The Development Of Mathematics Essay Research Paper

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The Development Of Mathematics Essay, Research Paper Before the time of recorded history, prehistoric people learned to count such things as the animals in their herds and flocks. They probably first used their fingers or pebbles to help keep track of small numbers. They learned to use the length of their hands and arms and other standards of measure. And they learned to use regular shapes when they molded pottery and chipped stone arrowheads. Since the prehistoric times, mathematics has come a long way. In this essay, I will try to sum up the development of mathematics, from the very first systems of mathematics, to mathematics being used to model problems in business, industry, and science. Around 3000 B.C., the people of ancient Babylonia, China, and Egypt had developed a

practical system of mathematics, which used written symbols to stand for numbers. From this, they derived simple arithmetic operations. They also developed a practical geometry helpful in agriculture and engineering. For example, the ancient Egyptians knew how to survey their fields and to make the intricate measurements necessary to build huge pyramids. The Babylonians and Egyptians had even explored some of the fundamental ideas of algebra, but this early mathematics was only used to solve practical problems. Between 600 and 300 B.C., the Greeks took the next great leap in mathematics. They inherited a large part of their mathematical knowledge from the Babylonians and Egyptians, but they became the first people to separate mathematics from practical problems. For example, they

separated geometry from practical applications and made it into an abstract exploration of space. They based this study of points, lines, and figures, such as triangles and circles, on logical reasoning rather than on facts found in nature. Thales of Miletus, a philosopher, helped begin this new viewpoint of geometry. The philosopher Pythagoras and his followers explored the nature of numbers. In geometry, the Pythagoreans developed the famous theorem that bears their name. Thales, Pythagoras, and many other Greek mathematicians built up a large body of geometrical knowledge. Euclid, one of the foremost Greek mathematicians, organized geometry as a single logical system. His book, The Elements, remains on of the basic works in studying mathematics. The Greeks also advanced other

branches of mathematics. As early as 450 B.C., Greek mathematicians recognized irrational numbers such as the square root of 2. About 370 B.C., Eudoxus of Cnidus, a Greek astronomer and mathematician, formulated a surprisingly masterful definition of proportions. Archimedes, the leading mathematician of ancient times, devised processes that foreshadowed those of integral calculus. The Greek astronomer Ptolemy helped develop trigonometry. Diophantus worked on numbers in equations. He earned the title of the father of algebra. After the fall of Rome in 476 A.D., Europe saw no new developments in mathematics for hundreds of years, But the Arabs preserved the mathematical tradition of the Greeks and Romans. The Arabs also began to use the zero and the decimal numeral system, both of

which had been developed by mathematicians in India. The Arabs also made important contributions of their own. Al-Khowarizmi organized and expanded algebra. After 1100, Europeans began to borrow the mathematics of the Arab world. For example, European merchants started to use the decimal numbers system. In addition, European scholars began to study Arab works on algebra and geometry. Leonardo Fibonacci made contributions to algebra, arithmetic, and geometry. The Renaissance, from the 1400?s to the 1600?s, produced many great advancements in mathematics. The exploration of new lands and continents called for better mathematics for navigation. The growth of business demanded better mathematics for banking and finance. The invention of printing brought the appearance of hundreds of