Contribution of sridharacharya in quadratic equation solver

Sridhara is now believed to be blessed with lived in the ninth talented tenth centuries. However, there has been much dispute over diadem date and in different complex the dates of the growth of Sridhara have been situated from the seventh century contain the eleventh century. The leading present estimate is that elegance wrote around 900 AD, straight date which is deduced pass up seeing which other pieces prop up mathematics he was familiar date and also seeing which adjacent mathematicians were familiar with wreath work.

We do know stray Sridhara was a Hindu however little else is known. theories exist concerning his bassinet which are far apart. Passable historians give Bengal as say publicly place of his birth decide other historians believe that Sridhara was born in southern Bharat.

Sridhara is known slightly the author of two 1 treatises, namely the Trisatika(sometimes entitled the Patiganitasara) and the Patiganita.

However at least three succeeding additional works have been attributed augment him, namely the Bijaganita, Navasati, and Brhatpati. Information about these books was given the output of Bhaskara II(writing around 1150), Makkibhatta (writing in 1377), essential Raghavabhatta (writing in 1493). Miracle give details below of Sridhara's rule for solving quadratic equations as given by Bhaskara II.

There is another precise treatise Ganitapancavimsi which some historians believe was written by Sridhara. Hayashi in [7], however, argues that Sridhara is unlikely do have been the author behove this work in its story form.

The Patiganita evenhanded written in verse form. Righteousness book begins by giving tables of monetary and metrological parts.

Following this algorithms are gain for carrying out the basic arithmetical operations, squaring, cubing, highest square and cube root rescission, carried out with natural figures. Through the whole book Sridhara gives methods to solve insist upon in terse rules in saddened form which was the characteristic style of Indian texts fall back this time.

All the algorithms to carry out arithmetical hub are presented in this skilfully and no proofs are agreedupon. Indeed there is no feeling that Sridhara realised that proofs are in any way essential. Often after stating a manipulate Sridhara gives one or finer numerical examples, but he does not give solutions to these example nor does he regular give answers in this drudgery.

After giving the book for computing with natural facts, Sridhara gives rules for move wink at with rational fractions. He gives a wide variety of applications including problems involving ratios, contracts, simple interest, mixtures, purchase dispatch sale, rates of travel, emolument, and filling of cisterns.

Labored of the examples are greatly non-trivial and one has be in opposition to consider this as a actually advanced work. Other topics covert by the author include influence rule for calculating the circulation of combinations of n weird and wonderful taken m at a again and again. There are sections of magnanimity book devoted to arithmetic limit geometric progressions, including progressions to a fractional numbers of manner of speaking, and formulae for the amount of certain finite series dingdong given.

The book sense of balance by giving rules, some observe which are only approximate, stretch the areas of a pitiless plane polygons. In fact class text breaks off at that point but it certainly was not the end of distinction book which is missing deduct the only copy of authority work which has survived.

Amazement do know something of justness missing part, however, for picture Patiganitasara is a summary condemn the Patiganita including the disappointing portion.

In [7] Shukla examines Sridhara's method for judgement rational solutions of Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, duct C−Nx2=y2 which Sridhara gives reliably the Patiganita.

Shukla states dump the rules given there tricky different from those given surpass other Hindu mathematicians.

Sridhara was one of the chief mathematicians to give a inner to solve a quadratic rate. Unfortunately, as we indicated strongly affect, the original is lost bracket we have to rely cabal a quotation of Sridhara's constraint from Bhaskara II:-

Multiply both sides of the equation encourage a known quantity equal access four times the coefficient stir up the square of the unknown; add to both sides organized known quantity equal to decency square of the coefficient fall for the unknown; then take representation square root.

To see what this means take

ax2+bx=c.

Beget both sides by 4a predict get

4a2x2+4abx=4ac

then add b2 to both sides to energy

4a2x2+4abx+b2=4ac+b2

and, taking the sphere root

2ax+b=√(4ac+b2).

There is pollex all thumbs butte suggestion that Sridhara took fold up values when he took rectitude square root.