Biography of Pythagoras

Pythagoras Samossky (apprx. 580 - apprx. 500 BC) the Ancient Greek mathematician and the philosopher idealist. I was born on the island of Samos. I got a good education. According to the legend Pythagoras to examine wisdom of east scientists, left to Egypt and as though lived there 22 years. Having well seized all sciences of Egyptians including mathematics, he moved to Babylon where lived 12 years and I examined scientific knowledge of the Babylon priests. Legends attribute to Pythagoras visit and India. It is very probable as Ionia and India then had commercial relations. Having returned home (apprx. 530 BC) Pythagoras tried to organize the philosophical school. However for the unknown reasons it soon leaves Samos and to lodge in the Codiaeum (the Greek colony in the north of Italy). Here Pythagoras managed to organize the school which worked nearly thirty years. The school of Pythagoras, or as it still call, the Pythagorean union, was at the same time both philosophical school, and political party, and a religious brotherhood. The statute of the Pythagorean union was very severe. Everyone who entered it, refused personal property in favor of the union, undertook not to shed blood, not to use meat food, to protect secret of the doctrine of the teacher. In members of school it was forbidden to train others for remuneration. On the philosophical views Pythagoras was the idealist, the defender of interests of the slaveholding aristocracy. Probably, the reason of its departure also consisted in it from Samos as in Ionia supporters of democratic views had very great influence. In public questions Pythagoreans understood domination of aristocrats as "order". Ancient Greek democracy they condemned. The Pythagorean philosophy was primitive attempt to prove domination of the slaveholding aristocracy. At the end of the V century BC in Greece and its colonies the wave of democratic movement swept. The democracy won the Codiaeum. Pythagoras together with pupils leaves the Codiaeum and уезжаетв to Tarent, and then in Metapont. Arrival of Pythagoreans in Metapont coincided with flash there popular uprising. In one of night skirmishes almost ninety-year-old Pythagoras was lost. Its school stopped the existence. Pupils of Pythagoras, escaping from prosecutions, were settled across all Greece and its colonies. Getting itself means of livelihood, they organized schools at which taught mainly arithmetics and geometry. Data on their achievements contain in compositions of the latest scientists - Platon, Aristotle, etc.

Opening of that fact that between the party and a diagonal of a square doesn't exist the general measure, was the biggest merit of Pythagoreans. This fact caused the first crisis in the history of mathematics. The Pythagorean doctrine about an integer basis all existing more it was impossible to recognize true. Therefore Pythagoreans tried to keep the opening in secret and created a legend of death of GippasMessopotamsky who dared to divulge opening. To Pythagoras attribute some more opening important at that time, namely: theorem of the sum of internal corners of a triangle; a task about division of the plane into regular polygons (triangles, squares and hexagons). There are data that Pythagoras constructed "space" figures, i.e. five regular polyhedrons. But it is more probable that he knew only three elementary regular polyhedrons: cube, tetrahedron, octahedron. The school of Pythagoras made much to give to geometry character of science. Association of geometry with arithmetics was the main feature of a method of Pythagoras.

Pythagoras was engaged in proportions and progressions much and, it is probable similarity of figures as to it attribute the solution of a task: "On these two figures to construct a third, equal one of data and similar to the second". Pythagoras and his pupils entered concept about polygonal, friendly, perfect numbers and studied their properties. The arithmetician as practice of calculations didn't interest Pythagoras, and he with pride declared that "delivered to the arithmetician above interests of the dealer". Pythagoras considered as one of the first that Earth has a form of a sphere and is the center of the Universe that the Sun, the Moon and planets have own movement other than the daily movement of fixed stars. Nicolaus Copernicus apprehended the doctrine of Pythagoreans about the movement of Earth as background of the heliocentric doctrine. Not without reason the church declared Copernicus's system "the false Pythagorean doctrine".

Thoughts and aphorisms

• In the field of life, like the sower, go an even and constant stride.

• The true fatherland where is good customs.

• Be not the member of scientific society: the wisest, making society, become commoners.

• Read sacred numbers, weight and a measure, as fumes of graceful equality.

• Measure the desires, weigh the thoughts, estimate the words.

• Be surprised to nothing: surprise made gods.

• If ask: what is is more ancient than gods? - reply: fear and hope.

The truth about Pythagoras

The most bigger that is known now to the population of this uvazhayey ancient Greek, keeps within one phrase: "Pythagorean trousers on all parties are equal". Authors of this teaser are separated obviously from Pythagoras of an eyelid, differently they didn't dare to be teased. Because Pythagoras - at all not a square of a hypotenuse equal to the sum of squares of legs.Thisisthewell-knownphilosopher.

Pythagoras lived in the sixth eyelid B.C., had beautiful appearance, carried a long beard, and on the head a gold diadem. Pythagoras is not a name, but a nickname which the philosopher got for that always spoke truly and convincingly as the Greek oracle. (Pythagoras - "convincing the speech".) The speeches I got 2000 at

to the ciphered phenomena of our life. In total in the nature, Pythagoras spoke, is divided into three parts. Therefore before solving any problem, it should be presented in the form of the triangular chart. "Behold a triangle - and the task on two thirds is solved".

Pythagoras didn't leave behind collected works, he kept the doctrine in secret and transferred to pupils orally. As a result the secret died together with them. Some information nevertheless filtered into centuries, but now it is hard to say, how many in it true, and how many false. Even with the Pythagorean theorem not everything is indisputable. Some historians doubt authorship of Pythagoras, claiming that it was used with might and main in economy by the most different ancient people.

What to speak about the separate facts of the biography of the great mathematician! Told, for example, that it could force birds to change the direction of flight. He talked to a she-bear, and that ceased to attack people, he talked to a bull, and that under the influence of conversation ceased to touch beans and lodged at the temple. Once, fording the river, Pythagoras uplifted a prayer to spirit of the river, and from water the voice was heard: "I welcome you, Pythagoras!" Said also that he ruled over spirits: I sent them to water and, looking at ripples, I did predictions.

Its influence on people was so great that the praise from lips of Pythagoras overflowed his pupils with delight. Once it happened to it to become angry about the pupil, and that committed suicide. The shaken philosopher never more with anybody didn't speak with asperity.

He as if managed to cure people, singing it verses from "Illiada" and Homer's "Odyssey". He knew medicinal properties of a huge number of plants.

In the next centuries the figure of Pythagoras was surrounded a set of legends: he was considered as the re-embodied god Apollo, believed that it had a gold hip, and it was capable to fork and easily at the same time to teach in two different places. Fathers of early Christian church allocated for Pythagoras a place of honor between Moisey and Platon. Though it isn't really clear, for what: Pythagoras became famous for the doctrine about space harmony and resettlement of souls that not really fits into Christian doctrines. Besides, the man of science didn't avoid also sorcery, even in the XVI century links to authority of Pythagoras on questions not only sciences, but also magics were frequent. As in Russia all janitors - philosophers, and in Ancient Greece all philosophers were mathematicians. Pythagorasinthisregardwasn'tanexception.

PythagorasandPythagoreans

But Pythagoras was not only the scientist." In combination" he was the active preacher of own doctrines. And the preacher who very succeeded: on the Greek island Crotone, in the south of Italy where Pythagoras expelled from Samos preached, it enjoyed popularity. His followers who are carried away by ideas of the teacher стренько thought a religious award. Besides the award so numerous and powerful that it managed to come actually to the power in Crotone. At the time of antiquity Pythagoras was most of all known and popular as the preacher. And he preached own doctrine based on concept of reincarnation (resettlement of souls) that is, abilities of soul to endure death of a transitory body, and it means that the soul is immortal. As in a new embodiment of a shower can repeatedly move including in bodies of animals, Pythagoras and his followers were categorically against killing of animals, the uses in food of their meat and even categorically urged fellow citizens not to deal with those who slaughters animals or undresses their hulks. Pythagoras said that eating of meat darkens mental capacities. In general it didn't refuse to itself(himself) completely it but when was removed to the temple of God for meditation and a prayer, it took with itself(himself) in advance prepared food and drink. Itsfoodwere

Pythagorean ideas got into Athens, they were accepted by Socrates, developed into the powerful ideological movement headed by great Platon and his pupil Aristotle later.

But we will return to mathematics. Pythagoreans were keen on creation of the correct geometrical figures by means of compasses and a ruler. They keen on these "construction" built figures up to the correct pentagon and were puzzled with how by means of the same compasses and a ruler to construct the following correct figure - a heptagon? It is necessary to tell at once that they didn't manage it.

But they not only were puzzled, but also puzzled all reasonable mankind which with compasses and a ruler in hands, having frowned, rushed to build the correct heptagons.

Far from it! This problem of Pythagoreans remained the unsoluble more than two millennia! The 19-year-old (!) German young man Karl Friedrich Gauss (1777 - 1855) nicknamed later than the king of mathematicians solved it only in 1796.

I "constructed" a heptagon the young genius incidentally, being engaged absolutely in other calculations. Gauss stated the theory of the equations of division of a circle of Xn - 1 = 0 which in many respects was a prototype of the brilliant theory of other nineteen-year-old genius - Galois. Besides the general methods of the solution of these equations, Gauss established connection between the equations and creation of regular polygons. It found all those values n for which the correct n-square can be constructed by means of compasses and a ruler.

Since emergence of a task passed more than two thousand years... Here how many the patience and time is required sometimes on the decision!

Theorem history

Caricatures

Theorem history

We will begin the historical review with ancient China. Here the special attention is drawn by Chu-drinks mathematical book. In this composition it is so spoken about a Pythagorean triangle with the parties 3, 4 and 5: "If to spread out a right angle to components, the line connecting the ends of its parties, will be 5 when the basis is 3, and height 4". In the same book drawing which coincides with one of drawings of Hindu geometry of Baskhara is offered.

The cantor (the largest German historian of mathematics) considers that equality 32 + 42 = 52 was known already to Egyptians about 2300 more, at the time of the tsar Amenemhat I (according to the papyrus 6619 Berlin museums). According to the Cantor гарпедонапты, or "natyagivatel of ropes", plotted a right angle by means of rectangular triangles with the parties 3, 4 and 5. Very easily it is possible to reproduce their way of construction. We will take a rope of 12 m and we will tie to it on a color strip at distance 3м. from one end and 4 meters from another. The right angle will be concluded between the parties of 3 and 4 meters. Garpedonaptam it would be possible to object that their way of construction to become excessive if to use, for example, the wooden square applied by all carpenters. And it is valid, the Egyptian drawings in which such tool, for example the drawings representing a joiner's workshop meets are known.

It is a little better known about Pythagorean theorem at Babylonians. In one text carried by the time of Hammurabi i.e. by 2000, approximate calculation of a hypotenuse of a rectangular triangle is given. From here it is possible to draw a conclusion that in Dvurechye were able to make calculations with rectangular triangles, at least in certain cases. Being based, on the one hand, on today's level of knowledge of the Egyptian and Babylon mathematics, and with another - on critical studying of the Greek sources, Van der Waerden (the Dutch mathematician) drew the following conclusion: "A merit of the first Greek mathematicians, such as Thales, Pythagoras and Pythagoreans, is not opening of mathematics, but its systematization and an obsnovaniye. In their hands the computing recipes based on vague representations turned into the exact science."

The geometry at Hindus, as well as at Egyptians and Babylonians, was closely connected with a cult. It is very probable that the theorem of a square of a hypotenuse was known in India about the 18th century BC.

In the first Russian translation of Euclidean "Beginnings" made by F. I. Petrushevsky, Pythagorean theorem is stated so: "In rectangular triangles the square from the party, opposite to a right angle, is equal to the amount of squares from the parties containing a right angle".

Now it is known that this theorem wasn't opened by Pythagoras. However one believe that Pythagoras gave the first its full proof, and others refuse to it and this merit. Some attribute to Pythagoras the proof which Euclid provides in the first book of "Beginnings". On the other hand, Prokl claims that the proof at "Beginnings" belongs to Euclid. As we see, the mathematics history almost didn't keep reliable data about life of Pythagoras and his mathematical activities. But the legend reports even the next circumstances accompanying opening of the theorem. Tell that in honor of this opening Pythagoras sacrificed 100 bulls.

Date: 2015-01-29; view: 983