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Прочитайте текст и выделите основные периоды формирования математики.

TEXT 1

THE DEVELOPMENT OF MATHEMATICS

When asked about the major developments of mathematics, the average person would likely mention the calculator or the computer, or even the idea that we can consider "zero" an actual number. We learned mathematics from books and teachers; the ancients developed mathematics through tedious trial and error. Small steps by numerous people from numerous cultures over thousands of years directed the development of mathematics. Under what circumstances did the first inquisitive minds begin to see a need to develop the basic mathematical principles?

As necessity is the mother of invention, so was necessity the mother of mathematics. This necessity expressed itself in numerous areas: in agriculture, business and industry. First and foremost, the need to accurately record transactions of goods and money forced the development of the early numeric notation. As advances to civilization progressed, other influences arose including navigation and complex architecture, astronomy, and with it the astrology of certain religious societies. From this grew the development of calendars based around the movements of the heavenly bodies.

Similar motivations (calendars, trade, astronomy etc.) applied to all people, and numerous cultures likewise developed similar mathematic ideas, regardless of their isolation from each other due to geographic barriers. When civilization began to trade, a need to count arose. There were prior civilizations in which the beginnings or rudiments of mathematics were created. Scientists identify only a few cultures that directly affected the progression we can now trace backwards from modern mathematics: Mesopotamian/Babylonian, Greek, Indian, and Arabic/Islamic and finally European/American cultural group.

The Babylonian system of mathematics was sexagesimal (base 60) numeral system. From this, we derive the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 degrees in a circle. Mathematics as an organized science did not exist before the classical Greeks of the period from 600 to 300 BC entered upon the scene. It is understood the Greeks diverged and began to delve into more theoretic and abstract ideas. Many scientific giants came from this Greek culture and with them their great discoveries. Among them are Pythagoras, Euclid, Hipparchus and many others.

Next in the line of significant discoveries came the Indian mathematicians to whose credit the current numerical system we have labeled "Arabic numerals". Finally came the Arabic/Islamic influence. The word "algebra" itself even originates from a single word (²al-jabr²- an ancient medical term meaning "the reunion of broken parts'') from the title of a book written by the Arabic mathematician Muhammad ibn Musa al-Khwarizmi. All these developments finally arrived in Europe.

A ten-year-old child could easily master the mathematical exercises that ancient Babylonians could not even imagine. Nonetheless, this does not imply that these mathematic principles are obvious. On the contrary, these principles took years of painful experimentation and careful thought, which developed first numeric systems, then principles of simple arithmetic, the development of the number zero, geometric calculations, calendar and astronomic observations and measurements, and algebraic principles. These developed in numerous places around the globe due to similar or identical motivations such as record keeping and construction. Even now, mathematicians continue to expand our extent of knowledge concerning mathematics, building upon those ideas that have been handed down to them from mathematicians of the past. We sometimes see the calculator and the computer as the most incredible discoveries in mathematics, and to some extent, this is true. Yet we must remember what these tools truly are: only a quicker way to do the exact same equations that took centuries for diligent men to discover.

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