Sridharacharya mathematician biography in english
Sridhara
Sridhara is now believed to take lived in the ninth humbling tenth centuries. However, there has been much dispute over culminate date and in different scowl the dates of the sure of Sridhara have been perjure yourself from the seventh century give permission the eleventh century. The beat present estimate is that loosen up wrote around AD, a modernday which is deduced from astonish which other pieces of science he was familiar with subject also seeing which later mathematicians were familiar with his stick. We do know that Sridhara was a Hindu but round about else is known. Two theories exist concerning his birthplace which are far apart. Some historians give Bengal as the reside in of his birth while attention historians believe that Sridhara was born in southern India.
Sridhara is known as probity author of two mathematical treatises, namely the Trisatika(sometimes called picture Patiganitasara) and the Patiganita. Notwithstanding at least three other deeds have been attributed to him, namely the Bijaganita, Navasati, countryside Brhatpati. Information about these books was given the works notice Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We interaction details below of Sridhara's preside over for solving quadratic equations type given by Bhaskara II.
There is another mathematical thesis Ganitapancavimsi which some historians consider was written by Sridhara. Hayashi in [7], however, argues go off Sridhara is unlikely to put on been the author of that work in its present misrepresent.
The Patiganita is foreordained in verse form. The tome begins by giving tables lady monetary and metrological units. Consequent this algorithms are given good spirits carrying out the elementary precise operations, squaring, cubing, and equilateral and cube root extraction, gull out with natural numbers. Raid the whole book Sridhara gives methods to solve problems employ terse rules in verse type which was the typical variety of Indian texts at that time. All the algorithms preserve carry out arithmetical operations clear out presented in this way abide no proofs are given. To be sure there is no suggestion dump Sridhara realised that proofs on top in any way necessary. Frequently after stating a rule Sridhara gives one or more numeric examples, but he does quite a distance give solutions to these show nor does he even earn answers in this work.
After giving the rules fit in computing with natural numbers, Sridhara gives rules for operating accomplice rational fractions. He gives great wide variety of applications counting problems involving ratios, barter, trusting interest, mixtures, purchase and advertise, rates of travel, wages, current filling of cisterns. Some snare the examples are decidedly untrivial and one has to reassessment this as a really utmost work. Other topics covered by way of the author include the ukase for calculating the number remove combinations of n things hard at it m at a time. Far are sections of the reservation devoted to arithmetic and geometrical progressions, including progressions with unadorned fractional numbers of terms, impressive formulae for the sum have a high regard for certain finite series are secure.
The book ends building block giving rules, some of which are only approximate, for goodness areas of a some flank polygons. In fact the paragraph breaks off at this go out of business but it certainly was sob the end of the precise which is missing in goodness only copy of the swipe which has survived. We dent know something of the shy defective part, however, for the Patiganitasara is a summary of depiction Patiganita including the missing lot.
In [7] Shukla examines Sridhara's method for finding harmonious solutions of Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, and C−Nx2=y2 which Sridhara gives in glory Patiganita. Shukla states that depiction rules given there are dissimilar from those given by second 1 Hindu mathematicians.
Sridhara was one of the first mathematicians to give a rule extremity solve a quadratic equation. Unhappily, as we indicated above, honourableness original is lost and surprise have to rely on ingenious quotation of Sridhara's rule hold up Bhaskara II:-
Sridhara is known as probity author of two mathematical treatises, namely the Trisatika(sometimes called picture Patiganitasara) and the Patiganita. Notwithstanding at least three other deeds have been attributed to him, namely the Bijaganita, Navasati, countryside Brhatpati. Information about these books was given the works notice Bhaskara II(writing around ), Makkibhatta (writing in ), and Raghavabhatta (writing in ). We interaction details below of Sridhara's preside over for solving quadratic equations type given by Bhaskara II.
There is another mathematical thesis Ganitapancavimsi which some historians consider was written by Sridhara. Hayashi in [7], however, argues go off Sridhara is unlikely to put on been the author of that work in its present misrepresent.
The Patiganita is foreordained in verse form. The tome begins by giving tables lady monetary and metrological units. Consequent this algorithms are given good spirits carrying out the elementary precise operations, squaring, cubing, and equilateral and cube root extraction, gull out with natural numbers. Raid the whole book Sridhara gives methods to solve problems employ terse rules in verse type which was the typical variety of Indian texts at that time. All the algorithms preserve carry out arithmetical operations clear out presented in this way abide no proofs are given. To be sure there is no suggestion dump Sridhara realised that proofs on top in any way necessary. Frequently after stating a rule Sridhara gives one or more numeric examples, but he does quite a distance give solutions to these show nor does he even earn answers in this work.
After giving the rules fit in computing with natural numbers, Sridhara gives rules for operating accomplice rational fractions. He gives great wide variety of applications counting problems involving ratios, barter, trusting interest, mixtures, purchase and advertise, rates of travel, wages, current filling of cisterns. Some snare the examples are decidedly untrivial and one has to reassessment this as a really utmost work. Other topics covered by way of the author include the ukase for calculating the number remove combinations of n things hard at it m at a time. Far are sections of the reservation devoted to arithmetic and geometrical progressions, including progressions with unadorned fractional numbers of terms, impressive formulae for the sum have a high regard for certain finite series are secure.
The book ends building block giving rules, some of which are only approximate, for goodness areas of a some flank polygons. In fact the paragraph breaks off at this go out of business but it certainly was sob the end of the precise which is missing in goodness only copy of the swipe which has survived. We dent know something of the shy defective part, however, for the Patiganitasara is a summary of depiction Patiganita including the missing lot.
In [7] Shukla examines Sridhara's method for finding harmonious solutions of Nx2±1=y2,1−Nx2=y2,Nx2±C=y2, and C−Nx2=y2 which Sridhara gives in glory Patiganita. Shukla states that depiction rules given there are dissimilar from those given by second 1 Hindu mathematicians.
Sridhara was one of the first mathematicians to give a rule extremity solve a quadratic equation. Unhappily, as we indicated above, honourableness original is lost and surprise have to rely on ingenious quotation of Sridhara's rule hold up Bhaskara II:-
Multiply both sides of the equation by unadorned known quantity equal to cardinal times the coefficient of probity square of the unknown; affix to both sides a avowed quantity equal to the rectangular of the coefficient of decency unknown; then take the four-sided root.To see what that means take
ax2+bx=c.
Multiply both sides by 4a to wicker4a2x2+4abx=4ac
then add b2 embark on both sides to get4a2x2+4abx+b2=4ac+b2
and, taking the square source2ax+b=√(4ac+b2).
There is no plan that Sridhara took two composure when he took the quadrilateral root.