Samos, v. 560 av. J. - C. - Métaponte, v. 480 av. J. - C.
Philosopher and mathematicianPythagore in Puthagoras Greek. A certain number of points appear established well on the life and the activity of Pythagore. Its voyages led it in Egypt and to Babylon. It would have studied there mathematics which one practiced in these countries.
In 530 av. J. - C., it settled in Italy of the South, in Crotona, to flee the tyranny of Polycrate. It founded there a company, organized around the Master and of his doctrines, which played a big role for the city and all Large-Greece. Its political position, favorable to the order and the hierarchy, was worth to him supports it local aristocracies. The opposition of the democrats forced Pythagore to leave Crotona. Towards 500 av. J. - C., it settled in Métaponte, where it passed the remainder of its life. The democratic revolutions of the medium of Ve century completed to destroy the sect, driving out the last disciples towards Tarente.
Importance of the numbers
Among the beliefs in progress in the Pythagorean ones the metempsychosis appears, i.e. the transmigration of the hearts, doctrines of Indian origin. But the most original feature is the importance attached to the number, or more exactly to the integer. This one gives place to a representation by points. Their possible regular arrangement in simple figures armature the consideration of families of “illustrated numbers”, numbers triangular (1, 2,3,6, etc) and square numbers (1, 4.9, etc) for example. The Pythagorean ones developed arithmetic around these considerations. They were also interested in the “perfect” numbers, those which equalize the sum of their factors, such 6 equal to 1 + 2 + 3, and of which Euclide with given the general theory in book IX of the Elements. The “friendly” numbers constituted another field of research. They are pairs of numbers in which the sum of the factors of equal other. The example of 284 and 220 would have been found by Pythagore, and it would have been the only known one in Antiquity. The proportions were also an object of pushed study, resumed by Euclide, which extended the theory from it to all kinds of sizes in the book V of the Elements.
Arithmetic and cosmology
The reason of this interest pronounced for the arithmetic one lies in the conviction that the numbers constitute the gasoline of the things. These doctrines undoubtedly drew its source from three considerations. One was the relation noted between the heights of the sounds and the lengths of the codes of the musical instruments. Another was perhaps the report which a triangle whose sides have as measurements 3.4 and 5 is right-angled. The third was the existence of numerical relations in the movements of the celestial bodies.
The theorem of Pythagore
Geometrical research was developed by the Pythagorean ones. The “theorem of Pythagore” neither discovered nor was undoubtedly shown by that which gave him its name. This research led nevertheless to a discovery of incommensurability, of first importance for the development of mathematics. The diagonal of the square not containing an integer of times the side, the problem was to find a fraction on the side which is contained an integer of times in one and in the other. The Pythagorean ones showed impossibility of finding such “common measures”, throwing a major disorder in the erudite circles of the company.
The statement of the theorem
The square on the hypotenuse (c) of a right-angled triangle is equal to the sum of the squares on the two other sides (has, b): C 2 = has 2 + B 2.
Stars and music
The latter in addition cultivated the theory of the musical intervals as well as the study of the stars. They were the first to classify planets, i.e., in addition to the Sun and the Moon, Mercure, Venus, Mars, Jupiter and Saturne, according to their distances supposed with the Earth. They tried to grant these distances, as well as the periods of revolutions, with the musical intervals, developing the design of the celestial spheres and their music.