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history of indian mathematics essay

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An overview of indian mathematics.

The ingenious method of expressing every possible number using a set of ten symbols ( each symbol having a place value and an absolute value ) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius .
India confronts Egypt and Babylonia by the 3 rd millennium with a thoroughly individual and independent civilisation of her own, technically the peer of the rest. And plainly it is deeply rooted in Indian soil. The Indus civilisation represents a very perfect adjustment of human life to a specific environment. And it has endured; it is already specifically Indian and forms the basis of modern Indian culture.

Here is one style of the Brahmi numerals :

The Hindu astronomers did not possess a general method for solving problems in spherical astronomy, unlike the Greeks who systematically followed the method of Ptolemy , based on the well-known theorem of Menelaus . But, by means of suitable constructions within the armillary sphere, they were able to reduce many of their problems to comparison of similar right-angled plane triangles. In addition to this device, they sometimes also used the theory of quadratic equations, or applied the method of successive approximations. ... Of the methods taught by Aryabhata and demonstrated by his scholiast Bhaskara I , some are based on comparison of similar right-angled plane triangles, and others are derived from inference. Brahmagupta is probably the earliest astronomer to have employed the theory of quadratic equations and the method of successive approximations to solving problems in spherical astronomy.
... laid the foundation for a complete system of fluxions ...
... abound with fluxional forms and series to be found in no work of foreign countries.

References ( show )

  • 1 . R Calinger, A conceptual history of mathematics ( Upper Straddle River, N. J., 1999) .
  • L V Gurjar, Ancient Indian Mathematics and Vedha ( Poona, 1947) .
  • G G Joseph, The crest of the peacock ( London, 1991) .
  • R Mukherjee, Discovery of zero and its impact on Indian mathematics ( Calcutta, 1991) .
  • C N Srinivasiengar, The history of ancient Indian mathematics ( Calcutta, 1967) .
  • A I Volodarskii, Outlines of the history of medieval Indian mathematics ( Russian ) "Nauka" ( Moscow, 1977) .
  • R C Gupta, A bibliography of selected Sanskrit and allied works on Indian mathematics and mathematical astronomy, Ganita Bharati 3 (3 - 4) (1981) , 86 - 102 .
  • R C Gupta, A select bibliography of articles on ancient Indian mathematics, Math. Education 9 (4) (1975) , B 65 -B 75 .
  • R C Gupta, Glimpses of ancient Indian mathematics, Math. Education 11 (4) (1977) , B 80 -B 81 .
  • R C Gupta, Indian mathematics abroad up to the tenth century A.D., Ganita Bharati 4 (1 - 2) (1982) , 10 - 16 .
  • R C Gupta, Indian mathematics and astronomy in the eleventh century Spain, Ganita Bharati 2 (3 - 4) (1980) , 53 - 57 .
  • T Hayashi and T Kusuba, Twenty-one algebraic normal forms of Citrabhanu, Historia Math. 25 (1) (1998) , 1 - 21 .
  • P Jha, Indian mathematics in the Dark Age, Ganita-Bharati 17 (1 - 4) (1995) , 75 - 79 .
  • R Lal and R Prasad, Integral solutions of the equation Nx 2 + 1 = y 2 in ancient Indian mathematics ( cakravala or the cyclic method ) , Ganita Bharati 15 (1 - 4) (1993) , 41 - 54 .
  • K M Marar and C T Rajagopal, Gregory's series in the mathematical literature of Kerala, Math. Student 13 (1945) , 92 - 98 .
  • V Mishra and S L Singh, Height and distance problems in ancient Indian mathematics, Ganita-Bharati 18 (1 - 4) (1996) , 25 - 30 .
  • Kh R Muzafarova, Indian mathematics in Central Asia after al-Khwarizmi ( Russian ) , in The great medieval scientist al-Khwarizmi ( Tashkent, 1985) , 240 - 247 .
  • I Oami, Ancient Indian mathematics ( Japanese ) , Sugakushi Kenkyu No. 74 (1977) , 31 - 43 .
  • S Parameswaran, Putumana Somayaji, Ganita Bharati 14 (1 - 4) (1992) , 37 - 44 .
  • K R Rajagopalan, State of Indian mathematics in the southern region up to 10 th century A.D., Ganita Bharati 4 (1 - 2) (1982) , 78 - 82 .
  • C T Rajagopal and M S Rangachari, On medieval Kerala mathematics, Arch. Hist. Exact Sci. 35 (2) (1986) , 91 - 99 .
  • R Rashed, Indian mathematics in Arabic, in The intersection of history and mathematics ( Basel, 1994) , 143 - 148 .
  • K V Sarma and S Hariharan, Yuktibhasa of Jyesthadeva : a book of rationales in Indian mathematics and astronomy - an analytical appraisal, Indian J. Hist. Sci. 26 (2) (1991) , 185 - 207 .
  • R K Sarma, A note on the use of words for numbers in ancient Indian mathematics, Math. Education 7 (1973) , A 44 -A 45 .
  • K Shankar Shukla, Early Hindu methods in spherical astronomy, Ganita 19 (2) (1968) , 49 - 72 .
  • T Thrivikraman, On the contribution of Kerala to mathematics in the late medieval and early modern periods, Math. Student 53 (1 - 4) (1985) , 204 - 208
  • A I Volodarskii, Indian mathematics and al-Biruni ( Russian ) , in History and methodology of the natural sciences XX ( Moscow, 1978) , 49 - 57 .
  • A I Volodarskii, al-Khwarizmi and Indian mathematics ( Russian ) , in The great medieval scientist al-Khwarizmi ( Tashkent, 1985) , 232 - 238 .

Additional Resources ( show )

Other websites about Indian mathematics:

  • Ancient India
  • Sudheer Birodkar
  • South Asia History Project