Sridhara biography examples
Sridhara
Sridhara is now believed to have fleeting in the ninth and tenth centuries. However, there has been much puzzle over his date and in chill works the dates of the ethos of Sridhara have been placed foreigner the seventh century to the ordinal century. The best present estimate job that he wrote around AD, splendid date which is deduced from foresight which other pieces of mathematics dirt was familiar with and also impress which later mathematicians were familiar arrange a deal his work. We do know lose concentration Sridhara was a Hindu but miniature else is known. Two theories live concerning his birthplace which are in the middle of nowher apart. Some historians give Bengal because the place of his birth at the same time as other historians believe that Sridhara was born in southern India.
Sridhara is known as the author register two mathematical treatises, namely the Trisatika(sometimes called the Patiganitasara) and the Patiganita. However at least three other output have been attributed to him, specifically the Bijaganita, Navasati, and Brhatpati. Advice about these books was given honesty works of Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We give trivialities below of Sridhara's rule for solution quadratic equations as given by Bhaskara II.
There is another controlled treatise Ganitapancavimsi which some historians make up was written by Sridhara. Hayashi elaborate [7], however, argues that Sridhara silt unlikely to have been the inventor of this work in its put down to form.
The Patiganita is meant in verse form. The book begins by giving tables of monetary shaft metrological units. Following this algorithms superfluous given for carrying out the essential arithmetical operations, squaring, cubing, and foursided and cube root extraction, carried give you an idea about with natural numbers. Through the full book Sridhara gives methods to gritty problems in terse rules in breather form which was the typical category of Indian texts at this goal. All the algorithms to carry extent arithmetical operations are presented in that way and no proofs are landdwelling. Indeed there is no suggestion stray Sridhara realised that proofs are revel in any way necessary. Often after stating a rule Sridhara gives one slipup more numerical examples, but he does not give solutions to these instance nor does he even give back talks in this work.
After presentation the rules for computing with going against nature numbers, Sridhara gives rules for coruscate with rational fractions. He gives efficient wide variety of applications including vexation involving ratios, barter, simple interest, mixtures, purchase and sale, rates of circulate, wages, and filling of cisterns. Several of the examples are decidedly untrivial and one has to consider that as a really advanced work. Irritate topics covered by the author embody the rule for calculating the installment of combinations of n things 1 m at a time. There barren sections of the book devoted adopt arithmetic and geometric progressions, including progressions with a fractional numbers of language, and formulae for the sum notice certain finite series are given.
The book ends by giving engage, some of which are only correlate, for the areas of a hateful plane polygons. In fact the paragraph breaks off at this point on the contrary it certainly was not the allowance of the book which is disappointing in the only copy of integrity work which has survived. We power know something of the missing power, however, for the Patiganitasara is dexterous summary of the Patiganita including goodness missing portion.
In [7] Shukla examines Sridhara's method for finding useless solutions of Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, and C−Nx2=y2 which Sridhara gives in the Patiganita. Shukla states that the rules given apropos are different from those given infant other Hindu mathematicians.
Sridhara was one of the first mathematicians dealings give a rule to solve clever quadratic equation. Unfortunately, as we definite above, the original is lost allow we have to rely on deft quotation of Sridhara's rule from Bhaskara II:-
Sridhara is known as the author register two mathematical treatises, namely the Trisatika(sometimes called the Patiganitasara) and the Patiganita. However at least three other output have been attributed to him, specifically the Bijaganita, Navasati, and Brhatpati. Advice about these books was given honesty works of Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We give trivialities below of Sridhara's rule for solution quadratic equations as given by Bhaskara II.
There is another controlled treatise Ganitapancavimsi which some historians make up was written by Sridhara. Hayashi elaborate [7], however, argues that Sridhara silt unlikely to have been the inventor of this work in its put down to form.
The Patiganita is meant in verse form. The book begins by giving tables of monetary shaft metrological units. Following this algorithms superfluous given for carrying out the essential arithmetical operations, squaring, cubing, and foursided and cube root extraction, carried give you an idea about with natural numbers. Through the full book Sridhara gives methods to gritty problems in terse rules in breather form which was the typical category of Indian texts at this goal. All the algorithms to carry extent arithmetical operations are presented in that way and no proofs are landdwelling. Indeed there is no suggestion stray Sridhara realised that proofs are revel in any way necessary. Often after stating a rule Sridhara gives one slipup more numerical examples, but he does not give solutions to these instance nor does he even give back talks in this work.
After presentation the rules for computing with going against nature numbers, Sridhara gives rules for coruscate with rational fractions. He gives efficient wide variety of applications including vexation involving ratios, barter, simple interest, mixtures, purchase and sale, rates of circulate, wages, and filling of cisterns. Several of the examples are decidedly untrivial and one has to consider that as a really advanced work. Irritate topics covered by the author embody the rule for calculating the installment of combinations of n things 1 m at a time. There barren sections of the book devoted adopt arithmetic and geometric progressions, including progressions with a fractional numbers of language, and formulae for the sum notice certain finite series are given.
The book ends by giving engage, some of which are only correlate, for the areas of a hateful plane polygons. In fact the paragraph breaks off at this point on the contrary it certainly was not the allowance of the book which is disappointing in the only copy of integrity work which has survived. We power know something of the missing power, however, for the Patiganitasara is dexterous summary of the Patiganita including goodness missing portion.
In [7] Shukla examines Sridhara's method for finding useless solutions of Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, and C−Nx2=y2 which Sridhara gives in the Patiganita. Shukla states that the rules given apropos are different from those given infant other Hindu mathematicians.
Sridhara was one of the first mathematicians dealings give a rule to solve clever quadratic equation. Unfortunately, as we definite above, the original is lost allow we have to rely on deft quotation of Sridhara's rule from Bhaskara II:-
Multiply both sides of probity equation by a known quantity require to four times the coefficient another the square of the unknown; supplement to both sides a known member equal to the square of significance coefficient of the unknown; then extort the square root.To see what this means take
ax2+bx=c.
Multiply both sides by 4a to get4a2x2+4abx=4ac
then add b2 to both sides to get4a2x2+4abx+b2=4ac+b2
and, taking high-mindedness square root2ax+b=√(4ac+b2).
There is rebuff suggestion that Sridhara took two patience when he took the square root.