its significance as a science. With its help, forecasts for the future were made.
• Studying music, the great genius established the dependence of sound on the length of a string or flute.

In the union of the Pythagoreans, all discoveries were attributed to Pythagoras, so now no one will determine which discoveries were made by Pythagoras and which by his students.

Of course, Pythagoras has come down to us as a mathematician, but he was more of a philosopher. The basic concepts of the philosophy of Pythagoras are extremely difficult to understand.

The main section of the philosophy of the Pythagoreans was numerology, which was created by Pythagoras.

“Everything is a number,” he said.

The main concept of the number theory of Pythagoras, in addition to the number, is the monad. The monad (from Greek unity, unity) is multifaceted - it is both the unity of everything and the sum of combinations of numbers considered as a whole. The monad has been compared to the seeds of a tree that has grown into many branches. Branches are like numbers - they are to the seed of the tree in the same way that numbers are to the monad. How the Monad is considered and the Universe. Apparently, one of the symbols of the picture (symbol No. 8) is the monad, as an integral part of the philosophy of the Pythagoreans.

Philosophy of Music

However, the theme of the philosophy of Pythagoras would be incomplete without mentioning the philosophy of music of Pythagoras.

Pythagoras was admitted to the so-called Mysteries - secret meetings of priests and magicians. Apparently, the philosophy of Pythagoras was based for the most part on the teachings of the priests of the Mysteries. They say that Pythagoras was not a musician, but he is credited with the discovery of the diatonic scale. Having received basic information about the divine theory of music from the priests of the various Mysteries, Pythagoras spent several years meditating on the laws governing consonance and dissonance. How he actually found the solution we do not know, but there is the following explanation.

Pythagoras the mystic

Further, regarding the mystical-religious component of the philosopher's teachings, it should be noted that there is a concept of the transmigration of souls and their circulation. The soul is eternal. Mortal souls descend from heaven and inhabit other objects (animals or people) and stay there until they are sufficiently purified to move back to heaven.

A certain secret society played a decisive role in the life of Pythagoras and his teachings (it must be added that this society also greatly influenced politics), in which the secret doctrine of the transmigration and the cycle of souls occupied a central place.

The collections of sayings of Pythagoras contain many rituals, texts about sacrifice, the behavior of followers, morality, and so on.

The next level of philosophical theories, which includes the philosophy of numbers and their conceptual explanation, the sequence of philosophical patterns, should be available only to those (chosen ones) who have realized and learned to comply with all the "canons" and requirements of previous teachings. Thus, Pythagoras created a whole religious cult, shrouded in secrets. Concerning this cult and secret society there are many opinions and various hypotheses ...

The scientific component of the philosophical teachings of Pythagoras was further explained by the Pythagoreans, but was not taken as a basis and gradually lost its significance. And the mystical-religious element received its further development within the current of neo-Pythagoreanism.

Pythagoras himself did not write great works. Of his works, only his sayings, philosophical and also religious and mystical teachings recorded by his followers are singled out.

Literary creativity

In the III century. BC e. a compilation of the sayings of Pythagoras appeared, known as " sacred word”, from which the so-called “Golden Verses” later arose (sometimes they are attributed to the 4th century BC without good reason). For the first time quotations from these verses are quoted by Chrysippus in the 3rd century. BC e., although, perhaps, at that time the compilation had not yet developed into a finished form. The final excerpt from the "Golden Verses" translated by I. Peter:

But you be firm: the divine race is present in mortals,
To them, proclaiming, sacred nature reveals everything.
If this is not alien to you, you will fulfill orders,
You will heal your soul and save you from many disasters.
Dishes, I said, leave those that I indicated in the cleansings.
And be guided by true knowledge - the best charioteer.
If you, leaving the body, ascend into the free ether,
You will become incorruptible, and eternal, and death does not know God.

Personal life

Returning from Babylonian captivity to his homeland in Greece, Pythagoras met unusual beauty a girl named Feana who secretly attended his meetings. The ancient philosopher was already in adulthood(56-60 years). The lovers got married, in marriage they had two children: a boy and a girl (names unknown).

Some historical sources claim that Theana was the daughter of Brontin - the philosopher, friend and student of Pythagoras.

Death of a Philosopher

There are four versions of the death of Pythagoras.

1. According to the first, the killer was a man whom a mathematician once refused to teach secret occult techniques. Being in feelings of hatred, the rejected set fire to the building of the Academy of Pythagoras, and the philosopher died saving the students.
2. The second legend says that in the burning house the adherents of the scientist created a bridge from own bodies wanting to save his teacher. And Pythagoras died of a broken heart, underestimating his efforts in the development of mankind.
3. A common version of the death of a sage is considered to be his death under random circumstances during a skirmish in Metapontum. At the time of his death, Pythagoras was 65-80 years old.
4. According to other sources, he managed to escape to Metapont, where his life ended around 497 BC. e.

Famous philosopher quotes

• never do what you do not know, but learn everything you need to know, and then you will lead a quiet life;
• bear meekly your lot as it is, and grumble not against it;
• learn to live without luxury.

Video about the history of Pythagoras

Pythagoras of Samos:

Pythagoras.

What do we know about this person? That he lived many years ago, wrote several essays “On Education”, “On the State”, “On Nature”, “On the Soul” and the Pythagorean theorem on the ratio of the sides of a right triangle (“Pythagorean pants are equal on all sides”).

Not enough for this outstanding personality. Let's dive into his biography and learn more about him.

short biography

Pythagoras of Samos - philosopher, mathematician, religious and political figure, was born in the VI century BC. in the city of Regia on the island of Samos (an island in the Aegean Sea - the territory of Greece). Pythagoras was a student of Anaximander - ancient Greek philosopher, a representative of the Miletus school (founded in Miletus by Thales, the first ancient Greek philosopher, he owns the teachings about nature, about water, about different forms and states of matter).

Anaximander was the first of the philosophers of those times to write philosophical work"On Nature", which appeared on Greek. He is credited with the invention sundial, the assumption of the existence of the Universe and the assumption that the Earth rests freely in the center of the World without support and without movement, and that it has the shape of a cylinder.

WITH young age Pythagoras was drawn to knowledge and travel. At the age of 18, he left his native island and went to foreign lands. He traveled to the East and to Egypt, Babylon and Phoenicia.

In Egypt itself, he lived for about 22 years, where, according to some reports, he comprehended the secret esoteric teachings of the priests - "initiates", and also studied astronomy, mathematics and other sciences. Especially for this, Pythagoras learned the Egyptian language.

Pythagoras came to Babylon as a prisoner of the Persian king Cambyses, who conquered Egypt in 525 BC, where he lived for 12 years.

At the age of 50, he finally returned to his native fatherland on the island of Samos. Unfortunately for him, bad news awaited him there: the tyrant Polycrates seized power on the island. Then he had to leave his native city and retire to southern Italy - the city of Croton. It was here that Pythagoras became so famous, made his discoveries, founded the Pythagorean school, it is also called the philosophical brotherhood, in which there were about 1900 students and followers of his teachings.

This is how Dicaearchus (an ancient Greek philosopher, student of Aristotle) ​​in his Fragments describes the appearance and arrival of Pythagoras in Croton:

“... he endeared himself to the whole city as a person who traveled a lot, unusual and by nature richly endowed with fate, for he possessed a stately appearance and great beauty, nobility of speech, character and everything else ...”

Among his students were many representatives of power and nobility. They tried to change the laws in accordance with the teachings of Pythagoras, this led to deplorable events. The discontent of citizens who did not share the point of view of the Pythagoreans led to bloody riots in Croton and Tarentum. Many people were killed, and Pythagoras himself had to flee.

Achievements and teachings of Pythagoras

We all know the basic teaching of Pythagoras about the soul (although not everyone has heard about it). It lies in the fact that the soul is immortal, the soul performs the so-called "circle of inevitability", thereby each time being reborn into new life. Therefore, both the soul and the body need to be cleansed. Purification for the body is abstinence from animal food (vegetarianism), and for the soul it is the knowledge of the musical-numerical structure of the cosmos.

In scientific achievements, Pythagoras became famous for his theorem (known to us from school): "The square of the hypotenuse of a triangle is equal to the sum of the squares of the legs", as well as teachings about numbers. He developed the theory of even and odd numbers, studied the properties of integers, created the theory of proportions, and made a great contribution to the development of planimetry.

By the way, from his theory of the parity of a number, he deduced that every thing, like numbers, has two opposites in itself: "limit" and "infinite." And he called the reconciliation or balancing of these two opposites “harmony”.

Pythagoras believed that the secret of everything that exists on earth is in numbers, one of his statements was: “God is the number of numbers, but everything is like a number”. He was the first to come up with the idea that the Universe and the Earth have a spherical shape (similar to a sphere), and the planets (including the Earth) move around the central fire, the so-called "source of light".

In conclusion, I want to talk about the death of Pythagoras. She, like his whole life, is also shrouded in mystery, because it is impossible to reliably say exactly how Pythagoras died. The description of the death of Pythagoras by his students and philosophers of those times is contradictory.

Some say that he died in Metapontum when someone he knew set fire to the house in which he was with his students. When Pythagoras ran out of the burning house, he had the opportunity to hide with the others, but he stopped and said: "Better to die than to be known as an idle talk". He was overtaken and killed, and about forty of his students died with him.

According to other sources, Pythagoras died of exhaustion in the Metapontic sanctuary of the Muses: "Forty days without eating anything"(Dicaearchus). There is another version that says that Pythagoras was killed in a street fight during a popular uprising.

Where is the truth here, and where is the lie, is no longer clear. His whole life was overgrown with legends and epics.

"Don't chase happiness: it is always in yourself" (Pythagoras).

What contribution of Pythagoras to science, philosophy and mathematics you will learn from this article.

What is the contribution of Pythagoras to mathematics?

The contribution to the geometry of which cannot be underestimated, made truly great discoveries. Pythagoras created his own school and, together with his students, he worked hard to give a scientific character to geometry. In addition to the fact that he created the famous Pythagorean theorem (it is very important for modern science and is used at every step in solving important geometric problems), the scientist owns many discoveries. Among them:

• Sum theorem internal corners triangle
• The problem of dividing a plane into regular polygons - equilateral squares, triangles and hexagons
• Invented geometric methods for solving quadratic equations
• Created rules for solving problems

What is the contribution of Pythagoras to science?

In addition to mathematical achievements, Pythagoras made a significant contribution to other sciences. In astronomy and geography, he was among the first scientists who expressed the hypothesis that our planet is round. He believed that we are not the only beings inhabiting the universe.

The discoveries of Pythagoras in the field of music are also significant. He determined that the sound directly depends on the length of the string or flute. Even the popular numerology today owes its existence to Pythagoras - he was the first to combine predictions for the future with numbers.

What is the contribution of Pythagoras to philosophy?

The contribution of Pythagoras to philosophy was that he first introduced the term "philosophy" into scientific use. He founded his school in Italy in 532 BC. At the same time, it was both a religious and monastic order and a political structure. The school had its own charter and fairly strict rules. Interestingly, all students of the school had to give up meat food and personal property, not tell others about the teachings of the mentor.