Ancient India saw the relationship between knowledge of science and technology, with religion and social relations. The archaeological remains of the Indus Valley reveal knowledge of applied sciences. Scientific techniques were used in irrigation, Metallurgy, making of fired bricks and pottery, and simple reckoning and measurement of areas and volumes. Aryan achievements in the field of astronomy, mathematics and medicine are well known. Chinese records indicate knowledge of a dozen books of Indian origin. Brahmagupta's Sidhanta as well as Charaka's and Susrata's Samhitas were translated into Arabic in the 9th or 10th centuries A.D.In ancient Indian mathematics was known by the general name of Ganita, which included arithmetic, geometry, algebra, astronomy and astrology. It was Aryabhatta, who gave a new direction to trigonometry. The decimal system too was an innovation of India. By the third century B.C. mathematics, astronomy and medicine began to develop separately. In the field of mathematics ancient Indians made three distinct contributions, the notation system, the decimal system and the use of zero. The earliest epigraphic evidence of the use of decimal system belongs to the fifth century A.D. Before these numerals appeared in the West they had been used in India for centuries. They are found in the inscriptions of Ashoka in the third century B.C.Indians were the first to use the decimal system. The famous mathematician Aryabhata (A.D. 476-500) was acquainted with it. The Chinese learnt this system from the Buddhist missionaries, and the western world borrowed it from the Arab as when they came in contact with India. Zero was discovered by Indians in about the second century B.C. From the very beginning Indian mathematicians considered zero as a separate numeral, and it was used in this sense in arithmetic. In Arabia the earliest use of zero appears in A.D. 873. The Arabs learnt and adopted it from India and spread it in Europe. So far as Algebra is concerned both Indians and Greeks contributed to it, but in Western Europe its knowledge was borrowed not from Greece but from the Arabs who had acquired it from India. In the second century B.C. Apastemba contributed to practical geometry for the construction of altars on which the kings could offer sacrifices. It describes acute angle, obtuse angle, right angle etc. Aryabhata formulated the rule for finding the area of a triangle, which led to the origin of trigonometry. The most famous work of his time is the Suryasiddanta the like of which was not found in Contemporary ancient east. During the Gupta period mathematics was developed to such an extent and more advanced than any other nation of antiquity. Quite early India devised a rudimentary algebra which led to more calculations than were possible for the Greeks and led to the study of number for its own sake. The earliest inscription regarding the data by a system of nine digits and a zero is dated as 595 A.D. evidently the system was known to mathematicians some centuries before it was employed in inscriptions. Indian mathematicians such as Brahmagupta (7th century), Mahavira (9th century) and Bhaskara (12th century) made several discoveries which were known to Europe only after Renaissance. The understood the importance of positive and negative quantities, evolved sound system of extracting squares and cube roots and could solve quadratic and certain types of indeterminate equations. Aryabhata gave approximate value of pie. It was more accurate than that of the Greeks. Also some strides were made in trigonometry, empirical geometry and calculus. Chiefly in astronomy the mathematical implications of zero and infinity were fully realized unlike anywhere in the world. Among the various branches of mathematics, Hindus gave astronomy the highest place of honour. Suryasidhanta is the best know book on Hindu astronomy. The text was later modified two or three times between 500 A.D. and 1500 A.D. The system laid...
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