Question

Project 2: Project on History of Mathematics​

Answer 1

Ancient Period (3000 B.C. to 260 A.D.)

A. Number Systems and Arithmetic

• Development of numeration systems. • Creation of arithmetic techniques, lookup tables, the abacus and other calculation tools

B. Practical Measurement, Geometry and Astronomy

• Measurement units devised to quantify distance, area, volume, and time Geometric reasoning used to measure distances indirectly. • Calendars invented to predict seasons, astronomical events. • Geometrical forms and patterns appear in art and architecture.

As ancient civilizations developed, the need for practical mathematics increased. They required numeration systems and arithmetic techniques for trade, measurement strategies for construction, and astronomical calculations to track the seasons and cosmic cycles.

A. Development and Spread of Hindu-Arabic Numbers A numeration system using base 1o, positional notation, the zero symbol and powerful arithmetic techniques is developed by the Hindus, approx. 150 B.C. to 800 A.D..

• The Hindu numeration system is adopted by the Arabs and spread throughout their sphere of influence (approx. 700 A.D. to 1250 A.D.),

B. Preservation of Greek Mathematics

• Arab scholars copied and studied Greek mathematical works, principally in Baghdad.

C. Development of Algebra and Trigonometry

• Arab mathematicians find methods of solution for quadratic, cubic and higher degree polynomial equations. The English word "algebra" is derived from the title of an Arabic book describing these methods - Hindu trigonometry, especially sine tables, is improved and advanced by Arab mathematicians

Period of Transmission (1000 AD - 1500 AD)

A. Discovery of Greek and Hindu-Arab mathematics

• Greek mathematics texts are translated from Arabic into Latin: Greek ideas about logic, geometrical reasoning, and a rational view of the world are re-discovered.

• Arab works on algebra and trigonometry are also translated into Latin and disseminated throughout Europe

B. Spread of the Hindu-Arabic numeration system

• Hindu-Arabic numerals slowly spread over Europe • Pen and paper arithmetic algorithms based on Hindu-Arabic numerals replace the use the abacus.

The study of mathematics as a "demonstrative discipline" begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction". ... Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations

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