MATHEMATICS IN ANCIENT INDIA

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ndian mathematicians since the Sulbasutras which were appendices giving ancient period have contributed to rules for constructing altars. They give the growth of modern mathematics. geometrical information however it was Indus valley civilization holds the meant only for the religious purposes. distinction of being the first to develop Baudhayana (about 800 BC), Manava mathematics. Much research still is to be (about750 BC), Apastamba (about 600 done to know the full extent of their BC) and Katyayana (about 200 BC) achievement composed main s. They Sulbasutras. adopted a These were Aryabhata's work contained summery of uniform scholars and Jaina mathematics and astronomy. He system of priest and not replaced the older theory of demons Rahu weights and mathematicians measures in modern and Ketu with new theory of eclipses. He suggesting sense of the also introduced trigonometry to make his that they term. Around astronomical calculations based on the belong to the middle of Greek epicycle theory. two series the third both being century BC the decimal in Brahmi nature numerals multiplied and divided in two giving began to appear. These were the earliest ratios of 0.05, 0.1, 0.2, and 0.5 etc.A numerals which after certain changes number of scales for measuring the length developed into modern numerals used were discovered during the excavations. A today. decimal scale known as 'Indus Inch' based Around 6th century BC the development of on a unit of measurement of 1.32 inches new religions like Buddhism and Jainism (3.35 cm) has been discovered. Another saw more development in mathematics. scale, a The main topics were theory of numbers, ARYABHATTA bronze rod arithmetical operations, geometry, and was operations with fractions, simple discovered equations, cubic equations, quartic marked 0.367 equations and other permutations and inches. The combinations. Jaina mathematicians measurement developed a theory of infinite containing of buildings different levels of infinity, a primitive revealed that understanding of indices and some notion these scales of logarithms to base 2.Astronomy became were used the base for developing mathematics with great because it required correct information accuracy. The about the planets and other heavenly earliest bodies. Religion also played a major role as literary accurate calendars were required to be records Vedas made to observe the religious ceremonies at had the correct time. Mathematics remained an

applied integer solutions to indeterminate science equations and worked on interpolation during the formulas invented to aid the computation of ancient sine tables. The educational system of India t i m e did not allow talented people to take up w h e r e studies in astronomy and mathematics mathemat rather the whole system was based on the i c i a n s traditions handed over to the generations to focused on generations. This helped in preserving developin commentaries of works done on g methods mathematics. It was common for the to solve mathematicians to write commentaries on practical their own work. It was considered as divine problems. In second century AD origin and each family would remain Yavanesvara translated Greek astrology faithful to their revelations of the subject. text (120 BC) popularizing it by adding They did not make any systematic Indian cultural icons using Hindu images observations. Mathematics was used only with the Indian caste system. 500 AD saw as a tool for making astronomical the beginning of classical era of Indian calculations. A contemporary of mathematics. Aryabhata's work contained Brahmagupta Bhaskara I led Asmaka summery of Jaina mathematics and school.He was a commentator on the works astronomy. He replaced the older theory of of Aryabhatta.Lalla another astronomer demons Rahu and Ketu with new theory of who was born 100 years later became eclipses. He commentator on a l s o Kusumapura emerged as leading centre of A r y a b h a t t a . T h e 9 t h i n t r o d u c e d astronomy and mathematics under century saw several trigonometry Aryabhata. The other centre which shot into s c h o l a r s l i k e to make his prominence was Ujjain under Varahamihira G o v i n d a s w a m i , astronomical who also made valuable contributions to M a h a v i r a , calculations astronomy and trigonometry. Prthudakasvami, based on the S a n k a r a a n d G r e e k Sridhara.They epicycle theory. commented on the works of Bhasker I while Mahavira became famous for updating He solved indeterminate equations with Brahmagupta's book. This period saw integer solutions . Kusumapura emerged as tremendous improvements in sine tables, leading centre of astronomy and s o l v i n g mathematics under Aryabhata. The other equations, centre which shot into prominence was a lgebraic Ujjain under Varahamihira who also made n otation, valuable contributions to astronomy and quadratics, t r i g o n o m e t r y. Ya t i v r s a b h a w a s a indetermina contemporary of Varahamihira who te equations worked on the main ideas of Jaina a n d mathematics. The next important figure of improveme Ujjain school was Brahmagupta in 7th nts to the century AD who made significant number contributions to the development of system .r negative number system and zero. He also made contributions to the understanding of