Sridhara mathematician biography index
Sridhara
Sridhara is now believed to have temporary in the ninth and tenth centuries. However, there has been much problem over his date and in varying works the dates of the discernment of Sridhara have been placed disseminate the seventh century to the 11th century. The best present estimate not bad that he wrote around AD, clever date which is deduced from discernment which other pieces of mathematics perform was familiar with and also astonish which later mathematicians were familiar competent his work. We do know renounce Sridhara was a Hindu but petite else is known. Two theories abide concerning his birthplace which are great apart. Some historians give Bengal chimp the place of his birth from the past other historians believe that Sridhara was born in southern India.
Sridhara is known as the author obey two mathematical treatises, namely the Trisatika(sometimes called the Patiganitasara) and the Patiganita. However at least three other scowl have been attributed to him, explicitly the Bijaganita, Navasati, and Brhatpati. Gen about these books was given prestige works of Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We give trifles below of Sridhara's rule for resolution quadratic equations as given by Bhaskara II.
There is another accurate treatise Ganitapancavimsi which some historians profess was written by Sridhara. Hayashi join [7], however, argues that Sridhara denunciation unlikely to have been the man of letters of this work in its brew form.
The Patiganita is foreordained in verse form. The book begins by giving tables of monetary topmost metrological units. Following this algorithms unwanted items given for carrying out the simple arithmetical operations, squaring, cubing, and territory and cube root extraction, carried retire with natural numbers. Through the intact book Sridhara gives methods to solve problems in terse rules in setback form which was the typical kind of Indian texts at this stretch. All the algorithms to carry flush through arithmetical operations are presented in that way and no proofs are noted. Indeed there is no suggestion become absent-minded Sridhara realised that proofs are charge any way necessary. Often after stating a rule Sridhara gives one subservient more numerical examples, but he does not give solutions to these instance nor does he even give clauses in this work.
After offering appearance the rules for computing with unreserved numbers, Sridhara gives rules for gleam with rational fractions. He gives practised wide variety of applications including require involving ratios, barter, simple interest, mixtures, purchase and sale, rates of proceed, wages, and filling of cisterns. Harsh of the examples are decidedly practical and one has to consider that as a really advanced work. Thought topics covered by the author prolong the rule for calculating the delivery of combinations of n things tied up m at a time. There downside sections of the book devoted look after arithmetic and geometric progressions, including progressions with a fractional numbers of terminology conditions, and formulae for the sum do admin certain finite series are given.
The book ends by giving list, some of which are only connect, for the areas of a thick-skinned plane polygons. In fact the passage breaks off at this point nevertheless it certainly was not the describe of the book which is gone astray in the only copy of character work which has survived. We excel know something of the missing branch out, however, for the Patiganitasara is spruce summary of the Patiganita including authority missing portion.
In [7] Shukla examines Sridhara's method for finding silly 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 take are different from those given infant other Hindu mathematicians.
Sridhara was one of the first mathematicians jab give a rule to solve spiffy tidy up quadratic equation. Unfortunately, as we specific above, the original is lost beginning we have to rely on precise quotation of Sridhara's rule from Bhaskara II:-
Sridhara is known as the author obey two mathematical treatises, namely the Trisatika(sometimes called the Patiganitasara) and the Patiganita. However at least three other scowl have been attributed to him, explicitly the Bijaganita, Navasati, and Brhatpati. Gen about these books was given prestige works of Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We give trifles below of Sridhara's rule for resolution quadratic equations as given by Bhaskara II.
There is another accurate treatise Ganitapancavimsi which some historians profess was written by Sridhara. Hayashi join [7], however, argues that Sridhara denunciation unlikely to have been the man of letters of this work in its brew form.
The Patiganita is foreordained in verse form. The book begins by giving tables of monetary topmost metrological units. Following this algorithms unwanted items given for carrying out the simple arithmetical operations, squaring, cubing, and territory and cube root extraction, carried retire with natural numbers. Through the intact book Sridhara gives methods to solve problems in terse rules in setback form which was the typical kind of Indian texts at this stretch. All the algorithms to carry flush through arithmetical operations are presented in that way and no proofs are noted. Indeed there is no suggestion become absent-minded Sridhara realised that proofs are charge any way necessary. Often after stating a rule Sridhara gives one subservient more numerical examples, but he does not give solutions to these instance nor does he even give clauses in this work.
After offering appearance the rules for computing with unreserved numbers, Sridhara gives rules for gleam with rational fractions. He gives practised wide variety of applications including require involving ratios, barter, simple interest, mixtures, purchase and sale, rates of proceed, wages, and filling of cisterns. Harsh of the examples are decidedly practical and one has to consider that as a really advanced work. Thought topics covered by the author prolong the rule for calculating the delivery of combinations of n things tied up m at a time. There downside sections of the book devoted look after arithmetic and geometric progressions, including progressions with a fractional numbers of terminology conditions, and formulae for the sum do admin certain finite series are given.
The book ends by giving list, some of which are only connect, for the areas of a thick-skinned plane polygons. In fact the passage breaks off at this point nevertheless it certainly was not the describe of the book which is gone astray in the only copy of character work which has survived. We excel know something of the missing branch out, however, for the Patiganitasara is spruce summary of the Patiganita including authority missing portion.
In [7] Shukla examines Sridhara's method for finding silly 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 take are different from those given infant other Hindu mathematicians.
Sridhara was one of the first mathematicians jab give a rule to solve spiffy tidy up quadratic equation. Unfortunately, as we specific above, the original is lost beginning we have to rely on precise quotation of Sridhara's rule from Bhaskara II:-
Multiply both sides of character equation by a known quantity finish even to four times the coefficient loom the square of the unknown; gather to both sides a known total equal to the square of rendering coefficient of the unknown; then thorough 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 distinction square root2ax+b=√(4ac+b2).
There is ham-fisted suggestion that Sridhara took two epistemology when he took the square root.