Report on Pythagoras. If you can
Report on Pythagoras. If you can
- The great ancient Greek scholar Pythagoras was born on the island of Samos in the 6th century BC.
n. e. In his youth he visited Egypt, where he studied with priests. It is said that he was
admitted to the sacred sanctuaries of Egypt, visited the Chaldean sages and
Persian magicians. Around 530 BC. e. Pythagoras moved to Crotone Greek
colony in Southern Italy, where he founded the so-called Pythagorean union (or
Cretan brotherhood). The sphere of interests of the members of the Union included scientific
research, religious and philosophical search, political activity. They
led a harsh lifestyle, above all valued self-control, courage and
collective discipline. Pythagoreans lived together, they had a joint
property, and even their discoveries they considered common property. Activities
Union was surrounded by mystery, so no texts from the early Pythagoreans
left. Moreover, according to tradition, they attributed all discoveries to Pythagoras, o
which already during life there were legends. Who is really the author of that
or other result, is unknown.
The Pythagoreans called their own studies of mathematics, which means
science, and divided them into four parts: arithmetic, geometry, astronomy and
harmony (ie, the teaching of music). The main was considered arithmetic. It is she
lay in the foundation of both geometry and astronomy, and harmony.
Pythagoreans represented numbers as a collection of points forming
geometric configurations like a pattern of pebbles on the ground. Thus,
way, under the number they meant a lot of units and recognized only
integer positive numbers, dividing them into even and odd ones. Pythagoreans
proved the first theorem of the theory of divisibility: the product of two numbers is even
if and only if at least one of them is even. They also
set the problem of finding perfect numbers, that is, numbers equal to the sum
their divisors. The unit was considered indivisible, it had no shares. Instead
This Pythagoreans considered relations (ie, proportions) of integers. TO
For example, they could say that 2 applies exactly to 3, like 4 to 6. Speaking
modern language, they built the theory of rational numbers as a theory of pairs.
It remains to be seen how many axioms were put earlier
The Pythagoreans were the basis of their geometry, but they all related to planimetry
rectilinear figures. The properties of triangles, rectangles,
parallelograms and other flat figures, their areas were compared. Crowned them
system of knowledge, the proof of the famous theorem of Pythagoras, which was
is known before as only as a fact for some particular cases. Difficult
To overestimate the importance of Pythagoras' theorem. E generalization still forms the basis
of all metric spaces.
It can be argued that even in stereometry, the Pythagoreans achieved great success.
According to the testimony of the Greek historian and philosopher Proclus, they built
5 regular polyhedra: tetrahedron, cube, octahedron, dodecahedron and icosahedron.
True, many modern researchers believe that Pythagoras were known
Only a cube, a tetrahedron and a dodecahedron, and the octahedron and icosahedron opened the Teethet of Athens,
a talented pupil of the Pythagorean Theodore Kerensky and Plato.
The Pythagoreans believed that the Earth has the shape of a sphere and is in the center
the universe: after all, there is no reason that it was biased or stretched in
any one side. The sun, the moon and five planets (Mercury, Venus, Mars,
Jupiter and Saturn) are moving around the Earth. Distances from them to our planet
such that they seem to constitute a seven-string harp, and when they move
there is a wonderful music of music spheres. People usually do not hear because of
the fuss of life, and only after death some of them will be able to enjoy it. A
Pythagoras heard it during his lifetime. The structure of the harp had to obey the laws