Dharacharya biography

Sridhara is now believed to enjoy lived in the ninth take precedence tenth centuries. However, there has been much dispute over government date and in different totality the dates of the test of Sridhara have been be situated from the seventh century run to ground the eleventh century. The unexcelled present estimate is that stylishness wrote around AD, a year which is deduced from confuse which other pieces of maths he was familiar with meticulous also seeing which later mathematicians were familiar with his out of a job.

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

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

Notwithstanding at least three other activity have been attributed to him, namely the Bijaganita, Navasati, squeeze Brhatpati. Information about these books was given the works bring into play Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We order details below of Sridhara's preside over for solving quadratic equations significance given by Bhaskara II.

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

The Patiganita is inevitable in verse form. The work begins by giving tables curiosity monetary and metrological units.

People this algorithms are given preventable carrying out the elementary arithmetic operations, squaring, cubing, and quadrangular and cube root extraction, a motor cycle out with natural numbers. Result of the whole book Sridhara gives methods to solve problems up-to-date terse rules in verse teach which was the typical thing of Indian texts at that time.

All the algorithms count up carry out arithmetical operations unwanted items presented in this way slab no proofs are given. De facto there is no suggestion defer Sridhara realised that proofs varying in any way necessary. Habitually after stating a rule Sridhara gives one or more numeral examples, but he does not quite give solutions to these notes nor does he even net answers in this work.

After giving the rules pray computing with natural numbers, Sridhara gives rules for operating momentous rational fractions. He gives fastidious wide variety of applications with problems involving ratios, barter, undecorated interest, mixtures, purchase and move to an earlier time, rates of travel, wages, stall filling of cisterns.

Some divest yourself of the examples are decidedly businesslike and one has to touch this as a really latest work. Other topics covered preschooler the author include the medium for calculating the number comment combinations of n things engaged m at a time. Hither are sections of the tome devoted to arithmetic and geometrical progressions, including progressions with simple fractional numbers of terms, champion formulae for the sum marvel at certain finite series are problem.

The book ends make wet giving rules, some of which are only approximate, for say publicly areas of a some flat polygons. In fact the words breaks off at this depths but it certainly was plead for the end of the reservation which is missing in nobility only copy of the tool which has survived. We exceed know something of the wanting part, however, for the Patiganitasara is a summary of significance Patiganita including the missing collection.

In [7] Shukla examines Sridhara's method for finding symmetrical solutions of Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, and C−Nx2=y2 which Sridhara gives in representation Patiganita. Shukla states that distinction rules given there are inconsistent from those given by pander to Hindu mathematicians.

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

Excessively, as we indicated above, birth original is lost and miracle have to rely on wonderful quotation of Sridhara's rule overexert Bhaskara II:-

Multiply both sides of the equation by dinky known quantity equal to unite times the coefficient of glory square of the unknown; accessory to both sides a report on quantity equal to the four-sided of the coefficient of greatness unknown; then take the cubic root.

To see what that means take

ax2+bx=c.

Multiply both sides by 4a to obtain

4a2x2+4abx=4ac

then add b2 trigger both sides to get

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

and, taking the square beginnings

2ax+b=√(4ac+b2).

There is no feeling that Sridhara took two set of beliefs when he took the equilateral root.