DISCOVERIES OF PYTHAGORUS

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 a 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 famous Pythagorean school and the spiritual teacher of a number of outstanding world-famous philosophers. Pythagoras became the founder of the teachings about Numbers, the Music of the celestial spheres and the Cosmos, created the basis of monadology and quantum theory 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 (Earthly monochord), psychology, pedagogy, ethics.

Pythagoras developed his philosophy on the basis of knowledge of the laws of the interrelations 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 transmigration (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 fundamentals of the teachings of Pythagoras, his sayings, practical and ethical advice, as well as theoretical postulates and spiritual tales of Pythagoras.

Perhaps not every one of us can remember the Pythagorean theorem, but everyone knows the saying “Pythagorean pants are equal on all sides.” Pythagoras, among other things, was a rather cunning man. The great scientist taught all his Pythagorean students a simple tactic that was very beneficial for him: if you made discoveries, attribute them to your teacher. This may be a rather controversial judgment, but it is thanks to his students that Pythagoras is credited with 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: he was 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 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 predictions for the future.

Pythagoras taught that both the beginning and the end of everything that exists lies 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. The 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, like a unit.

The Pythagoreans depicted the Monad as a figure that consists of ten points - the so-called nodes. All these ten nodes, called tetractys by the Pythagoreans, create nine equilateral triangles between themselves, which personify the fullness of 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 evidence in geometry, and created the doctrine of similarity.

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

History of Pythagorean Theorem

The great discoveries of Pythagoras the mathematician found their application at different times and around the world. This applies to the greatest extent to the Pythagorean theorem.

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

The outstanding German researcher of the history of mathematics Cantor believes that the Pythagorean equality 3? + 4? = 5? already known in Egypt around 2300 BC. BC, during the reign of King Amenemhat I (according to papyrus 6619 of the Berlin Museum). According to Kantor, the harpedonaptes, or the so-called “rope pullers,” built right angles using right triangles, the sides of which were 3, 4, 5. Their construction method is quite easily reproduced. If you take a piece of rope 12 m long, tie colored strips 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 enclosed between the two sides - 3 and 4 meters. One can object to the harpedonapts that this method of construction would be superfluous if we take, for example, the wooden triangle that all carpenters use. Indeed, there are Egyptian drawings, for example, depicting a carpenter's workshop, in which such a tool is found. But nevertheless, the fact remains that the Pythagorean triangle was used in ancient Egypt.

Little more information is available about the Pythagorean theorem used by the Babylonians. In the found text, which dates back to the time of Hammurabi, which is 2000 BC. e., there is an approximate definition of the hypotenuse of a right triangle. Consequently, this confirms that calculations with the sides of right triangles were already carried out in Mesopotamia, at least in some cases. Mathematician Van der Waerden from Holland, on the one hand, using the current level of knowledge about Babylonian and Egyptian mathematics, and on the other, based on a careful 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 justification 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 cult. It is quite possible that the Pythagorean theorem was known in India already in the 18th century BC. e.

The "list of mathematicians" supposedly compiled by Eudemus says of Pythagoras: "Pythagoras is reported to have turned the study of this branch of knowledge (geometry) into a real science, having analyzed its foundations from the highest point of view and examined its theories in a more mental and less material manner." .

Tree of Pythagoras

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

Proving his famous theorem, Pythagoras constructed a figure in which there were squares on each side of a right triangle. Over time, 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 regular 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 classic 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 the segments that somehow connect certain “centers” of the triangles, then you get a naked Pythagorean tree.

The Pythagorean tree is a fractal generated as follows:

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

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

On each side of a right triangle, construct a square with a side coinciding with this side.

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

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

Even during the scientist’s lifetime, the biography of Pythagoras was overgrown with all sorts of legends, sometimes completely fantastic. Without leaving anything about yourself personal records, Pythagoras remains significant figure both in philosophy and mathematics.

Biography ancient Greek philosopher, the mathematics and mysticism of Pythagoras are not reliably known. He left no records about himself, and the only sources about his life are the writings of the scientist’s students and followers. A huge amount of evidence about his life has reached us, but many of them are so fantastic and full of speculation that they can speak of his popularity, although they put historians in a difficult position. Researchers put the approximate date of birth of Pythagoras between 570 and 590 BC. From the writings of his closest student Aristoxenus, we know that Pythagoras spent his childhood on the island of Samos, off the coast of modern Turkey. His father, according to various versions, was either a merchant or a stone cutter, which is most likely. Pythagoras was well educated, learned to play the lyre and write poetry, and could declare the works of Homer. Already in his youth he had the makings of scientific activity, which were noticed by his senior teachers - Pherecydes, Anaximander, Hermodamant and Thales, the last of whom had a great influence on Pythagoras’ interest in mathematics and astronomy.

The grown-up scientist already feels close to his native Samos, and he sets off on a journey, information about which also varies greatly. However, the authors write that Pythagoras visited Miletus, Egypt, the Chaldean lands, Babylon, Crete and many other places, but this data cannot be considered reliable. The most reliable version is considered to be Porphyry’s version that at the age of 40 Pythagoras left for Italy and settled in the Greek colony city of Croton, where his philosophical activity flourished. Here he opens his own school, whose students later became known as “Pythagoreans.” It was a kind of religious order with a strong emphasis on ethics and morality. At the age of 60, Pythagoras married his student Theano, from whose marriage the scientist had a daughter Damo and sons Arimnest and Telaugus. Soon, due to contradictions with the local authorities, Pythagoras was forced to leave for another Greek colony - the city of Metapontus. Most authors indicate that it was here that he died, but the date of the scientist’s death also remains unknown. The approximate period 500 to 490 BC is widely used. as the date of death of Pythagoras.

It is traditionally believed that the works of Pythagoras himself have not reached us; there is a version that he did not write down his works at all. Because of his great popularity, many works were attributed to Pythagoras, even those written much later. It is also interesting that during his lifetime and about 150 years later, Pythagoras was known not as a mathematician, but as a famous mystic, expert in religious rituals and miracle worker. But, of course, mathematical activity became the main one for study in a later period, right up to the present day.

Known more than 2000 years before Pythagoras in Egypt, Babylon and China, the theorem on the equality of the sum of the squares of the lengths of the legs and the square of the length of the hypotenuse of a right triangle received its name precisely in honor of this scientist thanks to ancient authors. The Pythagorean theorem can be expressed as follows:

a 2 + b 2 = c 2, Where a And b- lengths of the legs, and c- the length of the hypotenuse of a right triangle.

On at the moment There are 367 different proofs of the theorem in science. Such an impressive number of proofs can be explained by the fact that the meaning of the theorem is truly fundamental to geometry. Pythagoras's actual contribution to the theorem is that he used algebraic methods to calculate "Pythagorean triplets" - an ordered set of three natural numbers, which satisfy the equation above.

One of the proofs proposed by Euclid is based on the method of areas. Squares are constructed to the sides of the triangle, and it is proved that the area of ​​the square built on the hypotenuse is equal to the sum of the areas of the squares built on the legs. This proof is called “Pythagorean Pants,” and the phrase “Pythagorean Pants are equal on all sides” is used for schoolchildren to memorize the theorem.

Another invention of the scientist, also known to all of us from school, is the Pythagorean table, better known as the multiplication table. This table was actively used by the students of his school. The Pythagorean table was written in the form of a 10 by 10 square, not in numbers, but in Greek and Phoenician letters with a line over each of them.

The teachings of Pythagoras were based on the fact that everything in the Universe is certain numbers, and the relationships between them are mathematical. In this sense, the mathematical research of Pythagoras in music is of great interest. It would seem, how can the study of music and such a rigorous science as mathematics be combined? But it was thanks to Pythagoras that the doctrine of the “Pythagorean scale” appeared - a mathematical expression of the frequency relationships between the steps of the scale. He established a mathematical relationship between the harmonic vibration of the lyre strings and the length of the strings. Pythagorean tuning can also be applied to other instruments.

Another interesting invention of the scientist was the so-called “Pythagorean mug,” otherwise called the “mug of greed.” This mug is an ordinary bowl at first glance, but in the center there is a special column, inside of which there is a curved channel from the bottom of the bowl that goes out. The essence of this invention is that if you pour more liquid than the mark, then all the contents will pour out through this channel according to the law of communicating vessels. According to legend, the mug was used to ensure that the person drinking wine from it did not drink too much wine, but could enjoy the drink. According to another version, slaves were given water from such mugs to save water, which was in short supply in Samos.

We will never be able to establish exactly what real contribution Pythagoras made to science. Having become a truly legendary personality already during his lifetime, Pythagoras and his biography were overgrown with numerous speculations and stories. But, undoubtedly, the philosophical teachings of Pythagoras played a role in his popularity, and only then were other scientists able to appreciate his mathematical genius. The desire to see an arithmetic pattern in everything and the idea that everything is numbers were one of the components of the mystical philosophy of the Pythagoreans. They praised the whole positive numbers, which were then depicted as dots and arranged in the form of regular geometric shapes. They represented numbers as “male” and “female” (even and odd, respectively), and studied their properties. The school opened by Pythagoras lasted for quite a long time, carrying the arithmetic mysticism of its philosophy through time and attracting more and more followers.

Since antiquity, works, discoveries, and socially significant places have been named in memory of Pythagoras. IN modern world there is the city of Pythagorion on the island of Samos, named after its famous inhabitant, a lunar crater, a museum-workshop in Sweden, one of the educational buildings in Cambridge and, of course, appeared in different times mathematical theorems, methods and figures related in one way or another to the activities of Pythagoras in mathematics.

One of the founders of many sciences, doctrines and concepts is Pythagoras. His biography is full of secrets, and is not thoroughly known even to professional historians. It is only clear that the basic facts of his life were recorded on paper by his own students, who were in different parts of the world. The biography of Pythagoras is briefly outlined in this article.

The beginning of life's journey

The biography of Pythagoras begins in 570 (approximate date), in the city of Sidon (now Saida, Lebanon). He was born into the family of a wealthy jeweler who was able to give the most better education and knowledge to your son. An interesting fact is the origin of the name of the future sage. His father, Mnesarchus, named his son after one of Apollo's priestesses, Pythia. He also named his wife Pyphasis after her. And everything turned out this way because it was this priestess who predicted to Mnesarch that he would have a son who would surpass every other person both in beauty and in intelligence.

First knowledge and teachers

The early years of the scientist, as the biography of Pythagoras tells, took place within the walls of the best temples in Greece. Back in adolescence he tried to learn as much as possible by reading the works of other sages and also by talking with spiritual teachers. Among them, it is worth highlighting Pherecydes of Syros, the greatest ancient Greek cosmologist. He helps young Pythagoras study mathematics, physics, and astronomy. Pythagoras also had the opportunity to communicate with Hermodamant, who taught him to love poetry and everything related to art.

Educational travel

In subsequent years, the biography of Pythagoras consists of his life experience in foreign lands. First he goes to Egypt, where he plunges into the local mystery. Later in this country he opens his own school, where he could study mathematics and philosophy. During the 20 years that he spent in Egypt, he gathered many disciples and supporters who called themselves Pythagoreans. It is also worth noting that during this period he introduced such a concept as a philosopher and called himself this word. The fact is that previously all great people called themselves sages, which meant “knows.” Pythagoras introduced the term “philosopher,” which was translated as “trying to find out.”

After his scientific discoveries, which were made in Egypt, Pythagoras went to Babylon, where he spent 12 years. There he studies eastern religions, their features, compares the development of science and the arts in the countries of Mesopotamia and Greece. After this, he returns to the Eastern Mediterranean, only now - to the shores of Phenicia and Syria. He spends very little time there, and after that he begins the journey again, only this time more distant. Crossing the country of the Achimenides and Media, the philosopher ends up in Hindustan. By gaining knowledge about a completely different religion and way of life, he further expands his horizons, which gives him the opportunity to make new discoveries in science.

Biography of Pythagoras: his last years

In 530 BC. Pythagoras ends up in Italy, where he discovers new school called the Pythagorean Union. Only those who have sufficient knowledge behind them can study there. During lessons in this institution, Pythagoras tells his students about the secrets of astronomy, teaches mathematics, geometry, and harmony. At the age of 60, he marries one of his students, and they have three children.

Around 500 BC. Persecution begins against the Pythagoreans. As the story goes, they were due to the fact that the philosopher himself chose not to take the son of a respected citizen into the ranks of his students. After numerous riots he disappeared.

Messages about Pythagoras, the ancient Greek philosopher and mathematician, creator of the Pythagorean school, are presented in this article.

Report on Pythagoras

Brief biography of Pythagoras

Pythagoras was born around 570 BC in Sidon, Phoenician, into the family of a rich merchant from Tire. Thanks to financial condition his parents, the young man met many sages of that era and absorbed their knowledge like a sponge.

At the age of 18, Pythagoras left hometown and left for Egypt. There he stayed for 22 years, learning the knowledge of the local priests. When the Persian king conquered Egypt, the scientist was taken to Babylon, where he lived for another 12 years. He returned to his native land at the age of 56, and his compatriots recognized him as a sage.

Pythagoras the donkey of Southern Italy, the Greek colony - Crotone. Here he found many followers and founded his school. His students practically deified their founder and teacher. But the omnipotence of the Pythagoreans led to the outbreak of rebellions and Pythagoras moved to another Greek colony - Metapontus. This is where he died.

He was married to a woman, Theano, from whom a son, Telaug, and a daughter, whose name is unknown, were born.

Features of the philosophical teachings of Pythagoras

The philosophical teaching of Pythagoras consists of two parts - a scientific approach to understanding the world and an occult way of life, preached by him. He reflected on the liberation of the soul through physical and moral purification through secret teachings. The philosopher founded the mystical doctrine of the cycle of migration of the soul. The eternal soul, according to the scientist, moves from heaven into the body of an animal or a person. And it moves from body to body until the soul earns the right to return back to heaven.

Pythagoras formulated a number of instructions from his school - about behavior, circulation human lives, sacrifices, food and burials.

The Pythagoreans put forward the idea of ​​quantitative patterns in the development of the world. And this, in turn, contributed to the development of physical, mathematical, geographical and astronomical knowledge. Pythagoras taught that the basis of the world and things is number. He developed numerical relationships that found applications in all human activities.

Pythagoras of Samos (580-500 BC) - ancient Greek thinker, mathematician and mystic. He created the religious and philosophical school of the Pythagoreans.

The life story of Pythagoras is difficult to separate from the legends that present him as a perfect sage and a great initiate into all the mysteries of the Greeks and barbarians. Herodotus also called him “the greatest Hellenic sage.” The main sources on the life and teachings of Pythagoras are the works of the Neoplatonist philosopher Iamblichus, “On Pythagorean life"; Porphyry "Life of Pythagoras"; Diogenes Laertius, Pythagoras. These authors relied on the writings of earlier authors, of which it should be noted that Aristotle’s student Aristoxenus was from Tarentum, where the Pythagoreans had a strong position.

Brief biography Pythagoras:

The earliest known sources about the teachings of this thinker appeared only 200 years after his death. However, it is on them that the biography of Pythagoras is based. He himself did not leave any works to his descendants, therefore all information about his teaching and personality is based only on the works of his followers, who were not always impartial.

Pythagoras was born in Sidon Phoenician around 580 (according to other sources around 570) BC. e. Pythagoras' parents are Parthenides and Mnesarchus from the island of Samos. Pythagoras' father was, according to one version, a stone cutter, according to another, a rich merchant who received citizenship of Samos for distributing bread during a famine. The first version is preferable, since Pausanias, who testified to this, gives the genealogy of this thinker. Parthenis, his mother, was later renamed Pyphaida by her husband. She came from the family of Ankeus, a noble man who founded a Greek colony on Samos.

The great biography of Pythagoras was supposedly predetermined even before his birth, which seemed to have been predicted at Delphi by the Pythia, which is why he was called that way. Pythagoras means "he who was announced by the Pythia." This fortuneteller allegedly told Mnesarchus that the future great man will bring as much good and benefit to people as no one else subsequently. To celebrate this, the child’s father even gave a new name to his wife, Pyphaida, and called his son Pythagoras “the one who was announced by Pythia.”

There is another version of the appearance of this name. Moreover, they say that this is a nickname, and he received it for his ability to speak the truth. On behalf of the priestess-soothsayer from the temple of Apollo Pythia. And its meaning is “persuasive by speech.”

The name of his first teacher is known. It was Hermodamas. This man, who instilled in the student a love of painting and music, introduced him to the Iliad and Odyssey.

When he was eighteen years old, Pythagoras left his native island. After several years spent traveling and meeting with sages from different lands, he arrived in Egypt. His plans include studying with priests and comprehending ancient wisdom. In this he is helped by a letter of recommendation from the tyrant of Samos Polycrates to Pharaoh Amasis. Now he has access to something that many foreigners cannot even dream of: not only mathematics and medicine, but also the sacraments. Pythagoras spent 22 years here. And he left the country as a prisoner of the king of Persia, Cambyses, who conquered Egypt in 525 BC. The next 12 years were spent in Babylon.

He was able to return to his native Samos only at 56, and was recognized by his compatriots as the wisest of people. He also had followers here. Many are attracted by mystical philosophy, healthy asceticism and strict morality. Pythagoras preached the moral ennoblement of the people. It could be achieved where power is in the hands of those who know and wise people, to which the people obey unconditionally in one thing and consciously in another, as a moral authority. It is Pythagoras who is traditionally credited with introducing such words as “philosopher” and “philosophy”.

The disciples of this thinker formed a religious order, a kind of brotherhood of initiates, which consisted of a caste of like-minded people who deified the teacher. This order actually came to power in Crotone. All members of the order became vegetarians, who were forbidden to eat meat or bring sacrificial animals to the gods. Eating food of animal origin is the same as engaging in cannibalism. History has even preserved funny practices in this almost religious order. For example, they did not allow swallows to build nests under the roofs of their houses, or could not touch the white rooster, or eat beans. There is another version according to which the restriction applied only to certain types meat.

At the end of the 6th century BC. e. Due to anti-Pythagorean sentiments, the philosopher had to go to Metapontum, another Greek colony, where he died. Here, 450 years later, during the reign of Cicero (1st century BC), the crypt of this thinker was shown as a local landmark. Like his date of birth, exact date The death of Pythagoras is unknown, it is only assumed that he lived 80 years.

Pythagoras, according to Iamblichus, led the secret society for 39 years. Based on this, the date of his death is 491 BC. e., when the period of the Greco-Persian wars began. Referring to Heraclides, Diogenes said that this philosopher died at the age of 80, or even 90, according to other unnamed sources. That is, the date of death from here is 490 BC. e. (or, less likely, 480). In his chronology, Eusebius of Caesarea indicated 497 BC as the year of death of this thinker. e. Thus, the biography of this thinker is largely questionable.

Scientific achievements and works of Pythagoras:

The earliest known sources about the teachings of Pythagoras appeared only 200 years after his death. Pythagoras himself did not leave any writings, and all information about him and his teachings is based on the works of his followers, who are not always impartial.

1) In the field of mathematics:

Pythagoras is today considered the great cosmologist and mathematician of antiquity, but early evidence does not mention such merits. Iamblichus writes about the Pythagoreans that they had a custom of attributing all achievements to their teacher. This thinker is considered by ancient authors to be the creator of the famous theorem that in right triangle the square of the hypotenuse is equal to the sum of the squares of its legs (Pythagorean theorem). Both the biography of this philosopher and his achievements are largely dubious. The opinion about the theorem, in particular, is based on the testimony of Apollodorus the calculator, whose identity has not been established, as well as on poetic lines, the authorship of which also remains a mystery. Modern historians suggest that this thinker did not prove the theorem, but could convey this knowledge to the Greeks, which was known 1000 years ago in Babylon before the time when the biography of the mathematician Pythagoras dates back to. Although there is doubt that this particular thinker was able to make this discovery, no compelling arguments can be found to challenge this point of view. In addition to proving the above theorem, this mathematician is also credited with the study of integers, their properties and proportions.

2) Aristotle’s discoveries in the field of cosmology:

Aristotle in his work “Metaphysics” touches on the development of cosmology, but the contribution of Pythagoras is not voiced in any way in it. The thinker we are interested in is also credited with the discovery that the Earth is round. However, Theophrastus, the most authoritative author on this issue, gives it to Parmenides. Despite controversial issues, the merits of the Pythagorean school in cosmology and mathematics are indisputable. According to Aristotle, the real ones were the acousmatists, who followed the doctrine of the transmigration of souls. They viewed mathematics as a science that came not so much from their teacher as from one of the Pythagoreans, Hippasus.

3) Works created by Pythagoras:

This thinker did not write any treatises. It was impossible to compile a work from oral instructions addressed to the common people. And the secret occult teaching, intended for the elite, could not be entrusted to the book either. Diogenes lists some of the titles of books that allegedly belonged to Pythagoras: “On Nature,” “On the State,” “On Education.” But for the first 200 years after his death, not a single author, including Aristotle, Plato, and their successors at the Lyceum and Academy, quotes from the works of Pythagoras or even indicates their existence. To ancient writers from the beginning new era the written works of Pythagoras were unknown. This is reported by Josephus, Plutarch, and Galen. A compilation of the sayings of this thinker appeared in the 3rd century BC. e. It's called "The Sacred Word". Later, the “Golden Poems” arose from it (which are sometimes attributed, without good reason, to the 4th century BC, when the biography of Pythagoras is considered by various authors).

4) Pythagoras mug:

Quite a clever invention. It is not possible to fill it to the brim, because the entire contents of the mug will immediately leak out. There should be liquid in it only up to a certain level. It looks like an ordinary mug, but what distinguishes it from others is the column in the center. It was called the “greed circle.” Even today in Greece it is in deserved demand. And for those who do not know how to limit their alcohol consumption, it is even recommended.

5) Oratorical talent:

No one questions it in Pythagoras. He was a great speaker. It is known for certain that after his very first public lecture, he had two thousand students. Entire families, imbued with the ideas of their teacher, were ready to begin new life. Their Pythagorean community became a kind of state within a state. All the rules and laws developed by the Teacher were in effect in their Magna Graecia. Property here was collective, even scientific discoveries, which, by the way, were attributed exclusively to Pythagoras, belonged to his personal merits even when the teacher was no longer alive.

Pythagoras - quotes, aphorisms, sayings:

*Two things make a person godlike: living for the good of society and being truthful.

*Just as old wine is unsuitable for drinking a lot, so rude treatment is unsuitable for an interview.

*Take care of your children's tears so that they can shed them at your grave.

*It is equally dangerous to give a sword to a madman and to a dishonest person to give power.

*Do not consider yourself a great person based on the size of your shadow at sunset.

*Of two people of equal strength, the one who is right is stronger.

*No matter how short the words “yes” and “no” are, they still require the most serious consideration.

*To learn the customs of any people, try to first learn their language.

*It is more useful to throw a stone at random than an empty word.

*Live with people so that your friends do not become enemies, and your enemies become friends.

*No one should exceed the limit in food or drink.

*Blessed be the divine number that gave birth to gods and men.

*Joke, like salt, should be consumed in moderation.

*In order to live long, buy for yourself old wine and an old friend.

*Choose the best, and habit will make it pleasant and easy.

*During anger one should neither speak nor act.

*A statue is painted by its appearance, but a man by his deeds.

*Flattery is like a weapon in a painting. It brings pleasure, but no benefit.

*Don’t chase happiness: it is always within you.

30 interesting facts about Pythagoras:

1. The name of Pythagoras is famous for his theorem. And this is this man's greatest achievement.

2. The name of the “father” of democracy has long been known. This is Plato. But he based his teaching on the ideas of Pythagoras, one might say, his grandfather.

3.According to Pythagoras, everything in the world is reflected in numbers. His favorite number was 10.

4. None of the evidence from early times contains any mention of the merits of Pythagoras as the greatest cosmologist and mathematician of antiquity. And he is considered as such today.

5.Already during his lifetime he was considered a demigod, a miracle worker and an absolute sage, a kind of Einstein of the 4th century BC. There is no more mysterious great man in history.

6. One day Pythagoras got angry with one of his students, who committed suicide out of grief. From then on, the philosopher decided never to take out his irritation on people again.

7. Legends also attributed to Pythagoras the ability to heal people, using, among other things, excellent knowledge of various medicinal plants. The influence of this personality on those around him is difficult to overestimate.

8. In fact, Pythagoras is not a name, but a nickname of the great philosopher.

9. Pythagoras was distinguished by an excellent memory and developed curiosity.

10. Pythagoras was a famous cosmologist.

11. The name of Pythagoras was always surrounded by many legends even during his lifetime. For example, it was believed that he was able to control spirits, knew the language of animals, knew how to prophesy, and birds could change the direction of their flight under the influence of his speeches.

12. Pythagoras was the first to say that the soul of a person is reborn again after his death.

13.From a young age, Pythagoras was drawn to travel.

14. Pythagoras had his own school, which included 3 directions: political, religious and philosophical.

15. Pythagoras conducted experiments with color on the human psyche.

16. Pythagoras tried to find the harmony of numbers in nature.

17. Pythagoras considered himself past life fighter for Troy.

18. The theory of music was developed by this talented sage.

19. Pythagoras died saving his own students from a fire.

20. The lever was invented by this philosopher.

21. Pythagoras was a great orator. He taught this art to thousands of people.

22. A crater on the Moon is named after Pythagoras.

23. Pythagoras has always been considered a mystic.

24. Pythagoras believed that the secret of all essence on Earth lies in numbers.

25. Pythagoras got married when he was 60 years old. And the student of this philosopher became his wife.

26. The first lecture that Pythagoras gave brought 2000 people to him.

27.When joining the school of Pythagoras, people had to give up their property.

28. Among the followers of this sage there were quite noble people.

29. The first mentions of the life and work of Pythagoras became known only after 200 years had passed since his death.

30. The school of Pythagoras fell under the disgrace of the state.