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MAHAVIRACHARYA (AD 850)
Posted Date: 17 Jan 2008 Resource Type: Articles/Knowledge Sharing Category: General
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Posted By: SajithkumarS Member Level: Diamond
Rating:  Points: 5
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Mahavira, the great Jaina mathematician, probably hailed from the Kanarese-
speaking areas fo south India and flourished during the reign of the Rastraku-
ta King Amoghavarsa Nrpatunga (814-877). In keeping with the Jaina tradition
he studied mathemnatics, for its own sake and not in association with astrono-
my as was the vogue with the Brahmana mathematicians. His Ganita-sara-sam-
graha does not, therefore, form part of any astronomical treatise, but treats
fo mathematical problems in a more simple and direct manner. The copious ill-
ustrations characterizing his work also bear this impress. But he seems to be
fully conversant with Brahmana mathematics and, in particular, with the works
of Brahmagupta whose reputation as an authority was far and wide. In fact, he
dealt with several of the problems which had engaged the attention of his ill-
ustrious predecessor and tried to improve upon them, often times with success
which shows that he was neither a mere compiler nor a commentator but an ori-
ginal investigator. From the fact that the manuscripts of his work and its
commentaries have come down to us in Kanarese and in Telugu translations, Bha-
skara II and other scholars in northern and central India do not refer to his
work and it is not even mentioned in Sudhakara Dvivedi's Ganakatarangini, it
is reasonable to infer that his work was in circulation only in the south. Ga-
nita-sara-samgraha is a work in nine chapters, dealing with operations with
numbers excluding those o f addition and subtraction which are taken for gra-
nted, squaring and cubing, determination of square and cube roots, summation
of arithmetic and geometric series, fractions, rule fo three, mensuration and
algebra, including quadratic and indeterminate equations. His arithmetical
operations are based on decimal place-value numeration. He mentions 24 nota-
tional places and uses word numerals as had been the established practice. He
gives operating with zero, but erroneously states thsat a number divided by
zero remains unchanged. Negative numbers are used. The process of summation
of a series from which the first few terms are omitted is called by him vyut-
kalita. In his treatment of fractions he was the first among the Indian
mathematicians to have used the method of lowest commong multiple, called by
him niruddha, in order to shorten the process. In mensuration, Mahavira's
treatment is similar in spirit with that of either Brahmagupta or Bhaskara II,
but much fuller and in certain cases a little more advanced. Like Brahmagupta
he gives the area of a quadrilateral as square root of [(s-a)(s-b)(s-c)(s-d)]
but does not mention that it holds good only for a cyclic one. For the volume
of a sphere, he gives an approximate rule as 9/2(1/2*d)**3 and an accurate one
as 9/10*9/2*(1/2*d)**3, which makes pie equal to 3.0375. Mahavira gives two
roots for quadratic equations and treats of simple and simultaneous indeter-
minate equations of the first degree.
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