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Pythagoras of Samos (c. 580 - c. 500 BC) - ancient Greek philosopher, religious and political figure, founder of Pythagoreanism, mathematician. Pythagoras is credited with studying the properties of integers and proportions, proving the Pythagorean theorem, etc.
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School of Pythagoras The school was founded by Pythagoras and existed until the beginning of the 4th century. BC, although the persecution of her began almost immediately after the death of Pythagoras in 500. Admission to the school took place in several stages
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The first stage Pythagoras usually sent the candidate back, advising him to wait and come back in three years. This outwardly very severe reception was carried out deep meaning- after all, any impulse, even the most beautiful and pure, must pass the test of time.
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The second stage During this period, a person was not yet considered a student of the School and was called an acusmatik (“listener”). He listened, absorbed, realized - and all this happened in silence. Pythagoras "prescribed a five-year silence to acousticians, testing their ability to refrain, since silence is the most difficult kind of abstinence."
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Third stage Only after for long years such work, an acoustician became a real Pythagorean student. Now he bore the title of mathematician - “cognizing”. In the classes conducted by Pythagoras himself or his closest students, mathematicians were given a complete picture of the world, the structure of Nature and man was revealed. The training of mathematicians took place over a long period of time, but it was also only a preparation.
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The Fourth Stage To devote oneself to serving the people, society, all who need help and protection is a natural step for a mature philosopher. And when the students of mathematics were ready for this, there was a choice of those directions and forms in which this service would be carried out, and then the final training of the chosen “specialty”. Some studied economics, others studied medicine, and so on.
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Fifth stage The highest stage in the Pythagorean school was considered the training of politicians - people capable of managing society. The task is to lead people on the basis of the common good, not following the lead of either one's own or other people's interests. Later, Plato revised and expanded the Pythagorean theory of the state - "Plato's ideal state model." Many students of Pythagoras became famous as legislators and fair keepers of laws. The years when the Pythagoreans participated in state affairs were prosperous,
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Aphorisms of Pythagoras Do not do anything shameful either in the presence of others or in secret. Your first law should be respect for yourself. In order to understand the manners of any people, try first to learn their language. If you can be an eagle, do not strive to be the first among the jackdaws. During anger one should neither speak nor act. Life is like a game: some come to compete, others to trade, and the happiest to watch. However short the words "yes" and "no" may be, they still require the most serious reflection.
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Wash the offense you have received not in blood, but in Lethe, the river of oblivion. Drunkenness is an exercise in madness. Ask a drunkard how he could stop drinking. I will answer for him: let him often remember the things he does while drunk. Friends have everything in common, and friendship is equality.
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great science to live happily consists in living only in the present What is the most reasonable of all? Time is the smartest of all. Keeps the past, and the future - the seed. What is the most essential? - Hope light. It exists where there is nothing else. Do not judge your greatness by your shadow at sunset.
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Even-odd The Pythagoreans divided all numbers into two categories - even and odd. Later it turned out that the Pythagorean "even - odd", "right - left" have deep and interesting consequences in quartz crystals, in the structure of viruses and DNA, in the famous experiments of Pasteur, in parity violation elementary particles and other theories.
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Even... Odd... The Pythagoreans considered even numbers to be feminine and odd numbers to be masculine. Marriage is five equal to three plus two. For the same reason, a right-angled triangle with sides three, four, five was called by them "the figure of the bride."
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Ten 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 the expression of 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?
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Tetrad Numbers 1, 2, 3 and 4 made up the famous "tetrad". Geometrically, the tetrad was represented by a "perfect triangle", arithmetically - by a "triangular number" 1 + 2 + 3 + 4 = 10. The Pythagoreans swore "by those who put the tetrad into our soul, the source and root of eternal nature."
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The ideal number The sum of the numbers included in the tetrad is equal to ten, which is why the Pythagoreans considered ten to be the ideal number and symbolized the Universe. Since the number ten is ideal, they reasoned, there should be exactly ten planets in the sky. It should be noted that at that time only the Sun, Earth and five planets were known.
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Justice and Equality The Pythagoreans saw justice and equality in the square of a number. Their symbol of constancy was the number nine, since all multiples of nine numbers have the sum of the digits, again nine. 9*2=18 1+8=9; 7*9=63 6+3=9; 11*9=99 9+9=18 1+8=9; 25*9= 225 2+2+5=9.
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The number eight among the Pythagoreans symbolized death, since multiples of eight have a decreasing sum of digits. 8*2=16 1+6=7; 8*3=24 2+4=6; 8*4=32 3+2=5; 8*5+40 4+0=4; 8*6=48 4+8=12 1+2=3
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"Bad numbers" In addition to the numbers that caused admiration and admiration, the Pythagoreans also had the so-called bad numbers. These are numbers that did not have any merit, and even worse if such a number was surrounded by "good" numbers. The famous number thirteen is the devil's dozen The number seventeen, which caused particular disgust among the Pythagoreans.
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The number of the beast The very concept of the “number of the beast” first appears in the Revelations of John the Theologian, which appeared for the first time probably in the 1st century AD. Interestingly, the problem has been known for a long time - already in the 2nd century, Bishop Irenaeus claimed that 616 is false, and the true number of the beast is 666. What is the meaning of the “number of the beast”? It is believed that this is the encrypted name of the persecutor of Christians - Emperor Nero. The Hebrew spelling “Neron Kaisar” adds up to just 666, but the Latin “Nero Caesar” just gives 616. This is a palindrome This is a Smith number, that is, the sum of its digits is equal to the sum of the digits of its prime factors 666 is the sum of the squares of the first seven prime numbers In China, the number 6 is, on the contrary, lucky, and on 06/06/06 a record number of marriages were concluded there.
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Biography of Pythagoras
Pythagoras (from the Greek “persuasive speech”) is an ancient Greek philosopher and mathematician, the creator of the religious and philosophical school of the Pythagoreans. Born in Sidon, Phoenicia around 570 BC. He studied at several temples in Greece. His first teachers were Ferikid of Syros and the elder Germodamant. At a young age, Pythagoras went to Egypt.
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What did Pythagoras do?
Pythagoras was one of the first to declare that the Earth has the shape of a ball, and the Sun, Moon and other planets have their own trajectory of motion. Pythagoras is credited with the study of the properties of integers and proportions, the proof of the Pythagorean theorem. The Pythagoreans compiled a table of 10 opposites; Aristotle cites it in his "Metaphysics": limit - infinite odd - even one - many right - left male - female peace - direct movement - crooked light - darkness good - evil square - elongated rectangle
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In Crotone (Southern Italy) Pythagoras founded a school - the Pythagorean Union. Only those who have gone through many stages of knowledge, Pythagoras calls his closest students. The Pythagoreans are engaged in geometry, mathematics, harmony, astronomy. The activities of Pythagoras as a religious innovator of the VI century. BC e. was to create secret society, which not only set itself political goals, but, mainly, the liberation of the soul through moral and physical purification with the help of secret teachings (the mystical teaching about the cycle of transmigration of the soul). According to Pythagoras, the eternal soul migrates from heaven into the mortal body of a person or animal and undergoes a series of transmigrations until it earns the right to return back to heaven.
The teachings of Pythagoras should be divided into two components: a scientific approach to understanding the world and a religious and mystical way of life.
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Symbol of Pythagoras
The five-pointed star was considered in the school of Pythagoras a symbol of friendship, it was something like a talisman that was presented to friends; secret sign by which the Pythagoreans recognized each other.
The school of Pythagoras gave Greece a galaxy of talented philosophers, physicists, and mathematicians. Such as Aristotle, Archytas from Tarentum, Philolaus from Croton, Hippasus from Metapont. The scientific component of the teachings of Pythagoras developed in the 5th century. BC e. by the efforts of his followers, but faded away in the 4th century. BC e., while the mystical-religious component was developed and reborn in the form of neo-Pythagoreanism during the Roman Empire.
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Thoughts and aphorisms
In the field of life, like a sower, walk with even and steady steps. The true fatherland is where there are good morals. Do not be a member of a learned society: the wisest, making up a society, become commoners. Revere sacred numbers, weight and measure, as a child of graceful equality. Measure your desires, weigh your thoughts, number your words. Be astonished at nothing: astonishment has produced gods. If they ask what is older than the gods? - answer: fear and hope. "Try first to be wise, and a scientist - when you have free time."
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Presentation on the topic: Pythagorean school
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Pythagoras (from the Greek “persuasive speech”) is an ancient Greek philosopher and mathematician, the creator of the religious and philosophical school of the Pythagoreans. Born in Sidon, Phoenicia around 570 BC. He studied at several temples in Greece. His first teachers were Ferikid of Syros and the elder Germodamant. At a young age, Pythagoras went to Egypt. Pythagoras (from the Greek “persuasive speech”) is an ancient Greek philosopher and mathematician, the creator of the religious and philosophical school of the Pythagoreans. Born in Sidon, Phoenicia around 570 BC. He studied at several temples in Greece. His first teachers were Ferikid of Syros and the elder Germodamant. At a young age, Pythagoras went to Egypt.
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Pythagoras was one of the first to declare that the Earth has the shape of a ball, and the Sun, Moon and other planets have their own trajectory of motion. Pythagoras was one of the first to declare that the Earth has the shape of a ball, and the Sun, Moon and other planets have their own trajectory of motion. Pythagoras is credited with the study of the properties of integers and proportions, the proof of the Pythagorean theorem. The Pythagoreans compiled a table of 10 opposites; Aristotle cites it in his "Metaphysics": limit - infinite odd - even one - many right - left male - female peace - direct movement - crooked light - darkness good - evil square - elongated rectangle
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In Crotone (Southern Italy) Pythagoras founded a school - the Pythagorean Union. Only those who have gone through many stages of knowledge, Pythagoras calls his closest students. The Pythagoreans are engaged in geometry, mathematics, harmony, astronomy. In Crotone (Southern Italy) Pythagoras founded a school - the Pythagorean Union. Only those who have gone through many stages of knowledge, Pythagoras calls his closest students. The Pythagoreans are engaged in geometry, mathematics, harmony, astronomy. The activities of Pythagoras as a religious innovator of the VI century. BC e. consisted in the creation of a secret society, which not only set itself political goals, but, mainly, the liberation of the soul through moral and physical purification with the help of secret teachings (the mystical teaching about the cycle of transmigration of the soul). According to Pythagoras, the eternal soul migrates from heaven into the mortal body of a person or animal and undergoes a series of transmigrations until it earns the right to return back to heaven.
He owns geometric discoveries, such as the well-known theorem Pythagoras about the ratio of the hypotenuse and the legs of a right triangle, the doctrine of ... the idea of \u200b\u200bthe cosmos in today's sense belongs to the Pythagoreans. Pythagoras first used the word cosmos in its current sense for ...
A conspiracy is brewing, orders his men to watch Pythagoras. Outraged Pythagoras leaves the island forever and settles in one of ... memories of "Pythagorean pants". The reason for the popularity of the theorem Pythagoras due to its simplicity, beauty, significance. The study of Babylonian, ancient Chinese...
Antiquities do not confirm this. Perhaps the most famous achievement Pythagoras- a theorem according to which the square of the hypotenuse of a right triangle ... 367 proofs of this theorem were recorded. Probably the theorem Pythagoras is the only theorem with such an impressive number of proofs...
The sea off the coast of Asia Minor, therefore it is called Pythagoras Samos. Was born Pythagoras in the family of a stone carver, who soon found ... he was allowed to get acquainted with the centuries-old achievements of Egyptian science. When Pythagoras comprehended the science of the Egyptian priests, then he was going home to ...
Pythagoras and his teaching presentation - Mo...
What is the essence of teaching Pythagoras? Who are the Pythagoreans? What is the connection between Pythagoras and the word "space"? LIFE PYTHAGORE Pythagoras was born on the island of Samos... and appeared in the Greek city of Crotone in southern Italy. SCHOOL PYTHAGORE Pythagoras and his followers, the Pythagoreans, formed a secret alliance. To...
Society. The school caused displeasure of the democratic authorities of the island, and PYTHAGORAS I had to leave my homeland. PYTHAGOREAN UNION In 531 BC, which gave it the significance of a special science. THEOREM PYTHAGORE With name PYTHAGORE the famous theorem is related (the square of the length of the hypotenuse is equal to the sum ...
"Theorem of the bride" - The sum of the areas of squares. Windblown Pythagorean tree. Euclid's proof. Triangle. Square. The similarity of the drawing with a butterfly. Areas of use. Pythagoras. A beautiful brand. Great secrets of the theorem. The Bride Theorem. The area of the first square is equal to one. Fresco fragment. Wide application. Pythagoras of Samos.
"Pythagorean theorem proof" - Look and prove by applying the properties of areas. Proof by the Indian mathematician Bashara. A square with side c consists of four triangles with legs a and b and one square with side b-a. Educational resources. Reasoning. Let's turn triangle ABC around C by 900. Reasoning: Various proofs of the Pythagorean theorem Grade 8.
"The History of the Pythagorean Theorem" - Over the centuries, numerous different proofs of the Pythagorean theorem have been given. And on each leg a square is built containing two triangles. THEOREM. Here the mathematical book of Chu-pei attracts special attention. A right angle will be enclosed between sides 3 and 4 meters long. Tasks on the topic "The Pythagorean Theorem".
"Assignments according to the Pythagorean theorem" - Pythagoras. A right triangle is a triangle whose one of the angles is ____. Stranger Island. The problem of the 12th century Indian mathematician Bhaskara. The Pythagoreans were engaged in mathematics, philosophy, natural sciences. The side of a triangle that is opposite the right angle is called ____________.
"Pythagoras and his theorem" - Pythagoras and music. Biography of Pythagoras. Pythagoreans. Pythagorean school. One of the main theorems of geometry. The Pythagorean theorem has a rich history. Pythagorean theorem. The idea of a number. Pythagoras was born on the island of Samos. Discoveries of Pythagoras. The triangle is rectangular. Circle center. Write the correct equation.
"Proof of the Pythagorean theorem" - Proof. The simplest proof. Proofs of the theorem. "IN right triangle the square of the hypotenuse is equal to the sum of the squares of the legs. Algebraic proof. And now the theorem of Pythagoras Vern, as in his distant age. Euclid's proof. The Pythagorean theorem is one of the most important theorems in geometry.
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