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Ganita Shastra (गणितशास्त्रम्) (view source)
Revision as of 17:42, 24 March 2020
, 17:42, 24 March 2020adding content and references
Thus ganita came to mean mathematics in general, while 'finger arithmetic' as well as 'mental arithmetic' were excluded from the scope of its meaning. For the calculations involved in ganita, the use of some writing material became essential. The calculations were performed on a board (patti) with a piece of chalk or on sand (dhuli) spread on the ground or on the patti, Thus the terms patti-ganita ("science of calculation on the board") or dhuli-karma ("dust-work"), came to be used for higher mathematics. Later on the section of ganita dealing with algebra was given the name Bija-ganita. The first to effect this separation was Brahmagupta, but he did not use the term Bijaganita. The chapter dealing with algebra in his Brahma-sphuta-siddhanta is called Kuttaka. Sridharacarya (750) regarded Pati-ganita and Bijaganita as separate and wrote separate treatises on each. This distinction between Pati-ganita and Bijaganita has been preserved by later writers.<ref name=":0" />
Thus ganita came to mean mathematics in general, while 'finger arithmetic' as well as 'mental arithmetic' were excluded from the scope of its meaning. For the calculations involved in ganita, the use of some writing material became essential. The calculations were performed on a board (patti) with a piece of chalk or on sand (dhuli) spread on the ground or on the patti, Thus the terms patti-ganita ("science of calculation on the board") or dhuli-karma ("dust-work"), came to be used for higher mathematics. Later on the section of ganita dealing with algebra was given the name Bija-ganita. The first to effect this separation was Brahmagupta, but he did not use the term Bijaganita. The chapter dealing with algebra in his Brahma-sphuta-siddhanta is called Kuttaka. Sridharacarya (750) regarded Pati-ganita and Bijaganita as separate and wrote separate treatises on each. This distinction between Pati-ganita and Bijaganita has been preserved by later writers.<ref name=":0" />
The development of numerical symbolism is intimately connected with the writing in ancient India.
The development of numerical symbolism is intimately connected with the writing in ancient India.
== Contribution of Ancient and Medieval Indian Mathematicians ==
Briefly the Dr. A. K. Bag discusses the contribution of Indian mathematicians to the world of computation, calculation and mathematics as follows.<ref>Bag, A. K., (1979) ''Mathematics in Ancient and Medieval India.'' Varanasi: Chaukhambha Orientalia. </ref>
* Expression of very large numbers by means of indices to ten and their use of fractions of various types.
* Concept of nine numerals, decimal place-value, with the introduction of zero significantly contributed to the development of Arithmetic.
* Formulation of rule of three methods of calculation
* Accurate calculation of Surd numbers.
* Geometrical knowledge and classification of geometrical figures on the basis of angles and sides was provided as early in as the Sulbasutras
* Pythogoras theorem was elucidated
* Calculation of the value of squareroot of 2 by geometrical method.
* Determination of diagonals of cyclic quadrilateral and methods for the construction of a quadrilateral given by Brahmagupta
* In the field of Algebra - symbols of operation, equation, rule of false position, quadratic equation, indeterminate equations of first and second degree, progressive series, permutations and combination, and Pascal's triangle with binomial theorem have been discussed.
* Development of trigonometrical formulae, sine table construction, and value of pi.
* Work on trigonometrical series - pi, sine, cosine, and tan was first carried out by the Indians more than a century before Newton (1664 CE) and Leibniz (1676 CE).
* Development of the concept of infinitesimal (integral) calculus occurred in Yuktibhasa in connection with the summation of Infinite Series prior to western discoveries.
== Sources on Mathematics ==
=== Vedic Sources ===
Critical mathematical knowledge of Sutra charana literature led us to assume that there are mathematical works of even earlier age but they are lost. Shulbasutra-karas, seven of them, namely, Baudhayana, Apastamba, Katyayana, Manava, Maitrayana, Varaha, and Hiranyakeshi are regarded as the geometricians of the Vedic times. The Shulba works of these authors give methods and solutions of various problems of construction of altars required for yajnas.
Baudhayana shulbasutras are one of the earliest texts that describe the problems of construction of yajna-kundas. These texts also gave a general enunciation of the Pythogoras theorem, an approximate value of square-root of two correct to five places of decimal,
== References ==
== References ==
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[[Category:Shastras]]
[[Category:Shastras]]