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Ganita Shastra (गणितशास्त्रम्) (view source)
Revision as of 08:00, 10 September 2020
, 08:00, 10 September 2020Text replacement - "शास्र" to "शास्त्र"
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Ganita shastra (Samskrit: गणितशास्त्रम्) or Ganita (गणितम्) means the science of calculation which is an equivalent name for the term mathematics. This ancient term occurs copiously in Vedic literature. Vedanga Jyotisha by Lagadha gives it the highest place of honour among the sciences which form the Vedanga. <blockquote>यथा शिखा मयूराणां नागानां मणयो यथा । तद्वद्वेदाङ्गशास्राणां ज्योतिषं (गणितं) मूर्धनि स्थितम् ॥ १९ ॥ (Veda. Jyot. 4)<ref name=":0">B.B. Datta and A. N. Singh (1962) ''History of Hindu Mathematics, A Source Book, Parts 1 and 2.'' Bombay: Asia Publishing House. (Page 7)</ref></blockquote><blockquote>yathā śikhā mayūrāṇāṁ nāgānāṁ maṇayo yathā । tadvadvedāṅgaśāsrāṇāṁ jyotiṣaṁ (gaṇitaṁ) mūrdhani sthitam ॥ 19 ॥</blockquote>As the crests on the heads of peacocks, as the gems on the hoods of the snakes (cobras), so is astronomy (mathematics) is at the highest position of vedanga shastras (which are the [[Shad Vedangas (षड्वेदाङ्गानि)|Shad Vedangas]] or the six ancillary branches of knowledge).<ref name=":0" />
Ganita shastra (Samskrit: गणितशास्त्रम्) or Ganita (गणितम्) means the science of calculation which is an equivalent name for the term mathematics. This ancient term occurs copiously in Vedic literature. Vedanga Jyotisha by Lagadha gives it the highest place of honour among the sciences which form the Vedanga. <blockquote>यथा शिखा मयूराणां नागानां मणयो यथा । तद्वद्वेदाङ्गशास्त्राणां ज्योतिषं (गणितं) मूर्धनि स्थितम् ॥ १९ ॥ (Veda. Jyot. 4)<ref name=":0">B.B. Datta and A. N. Singh (1962) ''History of Hindu Mathematics, A Source Book, Parts 1 and 2.'' Bombay: Asia Publishing House. (Page 7)</ref></blockquote><blockquote>yathā śikhā mayūrāṇāṁ nāgānāṁ maṇayo yathā । tadvadvedāṅgaśāsrāṇāṁ jyotiṣaṁ (gaṇitaṁ) mūrdhani sthitam ॥ 19 ॥</blockquote>As the crests on the heads of peacocks, as the gems on the hoods of the snakes (cobras), so is astronomy (mathematics) is at the highest position of vedanga shastras (which are the [[Shad Vedangas (षड्वेदाङ्गानि)|Shad Vedangas]] or the six ancillary branches of knowledge).<ref name=":0" />
== Introduction ==
== Introduction ==
== Contribution of Ancient and Medieval Indian Mathematicians ==
== 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 name=":2">Bag, A. K., (1979) ''Mathematics in Ancient and Medieval India.'' Varanasi: Chaukhambha Orientalia. </ref>
Briefly the Dr. A. K. Bag discusses the contribution of ancient and modern Indian mathematicians to the world of computation, calculation and mathematics as follows.<ref name=":2">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.
* Numeration in India was known since the earliest times. Expression of very large numbers by means of indices to ten and their use of fractions of various types has been mentioned in the Samhitas.
* Concept of nine numerals, decimal place-value, with the introduction of zero significantly contributed to the development of Arithmetic.
* 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
* Formulation of rule of three methods of calculation
== Modern Indian Mathematicians ==
== Modern Indian Mathematicians ==
Three schools - Ujjain, Mysore and Kusumpura have been referred to as important schools of mathematics in the early christian era. Here we discuss the important mathematicians of the modern era.
Three schools - Ujjain, Mysore and Kusumpura have been referred to as important schools of mathematics in the early christian era. Here we discuss the important mathematicians of the modern era and their significant contributions to astronomy and mathematics.
# '''Aryabhata I (476 A.D.)''' - Aryabhatiya or Aryasiddhanta consists of four chapters namely Dasagitika (the ten Gitikas), Ganitapada (mathematics), Kalakriya (reckoning of time) and Gola (sphere) deals with astronomy and arithmetic.
# '''Aryabhata I (476 A.D.)''' - Aryabhatiya or Aryasiddhanta consists of four chapters namely Dasagitika (the ten Gitikas), Ganitapada (mathematics), Kalakriya (reckoning of time) and Gola (sphere) deals with astronomy and arithmetic.
# '''Varahamihira (505 A.D.)''' - Panchasiddhantika among other works is considered important in the history of astronomy. In the history of mathematics this work has a high place for its amount of trigonometrical information.
# '''Varahamihira (505 A.D.)''' - Panchasiddhantika among other works is considered important in the history of astronomy. In the history of mathematics this work has a high place for its amount of trigonometrical information.
# '''Govindasvamin (800-850 A.D.)''' - Bhashya on Mahabhaskariya of Bhaskara I and Govindakrti. He belonged to the Kerala school of mathematics.
# '''Govindasvamin (800-850 A.D.)''' - Bhashya on Mahabhaskariya of Bhaskara I and Govindakrti. He belonged to the Kerala school of mathematics.
# '''Mahavira (850 A.D.)''' - Ganitasarasamgraha deals with arithmetic, geometry and algebra. A Jaina mathematician he is associated with the school of Mysore.
# '''Mahavira (850 A.D.)''' - Ganitasarasamgraha deals with arithmetic, geometry and algebra. A Jaina mathematician he is associated with the school of Mysore.
# '''Sridhara (850-950 A.D.)''' - Patiganita is a work on arithmetic and mensuration.
# '''Sridhara (850-950 A.D.)''' - Patiganita is a work on arithmetic and mensuration. Famous as Sridharacharya, he dealt with multiplication, division, square, cube, squareroot, cube-root, fraction, rule of three and the areas of plane figures. For the first time gave a rule to extract the root of ax²+bx = c, which is known usually as Sridhara's formula.
The Kerala school of mathematics in the more recent centuries has been the seat of learning and has produced great mathematical works.
# '''Aryabhata II (950 A.D.)''' - Mahabhaskariya, an astronomical work dealing with various problems of mathematical interest besides preliminary operations. He mentions separately about the three branches of mathematics, Pati, Kuttaka and Bija in this work.
# '''Sripati (1039 A.D.)''' - Ganitatilaka, Siddhantasekhara and Bijaganita besides five other works on astronomy and astrology. A Jaina astronomer, his Ganitatilaka is devoted exclusively to arithmetic. The Siddhantasekhara, an astronomical work, however, deals with algebra in two chapters. Bijaganita is now lost.
# '''Bhaskara II (1114 - 1200 A.D.)''' - Lilavati, Bijaganita and Siddhantasiromani are the famous works of Bhaskaracharya. He authored two other works Vasanabhaasya, his own commentary of the Siddhantasiromani, and Karanakutuhala, a treatise on planetary motion. The Lilavati which is based on Brahmagupta's Brahmasphutasiddhanta, Sridhara's Patiganita, and Mahasiddhanta of Aryabhata II exhibits a profound system of arithmetic and also contains many useful propositions in geometry and arithmetic. The full solution of the equation and of its more general form ax²+bx+c = y² was given by Bhaskaracharya II. He was acquainted with the principle of infinitesimal calculus and is often given credit for originating the idea of integration long before Newton and Leibniz.
#
The Kerala school of mathematics developed from fourteenth century onwards. Kerala has been seat of learning and has produced great mathematical works building an unbroken tradition for about five hundred years. The mathematicians of Kerala were staunch followers of Aryabhata I. The activities of the scholars of this period who attained an independent distinction are still unpublished and are yet to be studied.<ref name=":2" />
# '''Narayana Pandita (1356 A.D.)''' - Ganitakaumudi, a mathematical treatise and Bijaganitavatamsa, a work on algebra. Known as Narayana Daivajna, he was solely a mathematician.
# '''Madhava (1400 A.D.)''' - Venvaroha, a well known astronomical treatise. He is regarded as the authority on spherical astronomy and mathematics and is often referred to by later writers as a golavid (expert on spherical mathematics).
# '''Paramesvara (1430 A.D.)''' - author of many commentaries on all the popular classical works on astronomy and mathematics besides some original works on astronomy such as Drgganita and Goladipika. He was the founder of the drgganita system of astronomy in Kerala though mainly an astronomer was held with respect in the field of mathematics.
# '''Nilakantha Somasutvan (1443 - 1543 A.D.)''' - Aryabhattiyabhashya and Tantrasamgraha contribute much to mathematics. He is the author of many other astronomical works namely Golasara, Chandrachhayaganita, Chandrachhayaganita-tika.
# '''Jnanaraja (1503 A.D.)''' - Siddhantasundarabija and Siddhatasundara, both of which remain unpublished.
# '''Chitrabhanu (1475 - 1550 A.D.)''' - Karnaamrta, is a work on mathematics.
== Commentaries in Indian Mathematics ==
== Commentaries in Indian Mathematics ==