development of ideas about the number is an important part of our history.It is one of the basic mathematical concepts, which allows us to express the results of measurements or bills.The source for a variety of mathematical theories is the concept of numbers.It is also used in mechanics, physics, chemistry, astronomy and many other disciplines.Moreover, in everyday life we constantly use numbers.

## appearance of digits

followers of Pythagoras believed that the numbers contain mystical essence of things.These mathematical abstraction to lead the world, establishing order in it.The Pythagoreans assumed that all existing laws in the world can be expressed in numbers.It is with the Pythagorean theory of numbers became interested many scientists.These symbols were considered the basis of the material world, and not just expressions of a law-order.

history of the number and the account opened with what was established by the practical subjects, as well as measuring the volumes, surfaces and lines.

gradually formed the concept of the natural numbers.This process is complicated by the fact that primitive man could not be separated from the concrete representation of an abstract.Account as a result of a long time remained a real.We used the mark, stones, pins and so on. N. It is used for storing the results knots, nicks, etc. After the invention of writing the history of the number has been marked by the fact that they began to use letters as well as special icons, applied for reduced image on the letter of large numbers.Usually reproduce in such a numbering principle encoding similar to that used in the language.

Later, there was an idea to consider dozens, not just units.In 100 different Indo-European languages the names of numbers from two to ten are similar, as well as the names of tens.Therefore, for a long time, the notion of abstract numbers, even before these languages were divided.

score on the fingers initially was widespread, and this explains the fact that the majority of peoples in the formation of numerals occupies a special symbol for the decimal system 10 takes place from here.Although there are exceptions.For example, 80 is translated from French - "Twenty-four," and 90 - "Twenty-four plus ten."Use of this goes back to the bank on the toes and hands.Numerals are arranged similarly to the Abkhaz, Ossetian and Danish.

in Georgian language by twenties even clearer.The Aztecs and the Sumerians believed the original five.There are also more exotic options that have marked the history of the number.For example, in scientific calculations Babylonians used the sexagesimal system.In the so-called "unary" systems the number formed by the repetition of the sign, which symbolizes unity.Ancient people used this method of approximately 10-11 thousand. BC.e.

nonpositional There are also systems in which the numerical values are used for recording characters depending on their locations in the code number.Use the addition of numbers.

## of Ancient

knowledge of mathematics of ancient Egypt today is based on two papyri, which date from about 1700 year BC.e.Mathematical information expressed in them, go back to a more ancient period, around 3500 BC.e.The Egyptians used this knowledge to calculate the weight of the different bodies, the volume of grain silos and the area of crops, the amount of taxes, as well as necessary for the construction of buildings number of stones.However, the main area of application of mathematics was astronomy, associated with calendar calculations.Calendar was needed to determine the dates of various religious holidays, as well as predictions of flooding of the Nile.

Writing in ancient Egypt was based on hieroglyphs.At that time, the number system yielded vavilonyanskoy.Egyptians used nonpositional decimal system in which the number of vertical lines is a number from 1 to 9. The individual characters are introduced to the power of ten.The history of development of ancient Egypt has proceeded as follows.With the emergence of the papyrus was introduced in hieratic characters (ie cursive).The special character used therein to denote the numbers 1 to 9, and multiples of 10, 100 and so on. D. The development of rational numbers while slow.They are written as a sum of fractions with the numerator equal to one.

## numbers in ancient Greece

on the use of different letters of the alphabet was founded by Greek numerals.History of natural numbers in this country is marked by the fact that drink 6-3 centuries BC.e.Attic system to represent the unit applied the vertical line, and 5, 10, 100, and so on. d. were written using the initial letters of their names in the Greek language.In the Ionic system, later, used to denote the numbers 24 existing letters of the alphabet, as well as 3 archaic.As the first 9 numbers (1 to 9) stands for multiple 1000 and 9000, but before the letter was put with the vertical line."M" stands for the tens of thousands (from the Greek word "mirioi").After it should have the number by which to multiply followed 10000.

in Greece in the 3rd century BC.e.there was a numerical system in which its own sign of the alphabet corresponds to each digit.The Greeks, starting from the 6th century, as the numbers began to use the first ten characters of its alphabet.It was in this country not only actively developing history of natural numbers, and mathematics originated in its modern sense.In other states, the time it has been used or for everyday use, or for any magic rituals by which the will of the gods found out (numerology, astrology and so on. N.).

## Roman numerals

In ancient Rome used the numbering, which under the name of Roman persisted until today.We use it to refer to anniversaries, ages, names of conferences and congresses, numbering the stanzas of the poem or book chapters.By repeating numbers 1, 5, 10, 50, 100, 500, 1000, they denote, respectively, as I, V, X, L, C, D, M records all integers.If the figure is much lower before they are added together, if it costs less to more, the latter is deducted from it.The same number can not put more than three times.For a long time, Western European countries used as the main Roman numerals.

## Positioning System

These are systems in which the numerical values of the characters depends on their place in the code number.Their main advantages - ease of performing various arithmetic operations, as well as a small number of characters required for writing numbers.

there is quite a lot of such systems.For example, binary, octal, fivefold, decimal, vigesimal and others. Each has its own history.

## system that existed at the Inca

Kip - an ancient counting and mnemonic system that existed in the Inca and their predecessors in the Andes.She is quite distinctive.This complex intertwining knots and rope made from the wool of llamas and alpacas, or cotton.Maybe in a pile on a few strands hanging down to two thousand.She used messengers to transmit messages of imperial roads, as well as in various aspects of society (as a topographical system, calendar, to fix the laws and taxes, and others.).We read and write a pile of interpreters trained.They groped nodules fingers picking up the pile.Much of the information in it - the numbers shown in decimal notation.

## Babylonian numerals

cuneiform on clay tablets icons Babylonians wrote.They have survived in considerable quantity (more than 500 thousand., About 400 of which are associated with mathematics).It should be noted that the roots of the culture of the Babylonians were inherited largely from the Sumerians - counting method, cuneiform writing, and so on. N.

was far superior Egyptian Babylonian system account.The Babylonians and Sumerians used a 60-ary positional, which is now immortalized in the division of the circle into 360 degrees and the hour and minute for 60 minutes, and seconds, respectively.

## score in ancient China

development of the concept of the number carried out in ancient China.In this country, the figures are identified by special characters that have appeared about 2 thousand. BC.e.However, the final mark they established only to the 3 century BC.e.And today, these characters are used.First was the multiplicative method of recording.The number 1946, for example, can be represented using Roman numerals instead of characters as 1M9S4H6.But in practice, the calculations were made on the counting board, which was a record number - position, both in India, rather than decimal, like the Babylonians.Empty seats designated zero.Only about 12 century BC.e.He appeared for a special character.

## history notation in India

diverse and broad achievements of mathematics in India.This country has made a great contribution to the development of the concept of number.It was here that was invented by a decimal positional system, familiar to us.The Indians offered characters to write 10 digits, with some changes in use today across the board.It is in this country as the foundations were laid decimal arithmetic.

Current figures are descended from Indian icons that mark was used as early as the 1st century BC.e.Initially, the Indian numbering was exquisite.Means for recording up to ten numbers in the fiftieth degree used in Sanskrit.First, for the numbers used so-called "Syro-Phoenician" system, and from the 6th century BC.e.- "Brahmi", with some signs for them.These icons, somewhat modified, have become modern numbers, called today the Arab.

Unknown Indian mathematician around 500 CE.e.He invented a new system of records - a decimal positional.Performing various arithmetic operations it was immeasurably simpler than in others.The Indians later used counting boards that have been adapted to the positional notation.They have developed algorithms of arithmetic operations, including obtaining cubic and square roots.Indian mathematician Brahmagupta, who lived in the 7th century, coined the negative numbers.Indians are well advanced in algebra.Symbols of their richer than that of Diophantus, although a few words clogged.

## Historical development numbers in Russia

numbering is the main prerequisite for mathematical knowledge.She had a different look at the various peoples of antiquity.The emergence and development of early same in different parts of the world.First of all nations signified their notches on sticks, called tags.This way of recording taxes or debt used illiterate population of the world.We make cuts on a stick, which corresponded to the amount of tax or duty.Then it split in half, leaving one half of the payer or debtor.The other was kept in the treasury or the lender.Both halves of the reckoning when tested folding.

figures appeared with the emergence of writing.They reminded first notches on sticks.Then there were special badges for some of them, such as 5 and 10. All the numbers in the time were not positional, and are similar to Roman.In ancient Russia, while in Western European countries applied roman numerals, alphabet used, similar to the Greek, since our country, like other Slavic, as is known, is located in the cultural dialogue with the Byzantine Empire.

numbers from 1 to 9, and then dozens and hundreds of numbering depicted in ancient letters of the Slavic alphabet (Cyrillic entered in the ninth century).

Some exceptions were the rule.So, 2 is not "beech", was the second in the alphabet, and "lead" (the third), because the letter Z in Starorusskaya transmit sound "in".Is at the end of the alphabet, "the fit" refers to 9, "worm" - 90. Individual letters are not used.To indicate that this is a sign of the figure, not a letter, written on it on top of the sign, called "Tittle", "~"."Darkness" called tens of thousands.We denote them by circling the signs units.Hundreds of thousands were called "Legion".They are portrayed with circles of dots encircling signs units.Millions - "leodry."These characters were portrayed as circled in from comma or rays.

further development of a natural number was in the early seventeenth century, when Indian figures became known in Russia.Until the eighteenth century, it was used in the Russian Slavic numbering.After that, it was replaced by the modern.

## history of complex numbers

These numbers have been introduced for the first time in connection with what has been allocated a formula for calculating the roots of the cubic equation.Tartaglia, an Italian mathematician, was in the first half of the sixteenth century, the expression for calculating the root of the equation through some parameters to find that it was necessary to create the system.However, it was found that such a system was not the solution for all of cubic equations in real numbers.This phenomenon is explained Rafael Bombelli in 1572, which was in fact the introduction of complex numbers.However, the results have long been considered questionable by many scientists, and only in the nineteenth century, the history of complex numbers marked an important event - their existence was acknowledged after the appearance of the works of Karl F. Gauss.