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2532:"1. Ignited minds page 39 by APJ Abdul Kalam, 2. Prof Sudakara Divedi (1855-1910), 3. Dr B A Salethor (Indian Culture), 4. Govt of Karnataka Publications, 5. Dr Nararajan (Lilavati 1989), 6. Prof Sinivas details(Ganitashatra Chrithra by1955, 7. Aalur Venkarayaru (Karnataka Gathvibaya 1917, 8. Prime Minister Press Statement at sarawad in 2018, 9. Vasudev Herkal (Syukatha Karnataka articles), 10. Manjunath sulali (Deccan Herald 19/04/2010, 11. Indian Archaeology 1994-96 A Review page 32, Dr R K Kulkarni (Articles)"
562:, the leading mathematical centre of medieval India. History records his great-great-great-grandfather holding a hereditary post as a court scholar, as did his son and other descendants. His father Maheśvara (Maheśvaropādhyāya) was a mathematician, astronomer and astrologer, who taught him mathematics, which he later passed on to his son Lokasamudra. Lokasamudra's son helped to set up a school in 1207 for the study of Bhāskara's writings. He died in 1185 CE.
34:
1378:
results. In particular
Bhaskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhaskara, results found in his works include computation of sines of angles of 18 and 36 degrees, and
1814:
He also showed that when a planet is at its farthest from the earth, or at its closest, the equation of the centre (measure of how far a planet is from the position in which it is predicted to be, by assuming it is to move uniformly) vanishes. He therefore concluded that for some intermediate
2080:, he reasons: "In this quantity also which has zero as its divisor there is no change even when many quantities have entered into it or come out , just as at the time of destruction and creation when throngs of creatures enter into and come out of the infinite and unchanging ".
1500:
Evidence suggests
Bhaskara was acquainted with some ideas of differential calculus. Bhaskara also goes deeper into the 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of
1910:. Diurnal motion refers to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis, so every star apparently moves on a circle that is called the diurnal circle.
381:, the main mathematical centre of ancient India. Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work
412:, which are also sometimes considered four independent works. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala.
2088:
It has been stated, by several authors, that
Bhaskara II proved the Pythagorean theorem by drawing a diagram and providing the single word "Behold!". Sometimes Bhaskara's name is omitted and this is referred to as the
357:
by scholars. In a temple in
Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him.
775:
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Deshasthas have contributed to mathematics and literature as well as to the cultural and religious heritage of India. Bhaskaracharaya was one of the greatest mathematicians of ancient India.
877:
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contained excellent problems and it is thought that
Bhaskara's intention may have been that a student of 'Lilavati' should concern himself with the mechanical application of the method.
2129:
1819:, one of the most important theorems in analysis, which today is usually derived from Rolle's theorem. The mean value formula for inverse interpolation of the sine was later founded by
1173:
is divided into 13 chapters and covers many branches of mathematics, arithmetic, algebra, geometry, and a little trigonometry and measurement. More specifically the contents include:
1607:
349:
and engineer. From verses in his main work, Siddhāṁta Śiromaṇī, it can be inferred that he was born in 1114 in
Vijjadavida (Vijjalavida) and living in the Satpuda mountain ranges of
1461:
1419:
1238:), integer solutions (first and second order). His contributions to this topic are particularly important, since the rules he gives are (in effect) the same as those given by the
578:
1866:, the time that is required for the Earth to orbit the Sun, as approximately 365.2588 days which is the same as in Suryasiddhanta. The modern accepted measurement is 365.25636
681:
3938:
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1370:(written in 1150) demonstrates Bhaskara's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed
1662:
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1242:
European mathematicians of the 17th century, yet his work was of the 12th century. Bhaskara's method of solving was an improvement of the methods found in the work of
802:
3273:
1352:
for solving indeterminate quadratic equations of the form ax + bx + c = y. Bhaskara's method for finding the solutions of the problem Nx + 1 = y (the so-called "
508:(17th century), a commentator on Siddhānta Shiromani of Bhaskara has given the information about the location of Vijjadavida in his work Marīci Tīkā as follows:
1627:
822:
116:
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80:
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and the equinox J2000 given in Simon, J. L., et al., "Numerical
Expressions for Precession Formulae and Mean Elements for the Moon and the Planets"
2066:. This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale.
3915:
2096:
However, as mathematics historian Kim
Plofker points out, after presenting a worked-out example, Bhaskara II states the Pythagorean theorem:
699:, while treating the motion of planets, he considered their instantaneous speeds. He arrived at the approximation: It consists of 451 verses
624:(Algebra) has 213 verses. It discusses zero, infinity, positive and negative numbers, and indeterminate equations including (the now called)
2100:
Hence, for the sake of brevity, the square root of the sum of the squares of the arm and upright is the hypotenuse: thus it is demonstrated.
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2368:
Algebra with
Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bhascara by Henry Colebrooke, Scholiasts of Bhascara p., xxvii
4116:
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3962:
1014:. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the
2516:(1865). "Brief Notes on the Age and Authenticity of the Works of Aryabhata, Varahamihira, Brahmagupta, Bhattotpala and Bhaskaracharya".
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2125:
1839:
1788:
In computing the instantaneous motion of a planet, the time interval between successive positions of the planets was no greater than a
4032:
2350:गणिती (Marathi term meaning Mathematicians) by Achyut Godbole and Dr. Thakurdesai, Manovikas, First Edition 23, December 2013. p. 34.
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527:. However scholars differ about the exact location. Many scholars have placed the place near Patan in Chalisgaon Taluka of
2323:
1815:
position the differential of the equation of the centre is equal to zero. In this result, there are traces of the general
1667:
In this astronomical work he gave one procedure that looks like a precursor to infinitesimal methods. In terms that is if
1250:
His work is outstanding for its systematisation, improved methods and the new topics that he introduced. Furthermore, the
895:
This result had also been observed earlier by Muñjalācārya (or Mañjulācārya) mānasam, in the context of a table of sines.
3610:
1696:
1862:
in the 7th century, Bhāskara accurately defined many astronomical quantities, including, for example, the length of the
705:
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covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions,
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whereas a section of scholars identified it with the modern day Beed city. Some sources identified
Vijjalavida as
3830:
362:
who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as
1846:) from the 14th century to the 16th century expanded on Bhaskara's work and further advanced the development of
4065:
3680:
3434:
2112:
Plofker suggests that this additional statement may be the ultimate source of the widespread "Behold!" legend.
588:
3474:
3353:
2159:
1477:, is an astronomical treatise and contains many theories not found in earlier works. Preliminary concepts of
490:
512:सह्यकुलपर्वतान्तर्गत भूप्रदेशे महाराष्ट्रदेशान्तर्गतविदर्भपरपर्यायविराटदेशादपि निकटे गोदावर्यां नातिदूरे
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1808:
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family of scholars, mathematicians and astronomers, Bhaskara II was the leader of a cosmic observatory at
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1570:
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2990:
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd edition)
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1998:
4161:
3580:
3252:
2725:
2240:
Indian Journal of History of Science, Volume 35, National Institute of Sciences of India, 2000, p. 77
637:
1272:") was a work in twelve chapters. It was the first text to recognize that a positive number has two
3870:
3736:
3585:
3266:
3262:
2965:
White, Lynn Townsend (1978), "Tibet, India, and Malaya as Sources of Western Medieval Technology",
1632:
1160:
59:
3996:
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3469:
2867:
1954:
1835:
1113:
Calculated the derivatives of trigonometric functions and formulae. (See Calculus section below.)
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2014:
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1309:
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Bhāskara gives his date of birth, and date of composition of his major work, in a verse in the
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906:
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260:
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3107:, Ravivarma Samskr̥ta granthāvali, vol. 22, Govt. Sanskrit College (Tripunithura, India)
2001:
1877:
is written in two parts: the first part on mathematical astronomy and the second part on the
1490:
1482:
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1092:
1071:
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353:, believed to be the town of Patana in Chalisgaon, located in present-day Khandesh region of
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3635:
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1313:
1221:
1037:
608:), named after his daughter, consists of 277 verses. It covers calculations, progressions,
2499:. Bennett, Coleman & Company, Limited, at the Times of India Press. 1974. p. 30.
1804:
of a second, and his measure of velocity was expressed in this infinitesimal unit of time.
8:
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Bhāskara also stated that at its highest point a planet's instantaneous speed is zero.
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85:
3159:, eds. (2001), "Mathematics across cultures: the history of non-western mathematics",
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4156:
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Hindu achievements in exact science: a study in the history of scientific development
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Proceedings, Indian History Congress, Volume 40, Indian History Congress, 1979, p. 71
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544:
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1971:
The second part contains thirteen chapters on the sphere. It covers topics such as:
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2008:
1937:
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that is a derivative of sine although he did not develop the notion on derivative.
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630:
477:
421:
277:
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3449:
2606:
Mathematical Achievements of Pre-modern Indian Mathematicians von T.K Puttaswamy
1048:. This very equation was posed as a problem in 1657 by the French mathematician
3921:
3841:
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3701:
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3600:
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2256:
Studies in Indology and Medieval History: Prof. G. H. Khare Felicitation Volume
1907:
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367:
186:
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And otherwise, when one has set down those parts of the figure there seeing .
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2359:
Mathematics in India by Kim Plofker, Princeton University Press, 2009, p. 182
2299:
1925:
1919:
1863:
1502:
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350:
338:
49:
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3041:
The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
2217:
The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
2188:
2120:
A number of institutes and colleges in India are named after him, including
1332:
Solutions of indeterminate equations of the second, third and fourth degree.
20:
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3806:
3750:
3694:
3514:
3494:
3419:
2264:
1820:
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1375:
1125:
248:
69:
887:
446:
437:
429:
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3444:
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1992:
1981:
1859:
1273:
1239:
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988:
609:
482:
354:
142:
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1280:
is effectively a treatise on algebra and contains the following topics:
1106:, a special case of one of the most important theorems in analysis, the
3673:
3630:
3484:
3464:
3439:
3039:
Plofker, Kim (2007), "Mathematics in India", in Katz, Victor J. (ed.),
2248:
2246:
1783:, a quantity required for accurately predicting the time of an eclipse.
1181:
1138:
1110:. Traces of the general mean value theorem are also found in his works.
917:
Some of Bhaskara's contributions to mathematics include the following:
505:
464:
400:
346:
271:
244:
158:
3006:
Shukla, Kripa Shankar (1984), "Use of Calculus in Hindu Mathematics",
1513:
in his work. The modern formulation of Rolle's theorem states that if
3792:
3454:
3414:
3314:
2513:
1985:
1889:
1243:
987:). The rules he gives are (in effect) the same as those given by the
555:
548:
540:
494:
460:
222:
146:
122:
3288:. Vol. 2. New York: Charles Scribner's Sons. pp. 115–120.
2330:. Publications Division Ministry of Information & Broadcasting.
2277:
2243:
1319:
Simple equations (indeterminate of second, third and fourth degree).
475:
was completed during 1150 CE. He also wrote another work called the
3575:
3539:
3519:
2130:
Bhaskaracharya Institute For Space Applications and Geo-Informatics
2076:
1948:
1931:
1847:
1780:
1494:
1297:
1228:
1196:
1143:
1085:
1081:
981:
Integer solutions of linear and quadratic indeterminate equations (
520:
486:
394:
389:
265:
150:
1021:
The first general method for finding the solutions of the problem
3393:
2519:
Journal of the Royal Asiatic Society of Great Britain and Ireland
2020:
1807:
He was aware that when a variable attains the maximum value, its
1268:
1059:
Solved quadratic equations with more than one unknown, and found
532:
240:
3641:
Shanti Swarup Bhatnagar Prize recipients in Mathematical Science
1779:
Bhaskara uses this result to work out the position angle of the
3383:
2709:
2036:
1893:
1878:
1156:
684:
559:
378:
182:
2062:
Bhāskara II invented a variety of instruments one of which is
519:
This description locates Vijjalavida in Maharashtra, near the
2630:
Students& Britannica India. 1. A to C by Indu Ramchandani
1790:
889:
bimbārdhasya koṭijyā guṇastrijyāhāraḥ phalaṃ dorjyāyorantaram
536:
497:
located near Patan (Chalisgaon) in the vicinity of Sahyadri.
2150:, an Indian documentary short on the mathematician in 2015.
1884:
The twelve chapters of the first part cover topics such as:
966:
Solutions of indeterminate quadratic equations (of the type
592:. Use of the Pythagorean theorem in the corner. 1650 edition
392:
for "Crown of Treatises") is divided into four parts called
3237:
The Crest of the Peacock: Non-European Roots of Mathematics
2841:
1961:
1944:
1052:, but its solution was unknown in Europe until the time of
929:
in two different ways and then cancelling out terms to get
926:
154:
3842:
Infinite series expansions for the trigonometric functions
2614:
2612:
481:
when he was 69 (in 1183). His works show the influence of
2541:
B.I.S.M. quarterly, Poona, Vol. 63, No. 1, 1984, pp 14-22
2477:
2475:
1867:
3134:
Toward a global science: mining civilizational knowledge
2742:
2659:
2647:
2252:
2055:
machine date back to 1150, when Bhāskara II described a
1291:
The 'unknown' (includes determining unknown quantities).
2706:
2609:
2383:
2278:
K. V. Ramesh; S. P. Tewari; M. J. Sharma, eds. (1990).
1497:
that are found in the work are of particular interest.
1203:
493:, Padmanābha and other predecessors. Bhaskara lived in
2959:
Arithmetic and mensuration of Brahmegupta and Bhaskara
2754:
2730:
2472:
2187:
to avoid confusion with the 7th century mathematician
4091:
Ramanujan Institute for Advanced Study in Mathematics
3836:
3278:
at the MacTutor archive. St Andrews University, 2002.
2679:"The Great Bharatiya Mathematician Bhaskaracharya ll"
2407:
2395:
1699:
1673:
1635:
1615:
1573:
1519:
1427:
1385:
832:
810:
785:
708:
640:
3151:
2988:, ed. (2008), "Astronomical Instruments in India",
2371:
1769:{\displaystyle \sin(y)-\sin(x)\approx (y-x)\cos(y)}
1300:(includes evaluating surds and their square roots).
1191:Further extensive numerical work, including use of
3131:
2968:Medieval religion and technology: collected essays
2450:
2259:. Joshi & Lokhande Prakashan. pp. 42–47.
1768:
1685:
1656:
1621:
1601:
1559:
1455:
1413:
871:
816:
796:
770:{\displaystyle \sin y'-\sin y\approx (y'-y)\cos y}
769:
675:
3246:
3025:, vol. 146, American Philosophical Society,
1560:{\displaystyle f\left(a\right)=f\left(b\right)=0}
448:Rasa-guṇa-varṣeṇa mayā siddhānta-śiromaṇī racitaḥ
75:for phonetic transcriptions, with an appropriate
4108:
2321:
1276:(a positive and negative square root). His work
998:for solving indeterminate equations of the form
687:and his European contemporaries centuries later
1338:Quadratic equations with more than one unknown.
16:Indian mathematician and astronomer (1114–1185)
2213:
3330:
3230:A Short Account of the History of Mathematics
2907:(6th ed.), Saunders College Publishing,
2905:An Introduction to the History of Mathematics
2864:"Great Indian Mathematician - Bhaskaracharya"
2640:
2638:
2636:
2602:
2600:
1341:Operations with products of several unknowns.
554:Bhāskara is said to have been the head of an
459:This reveals that he was born in 1036 of the
3281:
3103:Poulose, K. G. (1991), K. G. Poulose (ed.),
2143:honouring the mathematician and astronomer.
1322:Simple equations with more than one unknown.
991:European mathematicians of the 17th century.
872:{\displaystyle {\frac {d}{dy}}\sin y=\cos y}
298:Bhaskara's proof of the Pythagorean Theorem.
3282:Pingree, David (1970–1980). "Bhāskara II".
3129:
2950:The positive sciences of the ancient Hindus
2887:The History of Mathematics: An Introduction
2807:
2805:
2705:. An SI day or mean solar day equals 86400
2220:. Princeton University press. p. 447.
1960:Conjunctions of the planets with the fixed
1084:, along with notable contributions towards
322:
3858:Kerala school of astronomy and mathematics
3337:
3323:
3083:The History of Mathematics: A Brief Course
2956:
2760:
2712:. From the mean longitude referred to the
2644:50 Timeless Scientists von K.Krishna Murty
2633:
2597:
2496:The Illustrated Weekly of India, Volume 95
2446:
2444:
2442:
2126:Bhaskaracharya College of Applied Sciences
1128:results. (See Trigonometry section below.)
634:method. In particular, he also solved the
3180:
3105:Scientific heritage of India, mathematics
2618:
2559:
2555:
2553:
2551:
2549:
2547:
2512:
2440:
2438:
2436:
2434:
2432:
2430:
2428:
2426:
2424:
2422:
2253:M. S. Mate; G. T. Kulkarni, eds. (1974).
2137:Indian Space Research Organisation (ISRO)
1858:Using an astronomical model developed by
565:
431:Rasa-guṇa-pūrṇa-mahī-sama-śakanṛpa-samaye
415:
4086:Homi Bhabha Centre for Science Education
3232:, 4th Edition. Dover Publications, 1960.
3022:Census of the Exact Sciences in Sanskrit
2802:
905:
577:
504:family near Vijjadavida (Vijjalavida).
293:
3258:MacTutor History of Mathematics Archive
3102:
3056:
3038:
3018:
2866:. indiavideodotorg. 22 September 2015.
2811:
2591:
2481:
2413:
2401:
4109:
3344:
3111:
3005:
2938:
2884:
2870:from the original on 12 December 2021.
2784:
2778:
2653:
2544:
2419:
2389:
2328:Cultural Leaders of India - Scientists
2214:Victor J. Katz, ed. (10 August 2021).
2209:
2207:
2083:
2042:Problems of astronomical calculations.
1509:There is evidence of an early form of
3318:
3201:
3076:
2984:
2964:
2920:
2796:
2748:
2736:
2665:
2563:ನವ ಜನ್ಮಶತಾಬ್ದಿಯ ಗಣಿತರ್ಷಿ ಭಾಸ್ಕರಾಚಾರ್ಯ
2454:ನವ ಜನ್ಮಶತಾಬ್ದಿಯ ಗಣಿತರ್ಷಿ ಭಾಸ್ಕರಾಚಾರ್ಯ
2377:
1456:{\displaystyle \sin \left(a-b\right)}
1414:{\displaystyle \sin \left(a+b\right)}
1188:, and rules of operations with zero).
543:. Identification of Vijjalavida with
307:
3008:Indian Journal of History of Science
2947:
2902:
2772:
2696:
2506:
2284:. Agam Kala Prakashan. p. 119.
1485:, along with a number of results in
27:
3611:Subbayya Sivasankaranarayana Pillai
2451:S. Balachandra Rao (13 July 2014),
2204:
2059:that he claimed would run forever.
232:Mathematician, astronomer, geometer
13:
4117:12th-century Indian mathematicians
4071:Institute of Mathematical Sciences
3285:Dictionary of Scientific Biography
3222:
3185:Undergraduate Texts in Mathematics
3114:Religions and communities of India
2971:, University of California Press,
2026:First visibilities of the planets.
1602:{\displaystyle f'\left(x\right)=0}
1356:") is of considerable importance.
1224:, and rules of 3, 5, 7, 9, and 11.
612:, permutations, and other topics.
65:for transliterated languages, and
45:of its non-English content, using
14:
4173:
4081:Harish-Chandra Research Institute
3591:K. R. Parthasarathy (probabilist)
3303:
2281:Dr. G. S. Gai Felicitation Volume
523:region and close to the banks of
2948:Seal, Sir Brajendranath (1915),
2093:, well known by schoolchildren.
1873:His mathematical astronomy text
1379:the now well known formulae for
115:
32:
4122:12th-century Indian astronomers
3085:, Wiley-Interscience, pp.
3079:"The Mathematics of the Hindus"
2878:
2856:
2829:
2817:
2790:
2766:
2671:
2624:
2581:
2535:
2526:
2487:
2362:
2029:Calculating the lunar crescent.
1957:of the planets with each other.
1899:True longitudes of the planets.
1870:, a difference of 3.5 minutes.
1374:, along with other interesting
1359:
1294:Determining unknown quantities.
1209:Arithmetical terms, methods of
1040:of the second order, such as 61
676:{\displaystyle 61x^{2}+1=y^{2}}
4066:Chennai Mathematical Institute
3435:Melpathur Narayana Bhattathiri
3130:Goonatilake, Susantha (1999),
3063:, Princeton University Press,
3043:, Princeton University Press,
2353:
2344:
2315:
2306:
2271:
2234:
2181:
2046:
1975:Praise of study of the sphere.
1967:The paths of the Sun and Moon.
1763:
1757:
1748:
1736:
1730:
1724:
1712:
1706:
1246:and subsequent mathematicians.
901:
755:
738:
690:
81:multilingual support templates
1:
3183:Mathematics and its history,
3019:Pingree, David Edwin (1970),
2957:Colebrooke, Henry T. (1817),
2889:(7th ed.), McGraw Hill,
2197:
2160:List of Indian mathematicians
1827:, a commentary on Bhaskara's
1657:{\displaystyle \ a<x<b}
1132:
1124:along with a number of other
615:
366:residing on the banks of the
314:
170:
133:
4056:Indian Statistical Institute
3138:, Indiana University Press,
2939:Sarkār, Benoy Kumar (1918),
2703:IERS EOP PC Useful constants
2051:The earliest reference to a
1853:
1033:") was given by Bhaskara II.
910:Bhaskaracharya proof of the
467:), and that he composed the
7:
4147:Scientists from Maharashtra
4076:Indian Institute of Science
4061:Bhaskaracharya Pratishthana
3939:A. A. Krishnaswamy Ayyangar
3904:Shankar Balakrishna Dikshit
3831:Hindu–Arabic numeral system
3235:George Gheverghese Joseph.
2153:
2122:Bhaskaracharya Pratishthana
1823:in the 15th century in the
1466:
1345:Bhaskara derived a cyclic,
888:
573:
515:पंचक्रोशान्तरे विज्जलविडम्।
447:
438:
430:
10:
4178:
3571:Subrahmanyan Chandrasekhar
3208:, Vikas Publishing House,
3112:Chopra, Pran Nath (1982),
2718:Astronomy and Astrophysics
2560:Scientist (13 July 2014),
2146:Invis Multimedia released
2069:
1842:mathematicians (including
1686:{\displaystyle x\approx y}
1257:
471:when he was 36 years old.
317:1114–1185), also known as
282:Grahagaṇita and Golādhyāya
18:
4152:Scholars from Maharashtra
4046:
4010:
3984:
3888:
3850:
3816:
3653:
3581:Veeravalli S. Varadarajan
3548:
3407:
3361:
3352:
2952:, Longmans, Green and co.
2943:, Longmans, Green and co.
2885:Burton, David M. (2011),
2322:T. A. Saraswathi (2017).
2115:
2032:Astronomical instruments.
1329:(of the type ax + b = y).
1234:Indeterminate equations (
1231:and interest computation.
551:has also been suggested.
288:
254:
236:
228:
218:
213:
209:
205:Astronomer, mathematician
201:
193:
166:
129:
121:Statue of Bhaskara II at
114:
107:
3997:Henry Thomas Colebrooke
3586:S. R. Srinivasa Varadhan
3267:University of St Andrews
3263:University of St Andrews
3181:Stillwell, John (2002),
2923:Euclid in the Rainforest
2562:
2453:
2175:
2135:On 20 November 1981 the
925:by calculating the same
824:, or in modern notation:
502:Deśastha Rigvedi Brahmin
19:Not to be confused with
3470:Mādhava of Saṅgamagrāma
3205:Pedagogy Of Mathematics
3161:Science Across Cultures
2726:1994A&A...282..663S
1310:indeterminate equations
1077:Preliminary concept of
1070:Preliminary concept of
961:indeterminate equations
683:case that was to elude
2992:, Springer Verlag Ny,
2921:Mazur, Joseph (2005),
2826:NASA 16 September 2017
2110:
2102:
2015:Spherical trigonometry
1770:
1687:
1658:
1623:
1603:
1561:
1479:infinitesimal calculus
1457:
1415:
1372:spherical trigonometry
1122:spherical trigonometry
914:
893:
873:
818:
798:
771:
677:
593:
586:, the first volume of
517:
457:
416:Date, place and family
364:Maharashtrian Brahmins
299:
3681:Brāhmasphuṭasiddhānta
3202:Sahni, Madhu (2019),
3077:Cooke, Roger (1997),
3057:Plofker, Kim (2009),
2903:Eves, Howard (1990),
2720:282 (1994), 663–683.
2141:Bhaskara II satellite
2106:
2104:This is followed by:
2098:
2004:model of the planets.
1978:Nature of the sphere.
1771:
1688:
1659:
1624:
1604:
1562:
1491:differential calculus
1483:mathematical analysis
1458:
1416:
1314:Diophantine equations
1120:, Bhaskara developed
1093:differential calculus
1091:preliminary ideas of
1072:mathematical analysis
1038:Diophantine equations
909:
885:
874:
819:
799:
772:
695:In the third section
678:
628:, solving it using a
581:
510:
426:
297:
3957:T. A. Saraswati Amma
3668:Bakhshali manuscript
3636:Kannan Soundararajan
3249:Robertson, Edmund F.
3157:D'Ambrosio, Ubiratan
3060:Mathematics in India
1838:(1340–1425) and the
1697:
1671:
1633:
1613:
1571:
1517:
1425:
1383:
1335:Quadratic equations.
1155:, the shadow of the
1056:in the 18th century.
830:
808:
783:
706:
638:
332:Bhāskara the teacher
43:specify the language
41:This article should
4127:People from Jalgaon
4033:Islamic mathematics
3992:Walter Eugene Clark
3786:Vasishtha Siddhanta
3758:Siddhānta Shiromani
3737:Paitamaha Siddhanta
3616:Tilak Raj Prabhakar
3561:Satyendra Nath Bose
3556:Srinivasa Ramanujan
3510:Nilakantha Somayaji
3247:O'Connor, John J.;
2751:, pp. 269–273.
2668:, pp. 213–215.
2587:Verses 128, 129 in
2522:. pp. 392–406.
1875:Siddhanta Shiromani
1474:Siddhānta Shiromani
1367:Siddhānta Shiromani
1327:quadratic equations
1227:Problems involving
1159:, methods to solve
923:Pythagorean theorem
912:pythagorean Theorem
620:The second section
473:Siddhānta Shiromani
469:Siddhānta Shiromani
309:[bʰɑːskərə]
261:Siddhānta Shiromani
3525:Gangesha Upadhyaya
3346:Indian mathematics
3228:W. W. Rouse Ball.
2683:The Times of India
2656:, pp. 95–104.
2594:, pp. 476–477
1817:mean value theorem
1766:
1683:
1654:
1619:
1599:
1557:
1453:
1411:
1118:Siddhanta-Śiromaṇi
1108:mean value theorem
915:
869:
814:
797:{\displaystyle y'}
794:
767:
673:
596:The first section
594:
589:Siddhānta Śiromaṇī
568:Siddhānta-Śiromaṇi
439:bhavan-mamotpattiḥ
384:Siddhānta-Śiromaṇi
300:
4104:
4103:
3910:Sudhakara Dvivedi
3730:Paulisa Siddhanta
3649:
3648:
3505:Jagannatha Samrat
3500:Achyuta Pisharati
3295:978-0-684-10114-9
3275:Bhaskaracharya II
3195:978-0-387-95336-6
3174:978-1-4020-0260-1
3145:978-0-253-21182-8
3123:978-0-85692-081-3
2999:978-1-4020-4559-2
2978:978-0-520-03566-9
2932:978-0-452-28783-9
2914:978-0-03-029558-4
2896:978-0-07-338315-6
2837:"Anand Narayanan"
2739:, pp. 52–53.
2392:, pp. 52–54.
2291:978-0-8364-2597-0
1638:
1622:{\displaystyle x}
1495:integral calculus
1086:integral calculus
996:Chakravala method
846:
817:{\displaystyle y}
500:He was born in a
375:Deshastha Brahmin
292:
291:
178:(aged 70–71)
103:
102:
83:may also be used.
4169:
4162:Sanskrit writers
3744:Romaka Siddhanta
3626:Akshay Venkatesh
3596:M. S. Narasimhan
3566:P.C. Mahalanobis
3359:
3358:
3339:
3332:
3325:
3316:
3315:
3299:
3265:
3218:
3198:
3177:
3148:
3137:
3126:
3116:, Vision Books,
3108:
3099:
3073:
3053:
3035:
3015:
3002:
2981:
2961:
2953:
2944:
2935:
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2871:
2860:
2854:
2853:
2851:
2849:
2833:
2827:
2821:
2815:
2809:
2800:
2799:, pp. 19–20
2794:
2788:
2782:
2776:
2770:
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2746:
2740:
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2387:
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2369:
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2360:
2357:
2351:
2348:
2342:
2341:
2324:"Bhaskaracharya"
2319:
2313:
2310:
2304:
2303:
2275:
2269:
2268:
2250:
2241:
2238:
2232:
2231:
2211:
2192:
2185:
2132:in Gandhinagar.
2053:perpetual motion
2009:armillary sphere
1938:Sunrise equation
1908:diurnal rotation
1803:
1802:
1798:
1775:
1773:
1772:
1767:
1692:
1690:
1689:
1684:
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1420:
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1412:
1410:
1406:
1286:negative numbers
1193:negative numbers
1050:Pierre de Fermat
1029:= 1 (so-called "
891:
878:
876:
875:
870:
847:
845:
834:
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529:Jalgaon district
453:
450:
444:
441:
436:
433:
373:Born in a Hindu
360:Henry Colebrooke
336:
333:
330:
327:
324:
316:
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278:Karaṇa-Kautūhala
194:Other names
179:
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4042:
4006:
3980:
3951:C. T. Rajagopal
3898:Bapudeva Sastri
3890:
3884:
3846:
3826:Brahmi numerals
3818:
3812:
3772:Surya Siddhanta
3645:
3621:Manjul Bhargava
3544:
3403:
3348:
3343:
3310:4to40 Biography
3306:
3296:
3239:, 2nd Edition.
3225:
3223:Further reading
3216:
3196:
3175:
3146:
3124:
3097:
3071:
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2761:Colebrooke 1817
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2195:
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2156:
2118:
2086:
2072:
2049:
1934:of the planets.
1856:
1825:Lilavati Bhasya
1800:
1796:
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1610:
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1515:
1514:
1511:Rolle's theorem
1469:
1438:
1434:
1426:
1423:
1422:
1396:
1392:
1384:
1381:
1380:
1376:trigonometrical
1362:
1354:Pell's equation
1260:
1163:equations, and
1135:
1104:Rolle's theorem
1031:Pell's equation
948:, solutions of
921:A proof of the
904:
838:
833:
831:
828:
827:
809:
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805:
786:
784:
781:
780:
741:
715:
707:
704:
703:
693:
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663:
648:
644:
639:
636:
635:
626:Pell's equation
618:
600:(also known as
576:
571:
558:observatory at
478:Karaṇa-kutūhala
456:
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451:
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418:
334:
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125:
110:
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93:
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84:
72:
66:
62:
60:transliteration
56:
52:
46:
37:
33:
24:
17:
12:
11:
5:
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3925:
3922:P. C. Sengupta
3919:
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3779:Tantrasamgraha
3775:
3768:
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3747:
3740:
3733:
3726:
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3712:
3705:
3702:Karanapaddhati
3698:
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3688:Ganita Kaumudi
3684:
3677:
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3665:
3657:
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3650:
3647:
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3606:Harish-Chandra
3603:
3601:C. S. Seshadri
3598:
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3588:
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3573:
3568:
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3535:Sankara Variar
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3356:
3354:Mathematicians
3350:
3349:
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3327:
3319:
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3305:
3304:External links
3302:
3301:
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3279:
3270:
3244:
3233:
3224:
3221:
3220:
3219:
3215:978-9353383275
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3199:
3194:
3178:
3173:
3153:Selin, Helaine
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2623:
2619:Stillwell 2002
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2596:
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2525:
2505:
2486:
2484:, p. 299.
2471:
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2148:Bhaskaracharya
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1591:
1588:
1585:
1580:
1577:
1556:
1553:
1549:
1546:
1543:
1539:
1536:
1532:
1529:
1526:
1522:
1503:infinitesimals
1471:His work, the
1468:
1465:
1451:
1447:
1444:
1441:
1437:
1433:
1430:
1409:
1405:
1402:
1399:
1395:
1391:
1388:
1361:
1358:
1343:
1342:
1339:
1336:
1333:
1330:
1325:Indeterminate
1323:
1320:
1317:
1301:
1295:
1292:
1289:
1259:
1256:
1248:
1247:
1232:
1225:
1218:
1211:multiplication
1207:
1202:Estimation of
1200:
1189:
1180:Properties of
1178:
1153:solid geometry
1149:plane geometry
1134:
1131:
1130:
1129:
1114:
1111:
1100:
1089:
1075:
1068:
1057:
1034:
1019:
992:
979:
964:
963:are explained.
942:
903:
900:
883:In his words:
881:
880:
868:
865:
862:
859:
856:
853:
850:
844:
841:
837:
825:
813:
792:
789:
778:
766:
763:
760:
757:
754:
751:
747:
744:
740:
737:
734:
731:
728:
725:
721:
718:
714:
711:
692:
689:
670:
666:
662:
659:
656:
651:
647:
643:
617:
614:
575:
572:
570:
564:
525:Godavari river
427:
417:
414:
319:Bhāskarāchārya
290:
289:
286:
285:
284:
283:
280:
275:
269:
263:
256:
252:
251:
238:
237:Main interests
234:
233:
230:
226:
225:
220:
216:
215:
211:
210:
207:
206:
203:
199:
198:
195:
191:
190:
187:Madhya Pradesh
181:
168:
164:
163:
140:
131:
127:
126:
120:
112:
111:
108:
101:
100:
79:. Knowledge's
40:
38:
31:
15:
9:
6:
4:
3:
2:
4174:
4163:
4160:
4158:
4155:
4153:
4150:
4148:
4145:
4143:
4140:
4138:
4135:
4133:
4130:
4128:
4125:
4123:
4120:
4118:
4115:
4114:
4112:
4097:
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4087:
4084:
4082:
4079:
4077:
4074:
4072:
4069:
4067:
4064:
4062:
4059:
4057:
4054:
4053:
4051:
4045:
4039:
4036:
4034:
4031:
4029:
4026:
4024:
4021:
4019:
4016:
4015:
4013:
4011:Other regions
4009:
4003:
4002:David Pingree
4000:
3998:
3995:
3993:
3990:
3989:
3987:
3983:
3976:
3973:
3970:
3967:
3964:
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3955:
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3949:
3946:
3943:
3940:
3937:
3935:
3932:
3929:
3926:
3923:
3920:
3917:
3916:M. Rangacarya
3914:
3911:
3908:
3905:
3902:
3899:
3896:
3895:
3893:
3889:Historians of
3887:
3880:
3876:
3872:
3868:
3864:
3863:Jantar Mantar
3861:
3859:
3856:
3855:
3853:
3849:
3843:
3840:
3838:
3834:
3832:
3829:
3827:
3824:
3823:
3821:
3815:
3809:
3808:
3804:
3802:
3801:
3797:
3795:
3794:
3790:
3788:
3787:
3783:
3781:
3780:
3776:
3774:
3773:
3769:
3767:
3766:
3762:
3760:
3759:
3755:
3753:
3752:
3748:
3746:
3745:
3741:
3739:
3738:
3734:
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3727:
3725:
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3720:
3718:
3717:
3713:
3711:
3710:
3706:
3704:
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3699:
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3692:
3690:
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3683:
3682:
3678:
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3663:
3659:
3658:
3656:
3652:
3642:
3639:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3617:
3614:
3612:
3609:
3607:
3604:
3602:
3599:
3597:
3594:
3592:
3589:
3587:
3584:
3582:
3579:
3577:
3574:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
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3553:
3551:
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3536:
3533:
3531:
3528:
3526:
3523:
3521:
3518:
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3513:
3511:
3508:
3506:
3503:
3501:
3498:
3496:
3493:
3491:
3488:
3486:
3483:
3481:
3480:Mahendra Sūri
3478:
3476:
3473:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3436:
3433:
3431:
3428:
3426:
3423:
3421:
3418:
3416:
3413:
3412:
3410:
3406:
3400:
3397:
3395:
3392:
3390:
3387:
3385:
3382:
3380:
3377:
3375:
3372:
3370:
3367:
3366:
3364:
3360:
3357:
3355:
3351:
3347:
3340:
3335:
3333:
3328:
3326:
3321:
3320:
3317:
3311:
3308:
3307:
3297:
3291:
3287:
3286:
3280:
3277:
3276:
3271:
3268:
3264:
3260:
3259:
3254:
3253:"Bhāskara II"
3250:
3245:
3242:
3241:Penguin Books
3238:
3234:
3231:
3227:
3226:
3217:
3211:
3207:
3206:
3200:
3197:
3191:
3187:
3186:
3179:
3176:
3170:
3166:
3162:
3158:
3154:
3150:
3147:
3141:
3136:
3135:
3128:
3125:
3119:
3115:
3110:
3106:
3101:
3098:
3096:0-471-18082-3
3092:
3088:
3084:
3080:
3075:
3072:
3070:9780691120676
3066:
3062:
3061:
3055:
3052:
3050:9780691114859
3046:
3042:
3037:
3034:
3032:9780871691460
3028:
3024:
3023:
3017:
3013:
3009:
3004:
3001:
2995:
2991:
2987:
2983:
2980:
2974:
2970:
2969:
2963:
2960:
2955:
2951:
2946:
2942:
2937:
2934:
2928:
2924:
2919:
2916:
2910:
2906:
2901:
2898:
2892:
2888:
2883:
2882:
2869:
2865:
2859:
2844:
2843:
2838:
2832:
2825:
2820:
2814:, p. 477
2813:
2808:
2806:
2798:
2793:
2787:, p. 106
2786:
2781:
2775:, p. 228
2774:
2769:
2762:
2757:
2750:
2745:
2738:
2733:
2727:
2723:
2719:
2715:
2714:mean ecliptic
2711:
2708:
2704:
2699:
2684:
2680:
2674:
2667:
2662:
2655:
2650:
2641:
2639:
2637:
2627:
2621:, p. 74.
2620:
2615:
2613:
2603:
2601:
2593:
2590:
2584:
2569:
2565:
2556:
2554:
2552:
2550:
2548:
2538:
2529:
2521:
2520:
2515:
2509:
2502:
2498:
2497:
2490:
2483:
2478:
2476:
2460:
2456:
2447:
2445:
2443:
2441:
2439:
2437:
2435:
2433:
2431:
2429:
2427:
2425:
2423:
2416:, p. 79.
2415:
2410:
2404:, p. 71.
2403:
2398:
2391:
2386:
2380:, p. 50.
2379:
2374:
2365:
2356:
2347:
2339:
2337:9788123024851
2333:
2329:
2325:
2318:
2309:
2301:
2297:
2293:
2287:
2283:
2282:
2274:
2266:
2262:
2258:
2257:
2249:
2247:
2237:
2229:
2223:
2219:
2218:
2210:
2208:
2203:
2190:
2184:
2180:
2171:
2168:
2166:
2165:Bride's Chair
2163:
2161:
2158:
2157:
2151:
2149:
2144:
2142:
2139:launched the
2138:
2133:
2131:
2127:
2123:
2113:
2109:
2105:
2101:
2097:
2094:
2092:
2081:
2079:
2078:
2067:
2065:
2060:
2058:
2054:
2041:
2038:
2034:
2031:
2028:
2025:
2023:calculations.
2022:
2019:
2016:
2013:
2010:
2006:
2003:
2000:
1997:
1994:
1990:
1987:
1983:
1980:
1977:
1974:
1973:
1972:
1966:
1963:
1959:
1956:
1953:
1950:
1946:
1942:
1939:
1936:
1933:
1930:
1927:
1924:
1921:
1918:
1915:
1912:
1909:
1905:
1901:
1898:
1895:
1891:
1887:
1886:
1885:
1882:
1880:
1876:
1871:
1869:
1865:
1864:sidereal year
1861:
1851:
1849:
1845:
1841:
1840:Kerala School
1837:
1830:
1826:
1822:
1818:
1813:
1810:
1806:
1793:
1792:
1787:
1782:
1778:
1777:
1760:
1754:
1751:
1745:
1742:
1739:
1733:
1727:
1721:
1718:
1715:
1709:
1703:
1700:
1680:
1677:
1674:
1666:
1651:
1648:
1645:
1642:
1639:
1616:
1596:
1593:
1589:
1586:
1583:
1578:
1575:
1554:
1551:
1547:
1544:
1541:
1537:
1534:
1530:
1527:
1524:
1520:
1512:
1508:
1507:
1506:
1504:
1498:
1496:
1492:
1488:
1484:
1480:
1476:
1475:
1464:
1449:
1445:
1442:
1439:
1435:
1431:
1428:
1407:
1403:
1400:
1397:
1393:
1389:
1386:
1377:
1373:
1369:
1368:
1357:
1355:
1351:
1349:
1340:
1337:
1334:
1331:
1328:
1324:
1321:
1318:
1315:
1311:
1308:(for solving
1307:
1306:
1302:
1299:
1296:
1293:
1290:
1287:
1284:Positive and
1283:
1282:
1281:
1279:
1275:
1271:
1270:
1265:
1255:
1253:
1245:
1241:
1237:
1233:
1230:
1226:
1223:
1222:rule of three
1219:
1216:
1212:
1208:
1205:
1201:
1198:
1194:
1190:
1187:
1183:
1179:
1176:
1175:
1174:
1172:
1168:
1166:
1162:
1161:indeterminate
1158:
1154:
1150:
1146:
1145:
1140:
1127:
1126:trigonometric
1123:
1119:
1115:
1112:
1109:
1105:
1101:
1098:
1094:
1090:
1087:
1083:
1080:
1079:infinitesimal
1076:
1073:
1069:
1066:
1062:
1058:
1055:
1051:
1047:
1043:
1039:
1036:Solutions of
1035:
1032:
1028:
1024:
1020:
1017:
1013:
1009:
1005:
1001:
997:
993:
990:
986:
985:
980:
977:
973:
969:
965:
962:
959:
955:
951:
947:
943:
940:
936:
932:
928:
924:
920:
919:
918:
913:
908:
899:
896:
892:
890:
884:
866:
863:
860:
857:
854:
851:
848:
842:
839:
835:
826:
811:
790:
787:
779:
764:
761:
758:
752:
749:
745:
742:
735:
732:
729:
726:
723:
719:
716:
712:
709:
702:
701:
700:
698:
688:
686:
668:
664:
660:
657:
654:
649:
645:
641:
633:
632:
627:
623:
613:
611:
607:
603:
599:
591:
590:
585:
580:
569:
563:
561:
557:
552:
550:
546:
542:
538:
534:
530:
526:
522:
516:
513:
509:
507:
503:
498:
496:
492:
488:
484:
480:
479:
474:
470:
466:
462:
455:
449:
440:
432:
425:
423:
413:
411:
407:
403:
402:
397:
396:
391:
387:
385:
380:
376:
371:
369:
365:
361:
356:
352:
351:Western Ghats
348:
344:
343:mathematician
340:
320:
312:
310:
304:
296:
287:
281:
279:
276:
273:
270:
267:
264:
262:
259:
258:
257:
255:Notable works
253:
250:
246:
242:
239:
235:
231:
227:
224:
221:
217:
214:Academic work
212:
208:
204:
202:Occupation(s)
200:
197:Bhāskarācārya
196:
192:
188:
184:
169:
165:
160:
156:
152:
148:
144:
141:Vijjadavida,
132:
128:
124:
118:
113:
106:
97:
87:
82:
78:
71:
61:
51:
44:
39:
30:
29:
26:
22:
4132:1110s births
4049:institutions
3969:K. S. Shukla
3941:(1892– 1953)
3807:Yavanajataka
3805:
3798:
3791:
3784:
3777:
3770:
3765:Śulba Sūtras
3763:
3756:
3751:Sadratnamala
3749:
3742:
3735:
3728:
3721:
3714:
3707:
3700:
3695:Kanakkusaram
3693:
3686:
3679:
3672:
3660:
3530:Varāhamihira
3495:Parameshvara
3450:Govindasvāmi
3429:
3420:Āryabhaṭa II
3283:
3274:
3272:Ian Pearce.
3256:
3236:
3229:
3204:
3188:, Springer,
3182:
3167:, Springer,
3164:
3160:
3133:
3113:
3104:
3082:
3059:
3040:
3021:
3011:
3007:
2989:
2967:
2958:
2949:
2940:
2922:
2904:
2886:
2879:Bibliography
2858:
2846:. Retrieved
2840:
2831:
2819:
2812:Plofker 2007
2792:
2780:
2768:
2756:
2744:
2732:
2717:
2698:
2686:. Retrieved
2682:
2673:
2661:
2649:
2626:
2592:Plofker 2007
2588:
2583:
2572:, retrieved
2570:, p. 21
2567:
2537:
2528:
2518:
2508:
2500:
2495:
2489:
2482:Pingree 1970
2463:, retrieved
2461:, p. 17
2458:
2414:Poulose 1991
2409:
2402:Plofker 2009
2397:
2385:
2373:
2364:
2355:
2346:
2327:
2317:
2308:
2280:
2273:
2255:
2236:
2216:
2183:
2147:
2145:
2134:
2119:
2111:
2107:
2103:
2099:
2095:
2090:
2087:
2075:
2074:In his book
2073:
2064:Yaṣṭi-yantra
2063:
2061:
2050:
1970:
1955:Conjunctions
1883:
1872:
1857:
1844:Parameshvara
1834:
1828:
1824:
1821:Parameshvara
1809:differential
1789:
1499:
1487:trigonometry
1472:
1470:
1365:
1363:
1360:Trigonometry
1347:
1344:
1303:
1277:
1274:square roots
1267:
1263:
1261:
1251:
1249:
1177:Definitions.
1170:
1169:
1165:combinations
1142:
1136:
1117:
1099:coefficient.
1097:differential
1045:
1041:
1026:
1022:
1015:
1011:
1007:
1003:
999:
982:
975:
971:
967:
945:
938:
934:
930:
916:
897:
894:
886:
882:
696:
694:
629:
621:
619:
605:
601:
597:
595:
587:
583:
567:
556:astronomical
553:
518:
514:
511:
499:
476:
472:
468:
458:
428:
419:
409:
405:
399:
393:
382:
372:
318:
306:
302:
301:
249:trigonometry
176:(1185-00-00)
91:
77:ISO 639 code
73:}}
67:{{
63:}}
57:{{
53:}}
47:{{
42:
25:
4142:Algebraists
4137:1185 deaths
3985:Translators
3977:(1919–2005)
3975:K. V. Sarma
3971:(1918–2007)
3965:(1918–1992)
3959:(1918–2000)
3953:(1903–1978)
3947:(1901–1954)
3945:A. N. Singh
3930:(1888–1958)
3928:B. B. Datta
3924:(1876–1962)
3918:(1861–1916)
3912:(1855–1910)
3906:(1853–1898)
3900:(1821–1900)
3891:mathematics
3835:Symbol for
3819:innovations
3716:Lokavibhaga
3662:Aryabhatiya
3460:Jyeṣṭhadeva
3445:Brahmagupta
3430:Bhāskara II
3415:Āryabhaṭa I
3399:Yajnavalkya
2848:21 February
2785:Burton 2011
2654:Shukla 1984
2574:12 November
2465:12 November
2390:Chopra 1982
2170:Bījapallava
2091:Hindu proof
2047:Engineering
1993:mean motion
1982:Cosmography
1860:Brahmagupta
1240:renaissance
1184:(including
1137:Bhaskara's
989:Renaissance
902:Mathematics
697:Grahagaṇita
691:Grahaganita
610:measurement
483:Brahmagupta
406:Grahagaṇita
355:Maharashtra
303:Bhāskara II
174: 1185
143:Maharashtra
137: 1114
109:Bhāskara II
4111:Categories
3934:T. Hayashi
3817:Pioneering
3800:Yuktibhāṣā
3723:Pātīgaṇita
3674:Bijaganita
3631:Ravi Vakil
3485:Munishvara
3465:Kamalakara
3440:Brahmadeva
3425:Bhāskara I
3374:Baudhayana
2797:Mazur 2005
2749:Selin 2008
2737:White 1978
2666:Cooke 1997
2589:Bijaganita
2568:Vijayavani
2459:Vijayavani
2378:Sahni 2019
2198:References
2189:Bhāskara I
2128:in Delhi,
1991:Planetary
1902:The three
1890:longitudes
1850:in India.
1348:chakravala
1278:Bījaganita
1264:Bījaganita
1139:arithmetic
1133:Arithmetic
1067:solutions.
1065:irrational
1016:chakravala
622:Bījagaṇita
616:Bijaganita
606:aṅkagaṇita
602:pāṭīgaṇita
582:Page from
506:Munishvara
422:Āryā metre
410:Golādhyāya
401:Bījagaṇita
347:astronomer
341:polymath,
337:), was an
272:Bījagaṇita
245:arithmetic
229:Discipline
159:Marathwada
145:(probably
94:March 2022
21:Bhāskara I
3963:S. N. Sen
3871:New Delhi
3793:Veṇvāroha
3654:Treatises
3455:Halayudha
3408:Classical
3379:Katyayana
3369:Apastamba
2925:, Plume,
2773:Eves 1990
2514:Bhau Daji
2300:464078172
2124:in Pune,
2084:"Behold!"
2002:epicyclic
1999:Eccentric
1986:geography
1932:Latitudes
1854:Astronomy
1811:vanishes.
1755:
1743:−
1734:≈
1722:
1716:−
1704:
1678:≈
1609:for some
1443:−
1432:
1390:
1244:Aryabhata
994:A cyclic
950:quadratic
864:
852:
804:close to
762:
750:−
736:≈
730:
724:−
713:
549:Telangana
541:Karnataka
495:Patnadevi
461:Shaka era
223:Shaka era
123:Patnadevi
4157:Acharyas
3879:Varanasi
3837:zero (0)
3709:Līlāvatī
3576:C.R. Rao
3540:Virasena
3520:Sridhara
3490:Narayana
3475:Mahāvīra
3014:: 95–104
2868:Archived
2824:Bhaskara
2154:See also
2077:Lilavati
1949:crescent
1914:Syzygies
1904:problems
1848:calculus
1829:Lilavati
1781:ecliptic
1579:′
1467:Calculus
1252:Lilavati
1229:interest
1220:Inverse
1215:squaring
1186:division
1171:Līlāvatī
1144:Līlāvatī
1082:calculus
1061:negative
946:Lilavati
791:′
746:′
720:′
598:Līlāvatī
584:Lilavati
574:Līlāvatī
521:Vidarbha
491:Mahāvīra
487:Śrīdhara
395:Līlāvatī
390:Sanskrit
368:Godavari
266:Līlāvatī
151:Khandesh
4018:Babylon
3851:Centres
3515:Śrīpati
3394:Pingala
3362:Ancient
3269:, 2000.
3243:, 2000.
3087:213–215
2722:Bibcode
2710:seconds
2265:4136967
2070:Legends
2037:seasons
2021:Ellipse
1894:planets
1892:of the
1836:Madhava
1799:⁄
1794:, or a
1567:, then
1305:Kuṭṭaka
1269:Algebra
1258:Algebra
1236:Kuṭṭaka
1102:Stated
1018:method.
984:Kuṭṭaka
958:quartic
631:kuṭṭaka
533:Bijapur
326:
241:Algebra
86:See why
4047:Modern
4038:Europe
4028:Greece
3875:Ujjain
3867:Jaipur
3549:Modern
3389:Pāṇini
3384:Manava
3292:
3212:
3192:
3171:
3142:
3120:
3093:
3067:
3047:
3029:
2996:
2975:
2929:
2911:
2893:
2688:24 May
2334:
2298:
2288:
2263:
2224:
2116:Legacy
1879:sphere
1637:
1350:method
1213:, and
1157:gnomon
1044:+ 1 =
685:Fermat
560:Ujjain
463:(1114
379:Ujjain
339:Indian
183:Ujjain
4023:China
2176:Notes
2057:wheel
1962:stars
1888:Mean
1801:33750
1791:truti
1693:then
1629:with
1298:Surds
1197:surds
1141:text
1054:Euler
954:cubic
545:Basar
537:Bidar
147:Patan
4096:TIFR
3290:ISBN
3210:ISBN
3190:ISBN
3169:ISBN
3140:ISBN
3118:ISBN
3091:ISBN
3065:ISBN
3045:ISBN
3027:ISBN
2994:ISBN
2973:ISBN
2927:ISBN
2909:ISBN
2891:ISBN
2850:2021
2842:IIST
2690:2023
2576:2019
2467:2019
2332:ISBN
2296:OCLC
2286:ISBN
2261:OCLC
2222:ISBN
2035:The
2007:The
1984:and
1945:Moon
1943:The
1868:days
1649:<
1643:<
1493:and
1481:and
1421:and
1364:The
1312:and
1262:His
1195:and
1182:zero
1095:and
1063:and
956:and
927:area
777:for.
566:The
408:and
323:lit.
167:Died
155:Beed
130:Born
50:lang
1947:'s
1906:of
1752:cos
1719:sin
1701:sin
1505:'.
1429:sin
1387:sin
1116:In
944:In
861:cos
849:sin
759:cos
727:sin
710:sin
604:or
547:in
539:in
535:or
219:Era
157:in
153:or
149:in
70:IPA
4113::
3877:,
3873:,
3869:,
3261:,
3255:,
3251:,
3163:,
3155:;
3089:,
3081:,
3012:19
3010:,
2839:.
2804:^
2707:SI
2681:.
2635:^
2611:^
2599:^
2566:,
2546:^
2474:^
2457:,
2421:^
2326:.
2294:.
2245:^
2206:^
1881:.
1489:,
1463:.
1316:).
1266:("
1167:.
1151:,
1027:ny
1025:−
1010:=
1006:+
1004:bx
1002:+
1000:ax
978:).
974:=
970:+
968:ax
952:,
937:=
933:+
642:61
489:,
485:,
465:CE
424::
404:,
398:,
370:.
345:,
315:c.
313:;
247:,
243:,
185:,
171:c.
134:c.
55:,
3881:)
3865:(
3338:e
3331:t
3324:v
3298:.
3165:2
2852:.
2763:.
2724::
2692:.
2340:.
2302:.
2267:.
2230:.
2191:,
2039:.
2017:.
2011:.
1995:.
1988:.
1964:.
1951:.
1940:.
1928:.
1922:.
1916:.
1896:.
1831:.
1797:1
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1758:(
1749:)
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1740:y
1737:(
1731:)
1728:x
1725:(
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1710:y
1707:(
1681:y
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1617:x
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1587:x
1584:(
1576:f
1555:0
1552:=
1548:)
1545:b
1542:(
1538:f
1535:=
1531:)
1528:a
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1521:f
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1450:)
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1436:(
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1401:+
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1394:(
1288:.
1217:.
1206:.
1204:π
1199:.
1088:.
1074:.
1046:y
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1008:c
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939:c
935:b
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855:y
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840:d
836:d
812:y
788:y
765:y
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753:y
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739:(
733:y
717:y
669:2
665:y
661:=
658:1
655:+
650:2
646:x
452:॥
443:।
435:ऽ
388:(
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321:(
305:(
274:,
268:,
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