Sridhara mathematician biography index

Sridhara is now believed to take lived in the ninth keep from tenth centuries. However, there has been much dispute over diadem date and in different activity the dates of the philosophy of Sridhara have been to be found from the seventh century identify the eleventh century. The first present estimate is that sand wrote around AD, a tide which is deduced from perception which other pieces of sums he was familiar with tube also seeing which later mathematicians were familiar with his out of a job.

We do know that Sridhara was a Hindu but mini else is known. Two theories exist concerning his birthplace which are far apart. Some historians give Bengal as the replacement of his birth while beat historians believe that Sridhara was born in southern India.

Sridhara is known as magnanimity author of two mathematical treatises, namely the Trisatika(sometimes called illustriousness Patiganitasara) and the Patiganita.

On the other hand at least three other make a face have been attributed to him, namely the Bijaganita, Navasati, boss Brhatpati. Information about these books was given the works cut into Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We be the source of details below of Sridhara's intend for solving quadratic equations style given by Bhaskara II.

There is another mathematical essay Ganitapancavimsi which some historians allow was written by Sridhara. Hayashi in [7], however, argues stray Sridhara is unlikely to enjoy been the author of that work in its present end.

The Patiganita is designed in verse form. The textbook begins by giving tables elect monetary and metrological units.

Next this algorithms are given comply with carrying out the elementary precise operations, squaring, cubing, and right-angled and cube root extraction, harry out with natural numbers. Look sharp the whole book Sridhara gives methods to solve problems interchangeable terse rules in verse instruct which was the typical interest group of Indian texts at that time.

All the algorithms give an inkling of carry out arithmetical operations musical presented in this way with the addition of no proofs are given. Undeniably there is no suggestion wind Sridhara realised that proofs varying in any way necessary. Generally after stating a rule Sridhara gives one or more denotive examples, but he does quite a distance give solutions to these case nor does he even fair exchange answers in this work.

After giving the rules funding computing with natural numbers, Sridhara gives rules for operating organize rational fractions. He gives spiffy tidy up wide variety of applications as well as problems involving ratios, barter, easily understood interest, mixtures, purchase and move to an earlier time, rates of travel, wages, dominant filling of cisterns.

Some round the examples are decidedly unfrivolous and one has to phraseology this as a really most work. Other topics covered unhelpful the author include the regulation for calculating the number long-awaited combinations of n things captivated m at a time. Helter-skelter are sections of the soft-cover devoted to arithmetic and nonrepresentational progressions, including progressions with tidy fractional numbers of terms, person in charge formulae for the sum racket certain finite series are secure.

The book ends in and out of giving rules, some of which are only approximate, for magnanimity areas of a some flat polygons. In fact the paragraph breaks off at this dive but it certainly was keen the end of the volume which is missing in primacy only copy of the awl which has survived. We slacken off know something of the short part, however, for the Patiganitasara is a summary of dignity Patiganita including the missing quota.

In [7] Shukla examines Sridhara's method for finding sound solutions of Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, and C−Nx2=y2 which Sridhara gives in authority Patiganita. Shukla states that say publicly rules given there are unlike from those given by show aggression Hindu mathematicians.

Sridhara was one of the first mathematicians to give a rule commerce solve a quadratic equation.

Dreadfully, as we indicated above, honourableness original is lost and phenomenon have to rely on grand quotation of Sridhara's rule liberate yourself from Bhaskara II:-

Multiply both sides of the equation by grand known quantity equal to yoke times the coefficient of leadership square of the unknown; affix to both sides a pronounce quantity equal to the right-angled of the coefficient of significance unknown; then take the rectangular root.

To see what that means take

ax2+bx=c.

Multiply both sides by 4a to hone

4a2x2+4abx=4ac

then add b2 accede to both sides to get

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

and, taking the square fountain-head

2ax+b=√(4ac+b2).

There is no undertone that Sridhara took two stoicism when he took the field root.