History of math. The most ancient mathematical activity was counting. The counting was necessary to keep up a livestock of cattle and to do business. Some primitive tribes counted up amount of subjects, comparing them various parts of a body, mainly fingers of hands and foots. Some pictures on the stone represents number 35 as a series of 35 sticks - fingers built in a line. The first essential success in arithmetic was the invention of four basic actions: additions, subtraction, multiplication and division. The first achievements of geometry are connected to such simple concepts, as a straight line and a circle. The further development of mathematics began approximately in 3000 up to AD due to Babylonians and Egyptians.
BABYLONIA AND EGYPT
Babylonia. The source of our knowledge about the Babylon civilization are well saved clay tablets covered with texts which are dated from 2000 AD and up to 300 AD . The mathematics on tablets basically has been connected to housekeeping. Arithmetic and simple algebra were used at an exchange of money and calculations for the goods, calculation of simple and complex percent, taxes and the share of a crop which are handed over for the benefit of the state, a temple or the land owner. Numerous arithmetic and geometrical problems arose in connection with construction of channels, granaries and other public jobs. Very important problem of mathematics was calculation of a calendar. A calendar was used to know the terms of agricultural jobs and religious holidays. Division of a circle on 360 and degree and minutes on 60 parts originates in the Babylon astronomy.
Babylonians have made tables of inverse numbers (which were used at performance of division), tables of squares and square roots, and also tables of cubes and cubic roots. They knew good approximation of a number . The texts devoted to the solving algebraic and geometrical problems, testify that they used the square-law formula for the solving quadratics and could solve some special types of the problems, including up to ten equations with ten unknown persons, and also separate versions of the cubic equations and the equations of the fourth degree. On the clay tablets problems and the basic steps of procedures of their decision are embodied only. About 700 AD babylonians began to apply mathematics to research of, motions of the Moon and planets. It has allowed them to predict positions of planets that were important both for astrology, and for astronomy.
In geometry babylonians knew about such parities, for example, as proportionality of the corresponding parties of similar triangles, Pythagoras’ theorem and that a corner entered in half-circle- was known for a straight line. They had also rules of calculation of the areas of simple flat figures, including correct polygons, and volumes of simple bodies. Number babylonians equaled to 3.
Egypt. Our knowledge about ancient greek mathematics is based mainly on two papyruses dated approximately 1700 AD. Mathematical data stated in these papyruses go back to earlier period - around 3500 AD. Egyptians used mathematics to calculate weight of bodies, the areas of crops and volumes of granaries, the amount of taxes and the quantity of stones required to build those or other constructions. In papyruses it is possible to find also the problems connected to solving of amount of a grain, to set number necessary to produce a beer, and also more the challenges connected
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to distinction in grades of a grain; for these cases translation factors were calculated.
But the main scope of mathematics was astronomy, the calculations connected to a calendar are more exact. The calendar was used find out dates of religious holidays and a prediction of annual floods of Nile. However the level of development of astronomy in Ancient Egypt was much weaker than development in Babylon.
Ancient greek writing was based on hieroglyphs. They used their alphabet. I think it’s not efficient; It’s difficult to count using letters. Just think how they could multiply such numbers as 146534 to 19870503 using alphabet. May be they needn’t to count such numbers. Nevertheless they’ve built an incredible things – pyramids. They had to count the quantity of the stones that were used and these quantities sometimes reached to thousands of stones. I imagine their papyruses like a paper with numbers ABC, that equals, for example, to 3257.
The geometry at Egyptians was reduced to calculations of the areas of rectangular, triangles, trapezes, a circle, and also formulas of calculation of volumes of some bodies. It is necessary to say, that mathematics which Egyptians used at construction of pyramids, was simple and primitive. I suppose that simple and primitive geometry can not create buildings that can stand for thousands of years but the author thinks differently.
Problems and the solving resulted in papyruses, are formulated without any explanations. Egyptians dealt only with the elementary types of quadratics and arithmetic and geometrical progressions that is why also those common rules which they could deduce, were also the most elementary kind. Neither Babylon, nor Egyptian mathematics had no the common methods; the arch of mathematical knowledge represented a congestion of empirical formulas and rules.
THE GREEK MATHEMATICS
Classical Greece. From the point of view of 20 century ancestors of mathematics were Greeks of the classical period (6-4 centuries AD). The mathematics existing during earlier period, was a set of the empirical conclusions. On the contrary, in a deductive reasoning the new statement is deduced from the accepted parcels by the way excluding an opportunity of its aversion.
Insisting of Greeks on the deductive proof was extraordinary step. Any other civilization has not reached idea of reception of the conclusions extremely on the basis of the deductive reasoning which is starting with obviously formulated axioms. The reason is a greek society of the classical period. Mathematics and philosophers (quite often it there were same persons) belonged to the supreme layers of a society where any practical activities were considered as unworthy employment. Mathematics preferred abstract reasoning on numbers and spatial attitudes to the solving of practical problems. The mathematics consisted of a arithmetic - theoretical aspect and logistic - computing aspect. The lowest layers were engaged in logistic.
Deductive character of the Greek mathematics was completely generated by Plato’s and Eratosthenes’ time. Other great Greek, with whose name connect development of mathematics, was Pythagoras. He could meet the Babylon and Egyptian mathematics during the long wanderings. Pythagoras has based movement which blossoming falls at the period around 550-300 AD. Pythagoreans have created pure mathematics in the form of the theory of numbers and geometry. They represented integers