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2543:"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)"
306:
573:, 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.
45:
1389:
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
1825:
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
2091:, 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 ".
1511:
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
1921:. 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.
392:, 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
589:
423:, 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.
2099:
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
368:
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.
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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.
888:
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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.
1830:, 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
1184:
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:
1618:
360:
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
1472:
1430:
1249:), 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
4101:
1877:, 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
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1381:(written in 1150) demonstrates Bhaskara's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed
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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
813:
3284:
1363:
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 "
519:(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:
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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"
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2077:. This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale.
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However, as mathematics historian Kim
Plofker points out, after presenting a worked-out example, Bhaskara II states the Pythagorean theorem:
710:, while treating the motion of planets, he considered their instantaneous speeds. He arrived at the approximation: It consists of 451 verses
635:(Algebra) has 213 verses. It discusses zero, infinity, positive and negative numbers, and indeterminate equations including (the now called)
2111:
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.
4157:
2379:
Algebra with
Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bhascara by Henry Colebrooke, Scholiasts of Bhascara p., xxvii
1025:. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the
3621:
2527:(1865). "Brief Notes on the Age and Authenticity of the Works of Aryabhata, Varahamihira, Brahmagupta, Bhattotpala and Bhaskaracharya".
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In computing the instantaneous motion of a planet, the time interval between successive positions of the planets was no greater than a
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2361:गणिती (Marathi term meaning Mathematicians) by Achyut Godbole and Dr. Thakurdesai, Manovikas, First Edition 23, December 2013. p. 34.
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538:. However scholars differ about the exact location. Many scholars have placed the place near Patan in Chalisgaon Taluka of
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position the differential of the equation of the centre is equal to zero. In this result, there are traces of the general
1678:
In this astronomical work he gave one procedure that looks like a precursor to infinitesimal methods. In terms that is if
1261:
His work is outstanding for its systematisation, improved methods and the new topics that he introduced. Furthermore, the
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This result had also been observed earlier by Muñjalācārya (or Mañjulācārya) mānasam, in the context of a table of sines.
1707:
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in the 7th century, Bhāskara accurately defined many astronomical quantities, including, for example, the length of the
1819:
716:
2226:
1527:
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covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions,
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2009:
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whereas a section of scholars identified it with the modern day Beed city. Some sources identified
Vijjalavida as
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who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as
1857:) from the 14th century to the 16th century expanded on Bhaskara's work and further advanced the development of
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2123:
Plofker suggests that this additional statement may be the ultimate source of the widespread "Behold!" legend.
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70:
1488:, is an astronomical treatise and contains many theories not found in earlier works. Preliminary concepts of
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1965:
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523:सह्यकुलपर्वतान्तर्गत भूप्रदेशे महाराष्ट्रदेशान्तर्गतविदर्भपरपर्यायविराटदेशादपि निकटे गोदावर्यां नातिदूरे
370:
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family of scholars, mathematicians and astronomers, Bhaskara II was the leader of a cosmic observatory at
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2012:
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374:
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3001:
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd edition)
305:
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Indian Journal of History of Science, Volume 35, National Institute of Sciences of India, 2000, p. 77
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1914:
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648:
1283:") was a work in twelve chapters. It was the first text to recognize that a positive number has two
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2976:
White, Lynn Townsend (1978), "Tibet, India, and Malaya as Sources of Western Medieval Technology",
1885:
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Calculated the derivatives of trigonometric functions and formulae. (See Calculus section below.)
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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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555:
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3118:, Ravivarma Samskr̥ta granthāvali, vol. 22, Govt. Sanskrit College (Tripunithura, India)
1888:
is written in two parts: the first part on mathematical astronomy and the second part on the
364:, believed to be the town of Patana in Chalisgaon, located in present-day Khandesh region of
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619:), named after his daughter, consists of 277 verses. It covers calculations, progressions,
432:
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2510:. Bennett, Coleman & Company, Limited, at the Times of India Press. 1974. p. 30.
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of a second, and his measure of velocity was expressed in this infinitesimal unit of time.
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Bhāskara also stated that at its highest point a planet's instantaneous speed is zero.
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378:
197:
3399:
3170:, eds. (2001), "Mathematics across cultures: the history of non-western mathematics",
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3435:
3251:
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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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1936:
1930:
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1982:
The second part contains thirteen chapters on the sphere. It covers topics such as:
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that is a derivative of sine although he did not develop the notion on derivative.
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259:
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2617:
Mathematical Achievements of Pre-modern Indian Mathematicians von T.K Puttaswamy
2003:
1992:
1870:
1284:
1250:
1175:
1059:. This very equation was posed as a problem in 1657 by the French mathematician
999:
620:
493:
365:
153:
2267:
Studies in Indology and Medieval History: Prof. G. H. Khare Felicitation Volume
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And otherwise, when one has set down those parts of the figure there seeing .
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516:
475:
411:
357:
282:
255:
169:
17:
2370:
Mathematics in India by Kim Plofker, Princeton University Press, 2009, p. 182
2310:
3803:
3465:
3425:
3052:
The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
2524:
2228:
The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
2131:
A number of institutes and colleges in India are named after him, including
1996:
1900:
1343:
Solutions of indeterminate equations of the second, third and fourth degree.
1254:
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471:
233:
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133:
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457:
448:
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405:
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276:
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1291:
is effectively a treatise on algebra and contains the following topics:
1117:, a special case of one of the most important theorems in analysis, the
3404:
3050:
Plofker, Kim (2007), "Mathematics in India", in Katz, Victor J. (ed.),
2259:
2257:
2031:
1794:, a quantity required for accurately predicting the time of an eclipse.
1279:
1121:. Traces of the general mean value theorem are also found in his works.
928:
Some of Bhaskara's contributions to mathematics include the following:
543:
251:
3017:
Shukla, Kripa Shankar (1984), "Use of Calculus in Hindu Mathematics",
1524:
in his work. The modern formulation of Rolle's theorem states that if
3394:
3325:
2720:
2047:
1904:
1889:
1167:
998:). The rules he gives are (in effect) the same as those given by the
695:
570:
389:
193:
3299:. Vol. 2. New York: Charles Scribner's Sons. pp. 115–120.
2341:. Publications Division Ministry of Information & Broadcasting.
1330:
Simple equations (indeterminate of second, third and fourth degree).
486:
was completed during 1150 CE. He also wrote another work called the
2141:
Bhaskaracharya Institute For Space Applications and Geo-Informatics
992:
Integer solutions of linear and quadratic indeterminate equations (
1801:
1032:
The first general method for finding the solutions of the problem
916:
588:
547:
2530:
Journal of the Royal Asiatic Society of Great Britain and Ireland
1818:
He was aware that when a variable attains the maximum value, its
1070:
Solved quadratic equations with more than one unknown, and found
3652:
Shanti Swarup Bhatnagar Prize recipients in Mathematical Science
2852:
1972:
1955:
1790:
Bhaskara uses this result to work out the position angle of the
937:
165:
3329:
2073:
Bhāskara II invented a variety of instruments one of which is
1878:
530:
This description locates Vijjalavida in Maharashtra, near the
38:
2641:
Students& Britannica India. 1. A to C by Indu Ramchandani
900:
bimbārdhasya koṭijyā guṇastrijyāhāraḥ phalaṃ dorjyāyorantaram
508:
located near Patan (Chalisgaon) in the vicinity of Sahyadri.
2161:, an Indian documentary short on the mathematician in 2015.
1895:
The twelve chapters of the first part cover topics such as:
977:
Solutions of indeterminate quadratic equations (of the type
603:. Use of the Pythagorean theorem in the corner. 1650 edition
403:
for "Crown of Treatises") is divided into four parts called
3248:
The Crest of the Peacock: Non-European Roots of Mathematics
2717:
1214:
1063:, but its solution was unknown in Europe until the time of
940:
in two different ways and then cancelling out terms to get
3853:
Infinite series expansions for the trigonometric functions
2625:
2623:
492:
when he was 69 (in 1183). His works show the influence of
3847:
2552:
B.I.S.M. quarterly, Poona, Vol. 63, No. 1, 1984, pp 14-22
2488:
2486:
3145:
Toward a global science: mining civilizational knowledge
2066:
machine date back to 1150, when Bhāskara II described a
1302:
The 'unknown' (includes determining unknown quantities).
2289:
K. V. Ramesh; S. P. Tewari; M. J. Sharma, eds. (1990).
1508:
that are found in the work are of particular interest.
504:, Padmanābha and other predecessors. Bhaskara lived in
2970:
Arithmetic and mensuration of Brahmegupta and Bhaskara
2198:
to avoid confusion with the 7th century mathematician
4102:
Ramanujan Institute for Advanced Study in Mathematics
3289:
at the MacTutor archive. St Andrews University, 2002.
2690:"The Great Bharatiya Mathematician Bhaskaracharya ll"
1710:
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719:
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3418:
3372:
3363:
2999:, ed. (2008), "Astronomical Instruments in India",
1780:{\displaystyle \sin(y)-\sin(x)\approx (y-x)\cos(y)}
1311:(includes evaluating surds and their square roots).
1202:Further extensive numerical work, including use of
265:
247:
239:
229:
224:
212:
204:
177:
140:
118:
3142:
2979:Medieval religion and technology: collected essays
2270:. Joshi & Lokhande Prakashan. pp. 42–47.
1779:
1696:
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1632:
1612:
1570:
1466:
1424:
882:
827:
807:
781:{\displaystyle \sin y'-\sin y\approx (y'-y)\cos y}
780:
686:
3036:, vol. 146, American Philosophical Society,
1571:{\displaystyle f\left(a\right)=f\left(b\right)=0}
459:Rasa-guṇa-varṣeṇa mayā siddhānta-śiromaṇī racitaḥ
86:for phonetic transcriptions, with an appropriate
1287:(a positive and negative square root). His work
1009:for solving indeterminate equations of the form
698:and his European contemporaries centuries later
2117:
2109:
1349:Quadratic equations with more than one unknown.
896:
521:
437:
27:Indian mathematician and astronomer (1114–1185)
3341:
3241:A Short Account of the History of Mathematics
2918:(6th ed.), Saunders College Publishing,
2916:An Introduction to the History of Mathematics
2875:"Great Indian Mathematician - Bhaskaracharya"
2651:
2649:
2647:
2613:
2611:
1352:Operations with products of several unknowns.
565:Bhāskara is said to have been the head of an
470:This reveals that he was born in 1036 of the
8:
3114:Poulose, K. G. (1991), K. G. Poulose (ed.),
2154:honouring the mathematician and astronomer.
1333:Simple equations with more than one unknown.
1002:European mathematicians of the 17th century.
883:{\displaystyle {\frac {d}{dy}}\sin y=\cos y}
309:Bhaskara's proof of the Pythagorean Theorem.
3293:Pingree, David (1970–1980). "Bhāskara II".
2961:The positive sciences of the ancient Hindus
2898:The History of Mathematics: An Introduction
2818:
2816:
2716:. An SI day or mean solar day equals 86400
2231:. Princeton University press. p. 447.
1971:Conjunctions of the planets with the fixed
1095:, along with notable contributions towards
333:
3869:Kerala school of astronomy and mathematics
3369:
3348:
3334:
3326:
3094:The History of Mathematics: A Brief Course
2771:
2723:. From the mean longitude referred to the
2655:50 Timeless Scientists von K.Krishna Murty
2507:The Illustrated Weekly of India, Volume 95
2457:
2455:
2453:
2137:Bhaskaracharya College of Applied Sciences
1139:results. (See Trigonometry section below.)
645:method. In particular, he also solved the
115:
3116:Scientific heritage of India, mathematics
2629:
2566:
2564:
2562:
2560:
2558:
2451:
2449:
2447:
2445:
2443:
2441:
2439:
2437:
2435:
2433:
2264:M. S. Mate; G. T. Kulkarni, eds. (1974).
2148:Indian Space Research Organisation (ISRO)
1869:Using an astronomical model developed by
1709:
1683:
1645:
1625:
1583:
1529:
1437:
1395:
844:
842:
820:
795:
718:
678:
659:
650:
442:Rasa-guṇa-pūrṇa-mahī-sama-śakanṛpa-samaye
4097:Homi Bhabha Centre for Science Education
3243:, 4th Edition. Dover Publications, 1960.
3033:Census of the Exact Sciences in Sanskrit
515:family near Vijjadavida (Vijjalavida).
304:
3269:MacTutor History of Mathematics Archive
2877:. indiavideodotorg. 22 September 2015.
2822:
2602:
2492:
2424:
2412:
2214:
2191:
2881:from the original on 12 December 2021.
2795:
2664:
2400:
2339:Cultural Leaders of India - Scientists
2225:Victor J. Katz, ed. (10 August 2021).
2220:
2218:
2053:Problems of astronomical calculations.
1520:There is evidence of an early form of
2807:
2759:
2747:
2676:
2574:ನವ ಜನ್ಮಶತಾಬ್ದಿಯ ಗಣಿತರ್ಷಿ ಭಾಸ್ಕರಾಚಾರ್ಯ
2465:ನವ ಜನ್ಮಶತಾಬ್ದಿಯ ಗಣಿತರ್ಷಿ ಭಾಸ್ಕರಾಚಾರ್ಯ
2388:
1467:{\displaystyle \sin \left(a-b\right)}
1425:{\displaystyle \sin \left(a+b\right)}
1199:, and rules of operations with zero).
554:. Identification of Vijjalavida with
318:
7:
3019:Indian Journal of History of Science
2783:
2295:. Agam Kala Prakashan. p. 119.
1496:, along with a number of results in
3622:Subbayya Sivasankaranarayana Pillai
2462:S. Balachandra Rao (13 July 2014),
2070:that he claimed would run forever.
243:Mathematician, astronomer, geometer
4128:12th-century Indian mathematicians
4082:Institute of Mathematical Sciences
3296:Dictionary of Scientific Biography
3196:Undergraduate Texts in Mathematics
3125:Religions and communities of India
2982:, University of California Press,
2037:First visibilities of the planets.
1613:{\displaystyle f'\left(x\right)=0}
1367:") is of considerable importance.
1235:, and rules of 3, 5, 7, 9, and 11.
623:, permutations, and other topics.
76:for transliterated languages, and
56:of its non-English content, using
25:
4092:Harish-Chandra Research Institute
3602:K. R. Parthasarathy (probabilist)
2292:Dr. G. S. Gai Felicitation Volume
534:region and close to the banks of
2959:Seal, Sir Brajendranath (1915),
2104:, well known by schoolchildren.
1884:His mathematical astronomy text
1390:the now well known formulae for
126:
43:
4133:12th-century Indian astronomers
3096:, Wiley-Interscience, pp.
3090:"The Mathematics of the Hindus"
2040:Calculating the lunar crescent.
1968:of the planets with each other.
1910:True longitudes of the planets.
1881:, a difference of 3.5 minutes.
1385:, along with other interesting
1305:Determining unknown quantities.
1220:Arithmetical terms, methods of
1051:of the second order, such as 61
687:{\displaystyle 61x^{2}+1=y^{2}}
4077:Chennai Mathematical Institute
3446:Melpathur Narayana Bhattathiri
3141:Goonatilake, Susantha (1999),
3074:, Princeton University Press,
3054:, Princeton University Press,
1986:Praise of study of the sphere.
1978:The paths of the Sun and Moon.
1774:
1768:
1759:
1747:
1741:
1735:
1723:
1717:
1257:and subsequent mathematicians.
766:
749:
92:multilingual support templates
1:
3194:Mathematics and its history,
3030:Pingree, David Edwin (1970),
2968:Colebrooke, Henry T. (1817),
2900:(7th ed.), McGraw Hill,
2171:List of Indian mathematicians
1838:, a commentary on Bhaskara's
1668:{\displaystyle \ a<x<b}
1135:along with a number of other
377:residing on the banks of the
325:
181:
144:
4067:Indian Statistical Institute
3149:, Indiana University Press,
2950:Sarkār, Benoy Kumar (1918),
2714:IERS EOP PC Useful constants
2062:The earliest reference to a
1044:") was given by Bhaskara II.
921:Bhaskaracharya proof of the
478:), and that he composed the
4158:Scientists from Maharashtra
4087:Indian Institute of Science
4072:Bhaskaracharya Pratishthana
3950:A. A. Krishnaswamy Ayyangar
3915:Shankar Balakrishna Dikshit
3842:Hindu–Arabic numeral system
3246:George Gheverghese Joseph.
2133:Bhaskaracharya Pratishthana
1834:in the 15th century in the
1356:Bhaskara derived a cyclic,
899:
526:पंचक्रोशान्तरे विज्जलविडम्।
458:
449:
441:
4189:
3582:Subrahmanyan Chandrasekhar
3219:, Vikas Publishing House,
3123:Chopra, Pran Nath (1982),
2729:Astronomy and Astrophysics
2571:Scientist (13 July 2014),
2157:Invis Multimedia released
1853:mathematicians (including
1697:{\displaystyle x\approx y}
482:when he was 36 years old.
328:1114–1185), also known as
293:Grahagaṇita and Golādhyāya
29:
4163:Scholars from Maharashtra
3592:Veeravalli S. Varadarajan
2963:, Longmans, Green and co.
2954:, Longmans, Green and co.
2896:Burton, David M. (2011),
2333:T. A. Saraswathi (2017).
2043:Astronomical instruments.
1340:(of the type ax + b = y).
1245:Indeterminate equations (
1242:and interest computation.
562:has also been suggested.
299:
220:
216:Astronomer, mathematician
132:Statue of Bhaskara II at
125:
4008:Henry Thomas Colebrooke
3597:S. R. Srinivasa Varadhan
3278:University of St Andrews
3274:University of St Andrews
3192:Stillwell, John (2002),
2934:Euclid in the Rainforest
2573:
2464:
2146:On 20 November 1981 the
936:by calculating the same
835:, or in modern notation:
513:Deśastha Rigvedi Brahmin
30:Not to be confused with
3481:Mādhava of Saṅgamagrāma
3216:Pedagogy Of Mathematics
3172:Science Across Cultures
2737:1994A&A...282..663S
1321:indeterminate equations
1088:Preliminary concept of
1081:Preliminary concept of
972:indeterminate equations
694:case that was to elude
3003:, Springer Verlag Ny,
2932:Mazur, Joseph (2005),
2837:NASA 16 September 2017
2121:
2113:
2026:Spherical trigonometry
1781:
1698:
1669:
1634:
1614:
1572:
1490:infinitesimal calculus
1468:
1426:
1383:spherical trigonometry
1133:spherical trigonometry
925:
904:
884:
829:
809:
782:
688:
604:
597:, the first volume of
528:
468:
427:Date, place and family
375:Maharashtrian Brahmins
310:
3692:Brāhmasphuṭasiddhānta
3213:Sahni, Madhu (2019),
3088:Cooke, Roger (1997),
3068:Plofker, Kim (2009),
2914:Eves, Howard (1990),
2731:282 (1994), 663–683.
2152:Bhaskara II satellite
2115:This is followed by:
2015:model of the planets.
1989:Nature of the sphere.
1782:
1699:
1670:
1635:
1615:
1573:
1502:differential calculus
1494:mathematical analysis
1469:
1427:
1325:Diophantine equations
1131:, Bhaskara developed
1104:differential calculus
1102:preliminary ideas of
1083:mathematical analysis
1049:Diophantine equations
920:
885:
830:
810:
783:
706:In the third section
689:
639:, solving it using a
592:
308:
3968:T. A. Saraswati Amma
3679:Bakhshali manuscript
3647:Kannan Soundararajan
3260:Robertson, Edmund F.
3168:D'Ambrosio, Ubiratan
3071:Mathematics in India
1849:(1340–1425) and the
1708:
1682:
1644:
1624:
1582:
1528:
1436:
1394:
1346:Quadratic equations.
1166:, the shadow of the
1067:in the 18th century.
841:
819:
794:
717:
649:
343:Bhāskara the teacher
54:specify the language
52:This article should
4138:People from Jalgaon
4044:Islamic mathematics
4003:Walter Eugene Clark
3797:Vasishtha Siddhanta
3769:Siddhānta Shiromani
3748:Paitamaha Siddhanta
3627:Tilak Raj Prabhakar
3572:Satyendra Nath Bose
3567:Srinivasa Ramanujan
3521:Nilakantha Somayaji
3258:O'Connor, John J.;
2762:, pp. 269–273.
2679:, pp. 213–215.
2598:Verses 128, 129 in
2533:. pp. 392–406.
1886:Siddhanta Shiromani
1485:Siddhānta Shiromani
1378:Siddhānta Shiromani
1338:quadratic equations
1238:Problems involving
1170:, methods to solve
934:Pythagorean theorem
923:pythagorean Theorem
631:The second section
484:Siddhānta Shiromani
480:Siddhānta Shiromani
320:[bʰɑːskərə]
272:Siddhānta Shiromani
3536:Gangesha Upadhyaya
3357:Indian mathematics
3239:W. W. Rouse Ball.
2694:The Times of India
2667:, pp. 95–104.
2605:, pp. 476–477
1828:mean value theorem
1777:
1694:
1665:
1630:
1610:
1568:
1464:
1422:
1129:Siddhanta-Śiromaṇi
1119:mean value theorem
926:
880:
825:
808:{\displaystyle y'}
805:
778:
684:
607:The first section
605:
600:Siddhānta Śiromaṇī
579:Siddhānta-Śiromaṇi
450:bhavan-mamotpattiḥ
395:Siddhānta-Śiromaṇi
311:
4115:
4114:
3921:Sudhakara Dvivedi
3741:Paulisa Siddhanta
3660:
3659:
3516:Jagannatha Samrat
3511:Achyuta Pisharati
3306:978-0-684-10114-9
3286:Bhaskaracharya II
3206:978-0-387-95336-6
3185:978-1-4020-0260-1
3156:978-0-253-21182-8
3134:978-0-85692-081-3
3010:978-1-4020-4559-2
2989:978-0-520-03566-9
2943:978-0-452-28783-9
2925:978-0-03-029558-4
2907:978-0-07-338315-6
2848:"Anand Narayanan"
2750:, pp. 52–53.
2403:, pp. 52–54.
2302:978-0-8364-2597-0
1649:
1633:{\displaystyle x}
1506:integral calculus
1097:integral calculus
1007:Chakravala method
857:
828:{\displaystyle y}
511:He was born in a
386:Deshastha Brahmin
303:
302:
189:(aged 70–71)
114:
113:
94:may also be used.
16:(Redirected from
4180:
4173:Sanskrit writers
3755:Romaka Siddhanta
3637:Akshay Venkatesh
3607:M. S. Narasimhan
3577:P.C. Mahalanobis
3370:
3350:
3343:
3336:
3327:
3310:
3276:
3229:
3209:
3188:
3159:
3148:
3137:
3127:, Vision Books,
3119:
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2864:
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2844:
2838:
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2826:
2820:
2811:
2810:, pp. 19–20
2805:
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2359:
2353:
2352:
2335:"Bhaskaracharya"
2330:
2324:
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2315:
2314:
2286:
2280:
2279:
2261:
2252:
2249:
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2242:
2222:
2203:
2196:
2143:in Gandhinagar.
2064:perpetual motion
2020:armillary sphere
1949:Sunrise equation
1919:diurnal rotation
1814:
1813:
1809:
1786:
1784:
1783:
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1297:negative numbers
1204:negative numbers
1061:Pierre de Fermat
1040:= 1 (so-called "
902:
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540:Jalgaon district
464:
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384:Born in a Hindu
371:Henry Colebrooke
347:
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289:Karaṇa-Kautūhala
205:Other names
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4053:
4017:
3991:
3962:C. T. Rajagopal
3909:Bapudeva Sastri
3901:
3895:
3857:
3837:Brahmi numerals
3829:
3823:
3783:Surya Siddhanta
3656:
3632:Manjul Bhargava
3555:
3414:
3359:
3354:
3321:4to40 Biography
3317:
3307:
3292:
3257:
3250:, 2nd Edition.
3236:
3234:Further reading
3227:
3212:
3207:
3191:
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2772:Colebrooke 1817
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2742:
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2283:
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2262:
2255:
2250:
2246:
2239:
2224:
2223:
2216:
2211:
2206:
2197:
2193:
2189:
2167:
2129:
2097:
2083:
2060:
1945:of the planets.
1867:
1836:Lilavati Bhasya
1811:
1807:
1806:
1706:
1705:
1680:
1679:
1642:
1641:
1622:
1621:
1593:
1585:
1580:
1579:
1551:
1534:
1526:
1525:
1522:Rolle's theorem
1480:
1449:
1445:
1434:
1433:
1407:
1403:
1392:
1391:
1387:trigonometrical
1373:
1365:Pell's equation
1271:
1174:equations, and
1146:
1115:Rolle's theorem
1042:Pell's equation
959:, solutions of
932:A proof of the
915:
849:
839:
838:
817:
816:
797:
792:
791:
752:
726:
715:
714:
704:
674:
655:
647:
646:
637:Pell's equation
629:
611:(also known as
587:
582:
569:observatory at
489:Karaṇa-kutūhala
467:
465:
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453:
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429:
345:
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200:
191:
186:
184:
173:
150:
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136:
121:
110:
104:
101:
95:
83:
77:
73:
71:transliteration
67:
63:
57:
48:
44:
35:
28:
23:
22:
15:
12:
11:
5:
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4036:
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4023:
4019:
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4005:
3999:
3997:
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3992:
3990:
3989:
3983:
3977:
3971:
3965:
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3942:
3936:
3933:P. C. Sengupta
3930:
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3800:
3793:
3790:Tantrasamgraha
3786:
3779:
3772:
3765:
3758:
3751:
3744:
3737:
3730:
3723:
3716:
3713:Karanapaddhati
3709:
3702:
3699:Ganita Kaumudi
3695:
3688:
3681:
3676:
3668:
3666:
3662:
3661:
3658:
3657:
3655:
3654:
3649:
3644:
3639:
3634:
3629:
3624:
3619:
3617:Harish-Chandra
3614:
3612:C. S. Seshadri
3609:
3604:
3599:
3594:
3589:
3584:
3579:
3574:
3569:
3563:
3561:
3557:
3556:
3554:
3553:
3548:
3546:Sankara Variar
3543:
3538:
3533:
3528:
3523:
3518:
3513:
3508:
3503:
3498:
3493:
3488:
3483:
3478:
3473:
3468:
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3443:
3438:
3433:
3428:
3422:
3420:
3416:
3415:
3413:
3412:
3407:
3402:
3397:
3392:
3387:
3382:
3376:
3374:
3367:
3365:Mathematicians
3361:
3360:
3355:
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3338:
3330:
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3323:
3316:
3315:External links
3313:
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3232:
3231:
3230:
3226:978-9353383275
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3164:Selin, Helaine
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2630:Stillwell 2002
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2516:
2497:
2495:, p. 299.
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2159:Bhaskaracharya
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1931:Lunar eclipses
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1911:
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1514:infinitesimals
1482:His work, the
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1406:
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1399:
1372:
1369:
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1347:
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1341:
1336:Indeterminate
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1331:
1328:
1312:
1306:
1303:
1300:
1270:
1267:
1259:
1258:
1243:
1236:
1229:
1222:multiplication
1218:
1213:Estimation of
1211:
1200:
1191:Properties of
1189:
1164:solid geometry
1160:plane geometry
1145:
1142:
1141:
1140:
1125:
1122:
1111:
1100:
1086:
1079:
1068:
1045:
1030:
1003:
990:
975:
974:are explained.
953:
914:
911:
894:In his words:
892:
891:
879:
876:
873:
870:
867:
864:
861:
855:
852:
848:
836:
824:
803:
800:
789:
777:
774:
771:
768:
765:
762:
758:
755:
751:
748:
745:
742:
739:
736:
732:
729:
725:
722:
703:
700:
681:
677:
673:
670:
667:
662:
658:
654:
628:
625:
586:
583:
581:
575:
536:Godavari river
438:
428:
425:
330:Bhāskarāchārya
301:
300:
297:
296:
295:
294:
291:
286:
280:
274:
267:
263:
262:
249:
248:Main interests
245:
244:
241:
237:
236:
231:
227:
226:
222:
221:
218:
217:
214:
210:
209:
206:
202:
201:
198:Madhya Pradesh
192:
179:
175:
174:
151:
142:
138:
137:
131:
123:
122:
119:
112:
111:
90:. Knowledge's
51:
49:
42:
26:
24:
18:Bhaskaracharya
14:
13:
10:
9:
6:
4:
3:
2:
4185:
4174:
4171:
4169:
4166:
4164:
4161:
4159:
4156:
4154:
4151:
4149:
4146:
4144:
4141:
4139:
4136:
4134:
4131:
4129:
4126:
4125:
4123:
4108:
4105:
4103:
4100:
4098:
4095:
4093:
4090:
4088:
4085:
4083:
4080:
4078:
4075:
4073:
4070:
4068:
4065:
4064:
4062:
4056:
4050:
4047:
4045:
4042:
4040:
4037:
4035:
4032:
4030:
4027:
4026:
4024:
4022:Other regions
4020:
4014:
4013:David Pingree
4011:
4009:
4006:
4004:
4001:
4000:
3998:
3994:
3987:
3984:
3981:
3978:
3975:
3972:
3969:
3966:
3963:
3960:
3957:
3954:
3951:
3948:
3946:
3943:
3940:
3937:
3934:
3931:
3928:
3927:M. Rangacarya
3925:
3922:
3919:
3916:
3913:
3910:
3907:
3906:
3904:
3900:Historians of
3898:
3891:
3887:
3883:
3879:
3875:
3874:Jantar Mantar
3872:
3870:
3867:
3866:
3864:
3860:
3854:
3851:
3849:
3845:
3843:
3840:
3838:
3835:
3834:
3832:
3826:
3820:
3819:
3815:
3813:
3812:
3808:
3806:
3805:
3801:
3799:
3798:
3794:
3792:
3791:
3787:
3785:
3784:
3780:
3778:
3777:
3773:
3771:
3770:
3766:
3764:
3763:
3759:
3757:
3756:
3752:
3750:
3749:
3745:
3743:
3742:
3738:
3736:
3735:
3731:
3729:
3728:
3724:
3722:
3721:
3717:
3715:
3714:
3710:
3708:
3707:
3703:
3701:
3700:
3696:
3694:
3693:
3689:
3687:
3686:
3682:
3680:
3677:
3675:
3674:
3670:
3669:
3667:
3663:
3653:
3650:
3648:
3645:
3643:
3640:
3638:
3635:
3633:
3630:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3585:
3583:
3580:
3578:
3575:
3573:
3570:
3568:
3565:
3564:
3562:
3558:
3552:
3549:
3547:
3544:
3542:
3539:
3537:
3534:
3532:
3529:
3527:
3524:
3522:
3519:
3517:
3514:
3512:
3509:
3507:
3504:
3502:
3499:
3497:
3494:
3492:
3491:Mahendra Sūri
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3457:
3454:
3452:
3449:
3447:
3444:
3442:
3439:
3437:
3434:
3432:
3429:
3427:
3424:
3423:
3421:
3417:
3411:
3408:
3406:
3403:
3401:
3398:
3396:
3393:
3391:
3388:
3386:
3383:
3381:
3378:
3377:
3375:
3371:
3368:
3366:
3362:
3358:
3351:
3346:
3344:
3339:
3337:
3332:
3331:
3328:
3322:
3319:
3318:
3314:
3308:
3302:
3298:
3297:
3291:
3288:
3287:
3282:
3279:
3275:
3271:
3270:
3265:
3264:"Bhāskara II"
3261:
3256:
3253:
3252:Penguin Books
3249:
3245:
3242:
3238:
3237:
3233:
3228:
3222:
3218:
3217:
3211:
3208:
3202:
3198:
3197:
3190:
3187:
3181:
3177:
3173:
3169:
3165:
3161:
3158:
3152:
3147:
3146:
3139:
3136:
3130:
3126:
3121:
3117:
3112:
3109:
3107:0-471-18082-3
3103:
3099:
3095:
3091:
3086:
3083:
3081:9780691120676
3077:
3073:
3072:
3066:
3063:
3061:9780691114859
3057:
3053:
3048:
3045:
3043:9780871691460
3039:
3035:
3034:
3028:
3024:
3020:
3015:
3012:
3006:
3002:
2998:
2994:
2991:
2985:
2981:
2980:
2974:
2971:
2966:
2962:
2957:
2953:
2948:
2945:
2939:
2935:
2930:
2927:
2921:
2917:
2912:
2909:
2903:
2899:
2894:
2893:
2889:
2880:
2876:
2870:
2867:
2855:
2854:
2849:
2843:
2840:
2836:
2831:
2828:
2825:, p. 477
2824:
2819:
2817:
2813:
2809:
2804:
2801:
2798:, p. 106
2797:
2792:
2789:
2786:, p. 228
2785:
2780:
2777:
2773:
2768:
2765:
2761:
2756:
2753:
2749:
2744:
2741:
2738:
2734:
2730:
2726:
2725:mean ecliptic
2722:
2719:
2715:
2710:
2707:
2695:
2691:
2685:
2682:
2678:
2673:
2670:
2666:
2661:
2658:
2652:
2650:
2648:
2644:
2638:
2635:
2632:, p. 74.
2631:
2626:
2624:
2620:
2614:
2612:
2608:
2604:
2601:
2595:
2592:
2580:
2576:
2567:
2565:
2563:
2561:
2559:
2555:
2549:
2546:
2540:
2537:
2532:
2531:
2526:
2520:
2517:
2513:
2509:
2508:
2501:
2498:
2494:
2489:
2487:
2483:
2471:
2467:
2458:
2456:
2454:
2452:
2450:
2448:
2446:
2444:
2442:
2440:
2438:
2436:
2434:
2430:
2427:, p. 79.
2426:
2421:
2418:
2415:, p. 71.
2414:
2409:
2406:
2402:
2397:
2394:
2391:, p. 50.
2390:
2385:
2382:
2376:
2373:
2367:
2364:
2358:
2355:
2350:
2348:9788123024851
2344:
2340:
2336:
2329:
2326:
2320:
2317:
2312:
2308:
2304:
2298:
2294:
2293:
2285:
2282:
2277:
2273:
2269:
2268:
2260:
2258:
2254:
2248:
2245:
2240:
2234:
2230:
2229:
2221:
2219:
2215:
2208:
2201:
2195:
2192:
2186:
2182:
2179:
2177:
2176:Bride's Chair
2174:
2172:
2169:
2168:
2164:
2162:
2160:
2155:
2153:
2150:launched the
2149:
2144:
2142:
2138:
2134:
2126:
2124:
2120:
2116:
2112:
2108:
2105:
2103:
2094:
2092:
2090:
2089:
2080:
2078:
2076:
2071:
2069:
2065:
2057:
2052:
2049:
2045:
2042:
2039:
2036:
2034:calculations.
2033:
2030:
2027:
2024:
2021:
2017:
2014:
2011:
2008:
2005:
2001:
1998:
1994:
1991:
1988:
1985:
1984:
1983:
1977:
1974:
1970:
1967:
1964:
1961:
1957:
1953:
1950:
1947:
1944:
1941:
1938:
1935:
1932:
1929:
1926:
1923:
1920:
1916:
1912:
1909:
1906:
1902:
1898:
1897:
1896:
1893:
1891:
1887:
1882:
1880:
1876:
1875:sidereal year
1872:
1864:
1862:
1860:
1856:
1852:
1851:Kerala School
1848:
1841:
1837:
1833:
1829:
1824:
1821:
1817:
1804:
1803:
1798:
1793:
1789:
1788:
1771:
1765:
1762:
1756:
1753:
1750:
1744:
1738:
1732:
1729:
1726:
1720:
1714:
1711:
1691:
1688:
1685:
1677:
1662:
1659:
1656:
1653:
1650:
1627:
1607:
1604:
1600:
1597:
1594:
1589:
1586:
1565:
1562:
1558:
1555:
1552:
1548:
1545:
1541:
1538:
1535:
1531:
1523:
1519:
1518:
1517:
1515:
1509:
1507:
1503:
1499:
1495:
1491:
1487:
1486:
1477:
1475:
1460:
1456:
1453:
1450:
1446:
1442:
1439:
1418:
1414:
1411:
1408:
1404:
1400:
1397:
1388:
1384:
1380:
1379:
1370:
1368:
1366:
1362:
1360:
1351:
1348:
1345:
1342:
1339:
1335:
1332:
1329:
1326:
1322:
1319:(for solving
1318:
1317:
1313:
1310:
1307:
1304:
1301:
1298:
1295:Positive and
1294:
1293:
1292:
1290:
1286:
1282:
1281:
1276:
1268:
1266:
1264:
1256:
1252:
1248:
1244:
1241:
1237:
1234:
1233:rule of three
1230:
1227:
1223:
1219:
1216:
1212:
1209:
1205:
1201:
1198:
1194:
1190:
1187:
1186:
1185:
1183:
1179:
1177:
1173:
1172:indeterminate
1169:
1165:
1161:
1157:
1156:
1151:
1143:
1138:
1137:trigonometric
1134:
1130:
1126:
1123:
1120:
1116:
1112:
1109:
1105:
1101:
1098:
1094:
1091:
1090:infinitesimal
1087:
1084:
1080:
1077:
1073:
1069:
1066:
1062:
1058:
1054:
1050:
1047:Solutions of
1046:
1043:
1039:
1035:
1031:
1028:
1024:
1020:
1016:
1012:
1008:
1004:
1001:
997:
996:
991:
988:
984:
980:
976:
973:
970:
966:
962:
958:
954:
951:
947:
943:
939:
935:
931:
930:
929:
924:
919:
912:
910:
907:
903:
901:
895:
877:
874:
871:
868:
865:
862:
859:
853:
850:
846:
837:
822:
801:
798:
790:
775:
772:
769:
763:
760:
756:
753:
746:
743:
740:
737:
734:
730:
727:
723:
720:
713:
712:
711:
709:
701:
699:
697:
679:
675:
671:
668:
665:
660:
656:
652:
644:
643:
638:
634:
626:
624:
622:
618:
614:
610:
602:
601:
596:
591:
584:
580:
576:
574:
572:
568:
563:
561:
557:
553:
549:
545:
541:
537:
533:
527:
524:
520:
518:
514:
509:
507:
503:
499:
495:
491:
490:
485:
481:
477:
473:
466:
460:
451:
443:
436:
434:
426:
424:
422:
418:
414:
413:
408:
407:
402:
398:
396:
391:
387:
382:
380:
376:
372:
367:
363:
362:Western Ghats
359:
355:
354:mathematician
351:
331:
323:
321:
315:
307:
298:
292:
290:
287:
284:
281:
278:
275:
273:
270:
269:
268:
266:Notable works
264:
261:
257:
253:
250:
246:
242:
238:
235:
232:
228:
225:Academic work
223:
219:
215:
213:Occupation(s)
211:
208:Bhāskarācārya
207:
203:
199:
195:
180:
176:
171:
167:
163:
159:
155:
152:Vijjadavida,
143:
139:
135:
129:
124:
117:
108:
98:
93:
89:
82:
72:
62:
55:
50:
41:
40:
37:
33:
19:
4143:1110s births
4060:institutions
3980:K. S. Shukla
3952:(1892– 1953)
3818:Yavanajataka
3816:
3809:
3802:
3795:
3788:
3781:
3776:Śulba Sūtras
3774:
3767:
3762:Sadratnamala
3760:
3753:
3746:
3739:
3732:
3725:
3718:
3711:
3706:Kanakkusaram
3704:
3697:
3690:
3683:
3671:
3541:Varāhamihira
3506:Parameshvara
3461:Govindasvāmi
3440:
3431:Āryabhaṭa II
3294:
3285:
3283:Ian Pearce.
3267:
3247:
3240:
3215:
3199:, Springer,
3193:
3178:, Springer,
3175:
3171:
3144:
3124:
3115:
3093:
3070:
3051:
3032:
3022:
3018:
3000:
2978:
2969:
2960:
2951:
2933:
2915:
2897:
2890:Bibliography
2869:
2857:. Retrieved
2851:
2842:
2830:
2823:Plofker 2007
2803:
2791:
2779:
2767:
2755:
2743:
2728:
2709:
2697:. Retrieved
2693:
2684:
2672:
2660:
2637:
2603:Plofker 2007
2599:
2594:
2583:, retrieved
2581:, p. 21
2578:
2548:
2539:
2529:
2519:
2511:
2506:
2500:
2493:Pingree 1970
2474:, retrieved
2472:, p. 17
2469:
2425:Poulose 1991
2420:
2413:Plofker 2009
2408:
2396:
2384:
2375:
2366:
2357:
2338:
2328:
2319:
2291:
2284:
2266:
2247:
2227:
2194:
2158:
2156:
2145:
2130:
2122:
2118:
2114:
2110:
2106:
2101:
2098:
2086:
2085:In his book
2084:
2075:Yaṣṭi-yantra
2074:
2072:
2061:
1981:
1966:Conjunctions
1894:
1883:
1868:
1855:Parameshvara
1845:
1839:
1835:
1832:Parameshvara
1820:differential
1800:
1510:
1498:trigonometry
1483:
1481:
1376:
1374:
1371:Trigonometry
1358:
1355:
1314:
1288:
1285:square roots
1278:
1274:
1272:
1262:
1260:
1188:Definitions.
1181:
1180:
1176:combinations
1153:
1147:
1128:
1110:coefficient.
1108:differential
1056:
1052:
1037:
1033:
1026:
1022:
1018:
1014:
1010:
993:
986:
982:
978:
956:
949:
945:
941:
927:
908:
905:
897:
893:
707:
705:
640:
632:
630:
616:
612:
608:
606:
598:
594:
578:
567:astronomical
564:
529:
525:
522:
510:
487:
483:
479:
469:
439:
430:
420:
416:
410:
404:
393:
383:
329:
317:
313:
312:
260:trigonometry
187:(1185-00-00)
102:
88:ISO 639 code
84:}}
78:{{
74:}}
68:{{
64:}}
58:{{
53:
36:
4153:Algebraists
4148:1185 deaths
3996:Translators
3988:(1919–2005)
3986:K. V. Sarma
3982:(1918–2007)
3976:(1918–1992)
3970:(1918–2000)
3964:(1903–1978)
3958:(1901–1954)
3956:A. N. Singh
3941:(1888–1958)
3939:B. B. Datta
3935:(1876–1962)
3929:(1861–1916)
3923:(1855–1910)
3917:(1853–1898)
3911:(1821–1900)
3902:mathematics
3846:Symbol for
3830:innovations
3727:Lokavibhaga
3673:Aryabhatiya
3471:Jyeṣṭhadeva
3456:Brahmagupta
3441:Bhāskara II
3426:Āryabhaṭa I
3410:Yajnavalkya
2859:21 February
2796:Burton 2011
2665:Shukla 1984
2585:12 November
2476:12 November
2401:Chopra 1982
2181:Bījapallava
2102:Hindu proof
2058:Engineering
2004:mean motion
1993:Cosmography
1871:Brahmagupta
1251:renaissance
1195:(including
1148:Bhaskara's
1000:Renaissance
913:Mathematics
708:Grahagaṇita
702:Grahaganita
621:measurement
494:Brahmagupta
417:Grahagaṇita
366:Maharashtra
314:Bhāskara II
185: 1185
154:Maharashtra
148: 1114
120:Bhāskara II
4122:Categories
3945:T. Hayashi
3828:Pioneering
3811:Yuktibhāṣā
3734:Pātīgaṇita
3685:Bijaganita
3642:Ravi Vakil
3496:Munishvara
3476:Kamalakara
3451:Brahmadeva
3436:Bhāskara I
3385:Baudhayana
2808:Mazur 2005
2760:Selin 2008
2748:White 1978
2677:Cooke 1997
2600:Bijaganita
2579:Vijayavani
2470:Vijayavani
2389:Sahni 2019
2209:References
2200:Bhāskara I
2139:in Delhi,
2002:Planetary
1913:The three
1901:longitudes
1861:in India.
1359:chakravala
1289:Bījaganita
1275:Bījaganita
1150:arithmetic
1144:Arithmetic
1078:solutions.
1076:irrational
1027:chakravala
633:Bījagaṇita
627:Bijaganita
617:aṅkagaṇita
613:pāṭīgaṇita
593:Page from
517:Munishvara
433:Āryā metre
421:Golādhyāya
412:Bījagaṇita
358:astronomer
352:polymath,
348:), was an
283:Bījagaṇita
256:arithmetic
240:Discipline
170:Marathwada
156:(probably
105:March 2022
32:Bhāskara I
3974:S. N. Sen
3882:New Delhi
3804:Veṇvāroha
3665:Treatises
3466:Halayudha
3419:Classical
3390:Katyayana
3380:Apastamba
2936:, Plume,
2784:Eves 1990
2525:Bhau Daji
2311:464078172
2135:in Pune,
2095:"Behold!"
2013:epicyclic
2010:Eccentric
1997:geography
1943:Latitudes
1865:Astronomy
1822:vanishes.
1766:
1754:−
1745:≈
1733:
1727:−
1715:
1689:≈
1620:for some
1454:−
1443:
1401:
1255:Aryabhata
1005:A cyclic
961:quadratic
875:
863:
815:close to
773:
761:−
747:≈
741:
735:−
724:
560:Telangana
552:Karnataka
506:Patnadevi
472:Shaka era
234:Shaka era
134:Patnadevi
4168:Acharyas
3890:Varanasi
3848:zero (0)
3720:Līlāvatī
3587:C.R. Rao
3551:Virasena
3531:Sridhara
3501:Narayana
3486:Mahāvīra
3025:: 95–104
2879:Archived
2835:Bhaskara
2165:See also
2088:Lilavati
1960:crescent
1925:Syzygies
1915:problems
1859:calculus
1840:Lilavati
1792:ecliptic
1590:′
1478:Calculus
1263:Lilavati
1240:interest
1231:Inverse
1226:squaring
1197:division
1182:Līlāvatī
1155:Līlāvatī
1093:calculus
1072:negative
957:Lilavati
802:′
757:′
731:′
609:Līlāvatī
595:Lilavati
585:Līlāvatī
532:Vidarbha
502:Mahāvīra
498:Śrīdhara
406:Līlāvatī
401:Sanskrit
379:Godavari
277:Līlāvatī
162:Khandesh
4029:Babylon
3862:Centres
3526:Śrīpati
3405:Pingala
3373:Ancient
3280:, 2000.
3254:, 2000.
3098:213–215
2733:Bibcode
2721:seconds
2276:4136967
2081:Legends
2048:seasons
2032:Ellipse
1905:planets
1903:of the
1847:Madhava
1810:⁄
1805:, or a
1578:, then
1316:Kuṭṭaka
1280:Algebra
1269:Algebra
1247:Kuṭṭaka
1113:Stated
1029:method.
995:Kuṭṭaka
969:quartic
642:kuṭṭaka
544:Bijapur
337:
252:Algebra
97:See why
4058:Modern
4049:Europe
4039:Greece
3886:Ujjain
3878:Jaipur
3560:Modern
3400:Pāṇini
3395:Manava
3303:
3223:
3203:
3182:
3153:
3131:
3104:
3078:
3058:
3040:
3007:
2986:
2940:
2922:
2904:
2699:24 May
2345:
2309:
2299:
2274:
2235:
2127:Legacy
1890:sphere
1648:
1361:method
1224:, and
1168:gnomon
1055:+ 1 =
696:Fermat
571:Ujjain
474:(1114
390:Ujjain
350:Indian
194:Ujjain
4034:China
2187:Notes
2068:wheel
1973:stars
1899:Mean
1812:33750
1802:truti
1704:then
1640:with
1309:Surds
1208:surds
1152:text
1065:Euler
965:cubic
556:Basar
548:Bidar
158:Patan
4107:TIFR
3301:ISBN
3221:ISBN
3201:ISBN
3180:ISBN
3151:ISBN
3129:ISBN
3102:ISBN
3076:ISBN
3056:ISBN
3038:ISBN
3005:ISBN
2984:ISBN
2938:ISBN
2920:ISBN
2902:ISBN
2861:2021
2853:IIST
2701:2023
2587:2019
2478:2019
2343:ISBN
2307:OCLC
2297:ISBN
2272:OCLC
2233:ISBN
2046:The
2018:The
1995:and
1956:Moon
1954:The
1879:days
1660:<
1654:<
1504:and
1492:and
1432:and
1375:The
1323:and
1273:His
1206:and
1193:zero
1106:and
1074:and
967:and
938:area
788:for.
577:The
419:and
334:lit.
178:Died
166:Beed
141:Born
61:lang
1958:'s
1917:of
1763:cos
1730:sin
1712:sin
1516:'.
1440:sin
1398:sin
1127:In
955:In
872:cos
860:sin
770:cos
738:sin
721:sin
615:or
558:in
550:in
546:or
230:Era
168:in
164:or
160:in
81:IPA
4124::
3888:,
3884:,
3880:,
3272:,
3266:,
3262:,
3174:,
3166:;
3100:,
3092:,
3023:19
3021:,
2850:.
2815:^
2718:SI
2692:.
2646:^
2622:^
2610:^
2577:,
2557:^
2485:^
2468:,
2432:^
2337:.
2305:.
2256:^
2217:^
1892:.
1500:,
1474:.
1327:).
1277:("
1178:.
1162:,
1038:ny
1036:−
1021:=
1017:+
1015:bx
1013:+
1011:ax
989:).
985:=
981:+
979:ax
963:,
948:=
944:+
653:61
500:,
496:,
476:CE
435::
415:,
409:,
381:.
356:,
326:c.
324:;
258:,
254:,
196:,
182:c.
145:c.
66:,
3892:)
3876:(
3349:e
3342:t
3335:v
3309:.
3176:2
2863:.
2774:.
2735::
2703:.
2351:.
2313:.
2278:.
2241:.
2202:,
2050:.
2028:.
2022:.
2006:.
1999:.
1975:.
1962:.
1951:.
1939:.
1933:.
1927:.
1907:.
1842:.
1808:1
1775:)
1772:y
1769:(
1760:)
1757:x
1751:y
1748:(
1742:)
1739:x
1736:(
1724:)
1721:y
1718:(
1692:y
1686:x
1675:.
1663:b
1657:x
1651:a
1628:x
1608:0
1605:=
1601:)
1598:x
1595:(
1587:f
1566:0
1563:=
1559:)
1556:b
1553:(
1549:f
1546:=
1542:)
1539:a
1536:(
1532:f
1512:'
1461:)
1457:b
1451:a
1447:(
1419:)
1415:b
1412:+
1409:a
1405:(
1299:.
1228:.
1217:.
1215:π
1210:.
1099:.
1085:.
1057:y
1053:x
1034:x
1023:y
1019:c
987:y
983:b
952:.
950:c
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890:.
878:y
869:=
866:y
854:y
851:d
847:d
823:y
799:y
776:y
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764:y
754:y
750:(
744:y
728:y
680:2
676:y
672:=
669:1
666:+
661:2
657:x
463:॥
454:।
446:ऽ
399:(
397:,
346:'
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332:(
316:(
285:,
279:,
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