Shridhara

flourished с 750, India

Highly esteemed Hindu mathematician who wrote several treatises on Indian mathematics.

His extant works are the partially preserved Patiganita ("Mathematics of Procedures"), Ganitasara ("Essence of Mathematics"), and Ganitapanchavimashi ("Mathematics in 25 Verses"). Patiganita consists of versified mathematical rules, without proofs. The first part treats arithmetic operations (including the calculation of squares, square roots, cubes, and cubic roots) for both integers and fractions, reductions of fractions, and proportions. The second part presents mixture problems and various series before it breaks off in the midst of rules for plane figures. He composed Ganitasara and Ganitapanchavimashi as epitomes of a larger work, which may or may not have been Patiganita. He gave the first correct formulas in India for the volume of a sphere and of a truncated cone.

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▪ Hindu mathematician

flourished c. 750, India

      highly esteemed Hindu mathematician who wrote several treatises on the two major fields of Indian mathematics, pati-ganita (“mathematics of procedures,” or algorithms (algorithm)) and bija-ganita (“mathematics of seeds,” or equations).

      Very little is known about Shridhara's life. Some scholars believe that he was born in Bengal, while others believe that he was born in South India. All three of Shridhara's extant works—the partially preserved Patiganita, Ganitasara (“Essence of Mathematics”), and Ganitapanchavimashi (“Mathematics in 25 Verses”)—belong to pati-ganita, but, according to Bhaskara II (Bhāskara II) (1114–c. 1185), he wrote at least one book on bija-ganita.

      Patiganita consists of versified mathematical rules, without proofs, and examples arranged under the two headings parikarman (“basic operations”) and vyavahara (applied or “procedural mathematics”). The first part treats arithmetic operations (including the calculation of squares, square roots, cubes, and cubic roots) for both integers and fractions, reductions of fractions, and proportions. The second part presents mixture problems and various series before it breaks off in the midst of rules for plane figures. The topics of the remaining sections are ditches, brick piling, timber sawing, heaped-up grain, shadows, and zero, according to the table of contents given at the beginning of the work.

      Shridhara composed Ganitasara and Ganitapanchavimashi as epitomes of a larger work, which may or may not have been Patiganita. He extended Aryabhata I's list (c. 499) of names of the first 10 decimal places to 18 places; the new list was inherited by most Hindu mathematicians after him. The topics treated by him included combinations of tastes ( combinatorics involving the six tastes of bitter, sour, sweet, salty, astringent, and hot), geometric progressions, geometric expressions of arithmetic progressions (by means of trapeziums called “series figures”), the problem of the “Hundred Fowls,” and the “Cistern Problem.” He gave the first correct formulas in India for the volume of a sphere and of a truncated cone. He used two approximations for π, the traditional Jain value of √10 as well as ²²/₇. Bhaskara II cites Shridhara's rule for quadratic equations (quadratic equation) that allows two solutions of a single equation, in so far as they are positive, probably from Shridhara's lost work on bija-ganita.

Takao Hayashi

 

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