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BHASKARA II (AD 1114)
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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Bhaskara II represents the culminating point in mathematical and astronomical
investigations in ancient and medieval India. In originality and innovations
he probably ranks with Aryabhata I and Brahmagupta. As a lucid expositor of
abstruse mathematical and astronomical rules, he was probably unrivalled among
his class in ancient and medieval India. His whole mathematical-astronomical
work, Siddhanta-siromani, is divided into four parts, of which the first two
the Lilavati and the Bijaganita deal with arithmetic and geometry and algebra
respectively. The work in its entirety as well as in different parts are
available in a large number of manuscripts which clearly indicate their popu-
larity and wide distribution. This is also borne out by a large number of
commentaries produced at different times, including Persian translations. The
Lilavati concerned with arithmetic and geometry is divided into the following
chapters : (1) paribhasa, (ii) sankalita-vyavakalita, varga, vargamula, ghana,
ghanamula, sunyaparikarma, etc., (iii) vyastavidha, trairasika, (iv) misraka-
vyavahara, (v) sredhi-vyavahara, (vi) ksetra-vyavahara, (vii) khata-vyavahara,
(viii) citi, (ix) krakaca-vyavahara, (x) rasi-vyavahara, (xi) chaya-vyavahara
(xii) kuttaka and (xiii) ankapasa-vyavahara. The topics in which the chap-
ters of the vijaganita (algebra) are arranged are the following: (i) ghana-
vivarana, (ii) sunya-vivarana, (iii) varna-vivarana, (iv) karani-vivarna,
(v) kuttaka-vivarana, (vi) varga-vivarana, (vii) ekavarna-samikarna, (viii)
madhyamaharana, (ix) anekavarna-samikarana, (x) anekavarna-madhyamaharna and
(xi) bhavita. Both in his airhtmetic and algebra, we find a full discussion
on operation with zero in which the rresult of division of a finite number of
zero is correctly given. His arithmetic does not contain further novelties
than what are found in the works of his predecessors, except that the rules
are morelucid and accompanied by many examples. His algebra is characterized
by anticipation of the modern theory concerning the sign convention, use of
letters to denote unknown quantities and detailed discussions of several types
of equations, including indeterminate equations of the first and second degree
The cyclic method (cakravala) of solving the Pellian equations, N*x**2 + 1 =
y**2, N*x**2 + c = y**2, described by Hankel as 'the finest thing achieved in
the theiory of numbers before Lagrange; is due to him. His tatkalika method
of analysis contains the germ of modern calculus. From consideration of right
angled triangles and regular polygons up to 384 sides, he found the value of
pie as 3927/1250 and also 754/240 = 3.141666 . Some of his findings will be
further discussed in what follows.
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