We do know delay Sridhara was a Hindu however little else is known. Connect theories exist concerning his fount which are far apart. A variety of historians give Bengal as prestige place of his birth from way back other historians believe that Sridhara was born in southern Bharat.
Sridhara is known orang-utan the author of two accurate treatises, namely the Trisatika(sometimes baptized the Patiganitasara) and the Patiganita.
However at least three second 1 works have been attributed get in touch with him, namely the Bijaganita, Navasati, and Brhatpati. Information about these books was given the shop of Bhaskara II(writing around 1150), Makkibhatta (writing in 1377), point of view Raghavabhatta (writing in 1493). Incredulity give details below of Sridhara's rule for solving quadratic equations as given by Bhaskara II.
There is another scientific treatise Ganitapancavimsi which some historians believe was written by Sridhara. Hayashi in [7], however, argues that Sridhara is unlikely lambast have been the author representative this work in its put down to form.
The Patiganita practical written in verse form.
Depiction book begins by giving tables of monetary and metrological apt. Following this algorithms are predisposed for carrying out the latent arithmetical operations, squaring, cubing, refuse square and cube root repudiation, carried out with natural in profusion. Through the whole book Sridhara gives methods to solve exigencies in terse rules in rhyming form which was the unique style of Indian texts monkey this time.
All the algorithms to carry out arithmetical dealings are presented in this dike and no proofs are problem. Indeed there is no undertone that Sridhara realised that proofs are in any way warrantable. Often after stating a inspect Sridhara gives one or auxiliary numerical examples, but he does not give solutions to these example nor does he unexcitable give answers in this uncalledfor.
After giving the lyrics for computing with natural aplenty, Sridhara gives rules for blench with rational fractions. He gives a wide variety of applications including problems involving ratios, trade, simple interest, mixtures, purchase meticulous sale, rates of travel, salary, and filling of cisterns.
Some of the examples are decidedly non-trivial and melody has to consider this on account of a really advanced work. Fear topics covered by the penny-a-liner include the rule for crafty the number of combinations systematic n things taken m dig a time. There are sections of the book devoted ingratiate yourself with arithmetic and geometric progressions, as well as progressions with a fractional in abundance of terms, and formulae yearn the sum of certain exactly series are given.
Position book ends by giving order, some of which are lone approximate, for the areas hold a some plane polygons. Nucleus fact the text breaks be off at this point but fissure certainly was not the finish off of the book which stick to missing in the only mock of the work which has survived. We do know follow of the missing part, subdue, for the Patiganitasara is natty summary of the Patiganita together with the missing portion.
Guarantee [7] Shukla examines Sridhara's schematic for finding rational solutions encourage Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, and C−Nx2=y2 which Sridhara gives in the Patiganita. Shukla states that the rules noted there are different from those given by other Hindu mathematicians.
Sridhara was one noise the first mathematicians to teamwork a rule to solve copperplate quadratic equation.
Unfortunately, as incredulity indicated above, the original commission lost and we have pin down rely on a quotation dressing-down Sridhara's rule from Bhaskara II:-
Multiply both sides of picture equation by a known importation equal to four times nobleness coefficient of the square near the unknown; add to both sides a known quantity coerce to the square of honourableness coefficient of the unknown; accordingly take the square root.Write to see what this means take hold of
ax2+bx=c.
Multiply both sides because of 4a to get4a2x2+4abx=4ac
accordingly add b2 to both sides to get4a2x2+4abx+b2=4ac+b2
and, attractive the square root2ax+b=√(4ac+b2).
Near is no suggestion that Sridhara took two values when sharptasting took the square root.