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# MATHEMATICS

## SOME FACTS ON THE DEVELOPMENT OF THE NUMBER SYSTEM

Our present number system has not always been so fully developed as it is today. The number system is closely connected with early prehistoric man and with the most recent discoveries in atomic science.

But there was a time when man did not know how to count. The origin of number and counting is hidden behind countless prehistoric ages. No one knows when counting first began. Before man learned to count, he probably used names or signs for each person or thing. It is believed that the early shepherds would call their sheep by name in order to determine if any of them were missing. Counting represents a very important milestone in the progress of civilization. Of course, there were no number names at first; so counters were used. For counters man used sticks, pebbles, his fingers, and in some instances, his toes also. In fact, the word calculus comes from the Latin, meaning pebble; our numerals are called digits from the Latin, meaning finger.

The early shepherd probably learned that, instead of calling his sheep by name, he could lay aside a pebble for each sheep as he led them to the corral for the night and thus learned if any one of them had been lost.

It is possible to mention only a few important achievements in the history of mathematics. Historical records give evidence of the astronomical and arithmetical achievements of the early Babylonians, Sumerians, and Chinese. Somewhere in the distant past man learned that number was useful for civilized living. As early as 5,700 В. С. predecessors of the Babylonians had calendar and a type of practical arithmetic.

One of the greatest mathematicians of recorded history was the Greek Archimedes (287 - 212 В. С.) who developed a dynamic mathematics which could be applied to the laws of nature.

The practical civilization of ancient Rome, great in many other fields, contributed little to mathematics.

Going to the Renaissance period, we find the tribes of Moslems coming to Europe, bringing with them the culture of many civilizations, including a strange number system acauired from the Hindus.

Only about 300 years ago a great mathematician and philosopher. Rene Descartes (1596 - 1650) represented number pairs by points. This creation made possible the great advance in science and mathematics during the eighteenth century. In 1642 one of the greatest minds of all time Isaac Newton was born (1642 - 1727). Newton was one of the inventors of the calculus which is now studied bv college students who are seriously interested in mathematics or physical science.

Few discoveries in world science can equal the discovery of Lobachevsky (1792 -1 856). Like Archimedes, Galileo, Copernicus and Newton, he is one of those who laid the foundations of science. Lobachevsky created one of the greatest masterpieces of mathematics - non- Euclidean geometry.

Our number-system uses only the symbols 0, 1, 2 ... 9; it has base ten and positional notation. Thus any integer can be expressed with these symbols in various, combinations and arrangements. The base of our system is ten. Ten is probably the base because we have ten fingers and the" fingers were used in the early stages of counting.

It is not known when or by whom zero (nought) was invented. Historians think that zero was introduced by the Hindus or the Babylonians not later than in the ninth century A. D. and probably as early as the second century В. С. The invention of zero and our number system is one of the greatest achievements of the human race, without which the progress of science, industry, and commerce could be impossible. This new system was introduced in Europe by the Arabs, or Moslems, at about the beginning of the tenth century. These new numbers were used, and finally, after about five centuries, the decimal system won the battle.

A.D наша эра

ancient Rome древний Рим

Archimedes Архимед

Babylonians вавилонцы

calculus исчисление

Chinese китайцы,

Copernicus Коперник

counters счетчики, считалки

counting счет

Descartes, Rene Декарт, Рене

dynamic mathematics динамическая математика

Hindus индусы

Galileo Галилей

If any of them were missing зд. не отсутствуют ли какие-нибудь из них

It is believed считают, полагают

milestone веха

non-Euclidean geometry Неевклидова геометрия

number names название чисел

number system система чисел

point точка

by point точками

positional notation позиционное обозначение

prehistoric age доисторические времена

Renaissance period эпоха Ренессанса (Возрождения)

Sumerians шумерийцы

zero (nought) ноль

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