1508:), he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the Moon enters into the Earth's shadow (verse gola.37). He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist
40:
1581:
1565:
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of ancient Kerala. This is based on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, old records show that the city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, the fact that several commentaries on the
Aryabhatiya have come from
767:
is also well-known for his description of relativity of motion. He expressed this relativity thus: "Just as a man in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so are the stationary stars seen by the people on earth as moving exactly towards the west."
1098:
means "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original factors in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole subject of
2805:
He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The
1471:
The positions and periods of the planets was calculated relative to uniformly moving points. In the case of
Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each
1407:
In the same way that someone in a boat going forward sees an unmoving going backward, so on the equator sees the unmoving stars going uniformly westward. The cause of rising and setting the sphere of the stars together with the planets turns due west at the equator, constantly pushed by the
386:
Kerala has been used to suggest that it was
Aryabhata's main place of life and activity; however, many commentaries have come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala. K. Chandra Hari has argued for the Kerala hypothesis on the basis of astronomical evidence.
1390:
Aryabhata correctly insisted that the Earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the Earth, contrary to the then-prevailing view, that the sky rotated. This is indicated in the first chapter of the
1794:(AKU), Patna has been established by Government of Bihar for the development and management of educational infrastructure related to technical, medical, management and allied professional education in his honour. The university is governed by Bihar State University Act 2008.
1552:, heliocentric model of which Indian astronomers were unaware, though the evidence is scant. The general consensus is that a synodic anomaly (depending on the position of the Sun) does not imply a physically heliocentric orbit (such corrections being also present in late
2309:: "Seven cardinal points are then defined on the equator, one of them called Laṅkā, at the intersection of the equator with the meridional line through Ujjaini. This Laṅkā is, of course, a fanciful name and has nothing to do with the island of Sri Laṅkā."
2331:: "The point on the equator that is below the city of Ujjain is known, according to the Siddhantas, as Lanka. (This is not the Lanka that is now known as Sri Lanka; Aryabhata is very clear in stating that Lanka is 23 degrees south of Ujjain.)"
1079:
That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. They were discussed extensively in ancient Vedic text
614:
literature, in which each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The text consists of the 108 verses and 13 introductory verses, and is divided into four
1732:
Aryabhata's astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the
Islamic world and used to compute many Arabic astronomical tables
748:
presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple
Bhaskara I
1231:
1333:
329:, but this is not to mean that the text was composed at that time. This mentioned year corresponds to 499 CE, and implies that he was born in 476. Aryabhata called himself a native of Kusumapura or
429:
was in
Pataliputra at the time, it is speculated that Aryabhata might have been the head of the Nalanda university as well. Aryabhata is also reputed to have set up an observatory at the Sun temple in
2647:
458:
Much of the research included subjects in astronomy, mathematics, physics, biology, medicine, and other fields. Aryabhata's major work were based on previous discoveries by Greeks, Mesapotamians.
1548:
model, in which the planets orbit the Sun, though this has been rebutted. It has also been suggested that aspects of
Aryabhata's system may have been derived from an earlier, likely pre-Ptolemaic
2287:: "In Indian astronomy, the prime meridian is the great circle of the Earth passing through the north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be on the Earth's equator."
2712:
Aryabhata gave the correct rule for the area of a triangle and an incorrect rule for the volume of a pyramid. (He claimed that the volume was half the height times the area of the base.)
1784:
calendars. This type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the
920:
1544:
anomaly) for the speeds of the planets in the sky in terms of the mean speed of the Sun. Thus, it has been suggested that
Aryabhata's calculations were based on an underlying
1528:(the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the
4147:
4112:
2383:
1817:
940:
895:
462:, a compendium of mathematics and astronomy, was referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the
405:
It is fairly certain that, at some point, he went to
Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as
1813:
572:. It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known. Probably dating from the 9th century, it is mentioned by the
45:
4299:
2644:
2129:
702:(25 verses): different units of time and a method for determining the positions of planets for a given day, calculations concerning the intercalary month (
521:
which was a
Sanskrit summary of Greek and mesapotamian theories in astronomy and mathematics and uses the midnight-day reckoning, as opposed to sunrise in
1084:, whose more ancient parts might date to 800 BCE. Aryabhata's method of solving such problems, elaborated by Bhaskara in 621 CE, is called the
3849:
2821:
1532:
at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days) is an error of 3 minutes and 20 seconds over the length of a year (365.25636 days).
1633:
Aryabhata's work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations. The
1947:
870:"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."
4124:
3304:
2551:
1075:
Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
1063:
that have the form ax + by = c. (This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the
3254:
2438:
3290:
1756:
Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the
3545:
2419:
2510:
2237:
1472:
planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic
311:'s references to him "in more than a hundred places by name". Furthermore, in most instances "Aryabhatta" would not fit the metre either.
4279:
4171:
1891:(1865). "Brief Notes on the Age and Authenticity of the Works of Aryabhata, Varahamihira, Brahmagupta, Bhattotpala, and Bhaskaracharya".
2836:"He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses."
2759:
2742:
4345:
4340:
4066:
3151:
1540:
As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis. His model also gave corrections (the
3037:
From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Kennedy
1129:
4241:
2087:
953:). If this is correct, it is quite a sophisticated insight, because the irrationality of pi (π) was proved in Europe only in 1761 by
4294:
1242:
4355:
4350:
3469:
2829:
3035:
B.L. van der Waerden, "The Heliocentric System in Greek, Persian and Hindu Astronomy", in David A. King and George Saliba, ed.,
4304:
2414:
Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late 5th and the early 6th centuries at
4375:
4246:
3494:
3380:
3181:
3114:
3011:
2972:
2367:
2346:
2324:
2302:
2280:
2220:
2064:
2037:
2007:
1980:
1919:
4370:
3819:
3224:
3126:
610:(literally, Aryabhata's 108), because there are 108 verses in the text. It is written in the very terse style typical of
1516:
of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.
4289:
3799:
3432:
3406:
3344:
3062:
2945:
2925:
2894:
2798:
2705:
2672:
2626:
2601:
2407:
1620:
598:. The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name. His disciple
577:
3538:
3054:
1852:
181:
4039:
1791:
1553:
2144:
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4274:
3889:
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1602:
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and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by
3683:
3562:
1864:
819:, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a
4365:
4335:
4264:
2818:
1480:, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying
3308:
2292:
307:" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus, including
4284:
4269:
3531:
2357:
2336:
2314:
2270:
3202:
1843:
949:(approaching), to mean that not only is this an approximation but that the value is incommensurable (or
3779:
1943:
1780:
today. The dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier
1598:
900:
505:, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary,
303:
While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "
20:
3448:
3358:
393:, but his "Lanka" is an abstraction, standing for a point on the equator at the same longitude as his
3789:
3464:
2556:
1336:
1064:
661:
495:
362:
country." During the Buddha's time, a branch of the Aśmaka people settled in the region between the
1360:
or "equator". Some of his later writings on astronomy, which apparently proposed a second model (or
990:
that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."
290:
For his explicit mention of the relativity of motion, he also qualifies as a major early physicist.
4079:
3945:
3794:
3474:
3264:
2445:
1812:. An Institute for conducting research in astronomy, astrophysics and atmospheric sciences is the
4205:
4087:
3678:
3508:
3286:
2546:
1591:
954:
2399:
1428:(c. 425 CE), the motions of the planets are each governed by two epicycles, a smaller
4226:
4153:
3173:
3113:
Dennis Duke, "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models."
2444:. National Council of Science Museums, Ministry of Culture, Government of India. Archived from
2247:
685:
479:
3966:
2790:
2784:
2054:
1892:
189:
4083:
4075:
3577:
2962:
2910:
Otto Neugebauer, "The Transmission of Planetary Theories in Ancient and Medieval Astronomy,"
2754:
2739:
2476:
2210:
2027:
1997:
1970:
1909:
1798:
1568:
1512:, during a visit to Pondicherry, India, found the Indian computations of the duration of the
1473:
1060:
1056:
737:
689:
925:
4165:
3876:
3844:
3167:
3091:
2183:
1465:
1120:
786:
270:
150:
1808:
are both named in his honour, the Aryabhata satellite also featured on the reverse of the
880:
8:
4330:
4325:
4231:
4200:
4008:
3994:
3931:
3824:
3769:
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3482:
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3354:
2964:
Encyclopaedia of the history of science, technology, and medicine in non-western cultures
2912:
2776:
2515:
1809:
1509:
1375:
1032:
838:(π), and may have come to the conclusion that π is irrational. In the second part of the
754:
681:
173:
2187:
1492:
Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the
874:
This implies that for a circle whose diameter is 20000, the circumference will be 62832
3733:
3554:
3334:
2694:
2689:
2392:
1859:
1805:
1785:
1638:
802:
798:
487:
483:
261:
185:
1641:(c. 820 CE), was particularly influential. Some of his results are cited by
410:
4236:
4118:
3938:
3713:
3708:
3582:
3490:
3428:
3402:
3376:
3340:
3177:
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3100:
3058:
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2968:
2941:
2921:
2890:
2794:
2780:
2701:
2668:
2622:
2597:
2403:
2363:
2342:
2320:
2298:
2276:
2216:
2060:
2033:
2003:
1976:
1915:
1710:
1525:
729:
3024:
Das heliozentrische System in der griechischen, persischen und indischen Astronomie.
3952:
3834:
3804:
3774:
2998:
2191:
2092:
1746:
1501:
1441:
1424:. They in turn revolve around the Earth. In this model, which is also found in the
721:
640:
265:
3917:
3688:
3094:(3rd century BCE) is credited with holding an heliocentric theory, the version of
3026:
Naturforschenden Gesellschaft in Zürich. Zürich:Kommissionsverlag Leeman AG, 1970.
1436:(fast). The order of the planets in terms of distance from earth is taken as: the
4159:
4106:
4034:
3980:
3829:
3698:
3512:
3095:
3022:
The concept of Indian heliocentrism has been advocated by B. L. van der Waerden,
2825:
2763:
2746:
2651:
1765:
1693:
In fact, the modern terms "sine" and "cosine" are mistranscriptions of the words
1690:) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.
1549:
1094:
961:
561:
518:
111:
3738:
3658:
2579:
A Universal History of Numbers: From Prehistory to the Invention of the Computer
1374:. In some texts, he seems to ascribe the apparent motions of the heavens to the
1005:, which literally means "half-chord". For simplicity, people started calling it
4130:
4050:
3987:
3910:
3896:
3814:
3809:
3743:
3587:
1761:
1649:
stated that Aryabhata's followers believed that the Earth rotated on its axis.
1370:
650:), given in a single verse. The duration of the planetary revolutions during a
573:
3638:
3232:
3119:
4319:
4210:
4142:
4071:
3973:
3394:
2958:
2882:
1545:
1529:
1513:
1019:. However, in Arabic writings, vowels are omitted, and it was abbreviated as
794:
733:
717:
363:
253:
197:
169:
165:
3633:
3597:
2174:
Ansari, S.M.R. (March 1977). "Aryabhata I, His Life and His Contributions".
1772:, versions of which (modified in 1925) are the national calendars in use in
1364:, midnight) are lost but can be partly reconstructed from the discussion in
1068:
406:
349:
4177:
4015:
3959:
3903:
3723:
3703:
3628:
2872:, New Delhi: Indian National Science Academy, 1976. Quoted in Plofker 2009.
1825:
1802:
1769:
1679:
1642:
1481:
1081:
965:
816:
805:
606:(or the treatise from the Ashmaka). It is also occasionally referred to as
525:. It also contained a description of several astronomical instruments: the
506:
491:
475:
239:
219:
126:
69:
3367:
3361:
1850:
1841:
1086:
981:
861:
853:
843:
638:—which present a cosmology different from earlier texts such as Lagadha's
419:
4183:
4136:
3924:
3870:
3653:
3607:
3389:
2125:
1777:
1670:
1505:
1420:
model of the Solar System, in which the Sun and Moon are each carried by
1409:
1365:
1035:
translated these writings from Arabic into Latin, he replaced the Arabic
782:
589:
554:
510:
451:
442:
378:
377:(Sanskrit for "stone") where Aryabhata originated may be the present day
330:
308:
215:
136:
64:
3882:
3839:
3693:
3673:
3648:
2728:(6 ed.). Saunders College Publishing House, New York. p. 237.
2415:
1757:
1742:
1738:
1605: in this section. Unsourced material may be challenged and removed.
1417:
950:
599:
514:
467:
257:
249:
211:
1564:
789:, was clearly in place in his work. While he did not use a symbol for
4001:
3663:
3523:
3375:. University of Chicago Press; reprint: Kessinger Publishing (2006).
3259:
3039:, Annals of the New York Academy of Science, 500 (1987), pp. 529–534.
2355:
2242:
1888:
1781:
1750:
1646:
1524:
Considered in modern English units of time, Aryabhata calculated the
1001:
446:
325:
283:
276:
235:
177:
154:
140:
39:
2195:
1580:
358:
3784:
3748:
3728:
2334:
1421:
1012:
820:
812:
811:
However, Aryabhata did not use the Brahmi numerals. Continuing the
725:
430:
394:
367:
2621:(Third ed.). New York: W.H. Freeman and Company. p. 70.
1701:
as introduced by Aryabhata. As mentioned, they were translated as
417:. A verse mentions that Aryabhata was the head of an institution (
3602:
1968:
1894:
Journal of the Royal Asiatic Society of Great Britain and Ireland
1683:
1457:
1379:
471:
426:
3850:
Shanti Swarup Bhatnagar Prize recipients in Mathematical Science
3297:
1556:), and that Aryabhata's system was not explicitly heliocentric.
1226:{\displaystyle 1^{2}+2^{2}+\cdots +n^{2}={n(n+1)(2n+1) \over 6}}
537:), possibly angle-measuring devices, semicircular and circular (
3592:
3399:
Astronomy Across Cultures: The History of Non-Western Astronomy
1768:
introduced in 1073 CE by a group of astronomers including
1634:
1461:
669:
526:
304:
3518:
3392:(2000). 'Birth and Early Development of Indian Astronomy'. In
3077:
Noel Swerdlow, "Review: A Lost Monument of Indian Astronomy,"
732:, node, shape of the earth, cause of day and night, rising of
3198:
3006:, Mohan Apte, Pune, India, Rajhans Publications, 2009, p.25,
1737:). In particular, the astronomical tables in the work of the
1714:
1664:
1445:
1328:{\displaystyle 1^{3}+2^{3}+\cdots +n^{3}=(1+2+\cdots +n)^{2}}
1043:, which means "cove" or "bay"; thence comes the English word
611:
414:
338:
334:
207:
193:
82:
78:
74:
2885:(1996). "Astronomy in India". In Walker, Christopher (ed.).
2422:, a village near the city of Patna) and wrote a book called
2471:
1829:
1773:
1653:
1497:
1493:
1453:
1437:
1395:, where he gives the number of rotations of the Earth in a
995:
976:
In Ganitapada 6, Aryabhata gives the area of a triangle as
964:(c. 820 CE), this approximation was mentioned in
790:
594:
Direct details of Aryabhata's work are known only from the
49:
4051:
Infinite series expansions for the trigonometric functions
2338:
Pride of India: A Glimpse into India's Scientific Heritage
1119:, Aryabhata provided elegant results for the summation of
1059:
since ancient times has been to find integer solutions to
797:
argues that knowledge of zero was implicit in Aryabhata's
1734:
1658:
1449:
1027:, meaning "pocket" or "fold (in a garment)". (In Arabic,
1007:
740:
added at the end, extolling the virtues of the work, etc.
646:
2916:, 22 (1956), pp. 165–192; reprinted in Otto Neugebauer,
2806:
square of the sum of the series is the sum of the cubes.
2212:
An Introduction to the History and Philosophy of Science
1031:
is a meaningless word.) Later in the 12th century, when
983:
tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ
710:
s, and a seven-day week with names for the days of week.
3287:"New Microorganisms Discovered in Earth's Stratosphere"
2789:(Second ed.). John Wiley & Sons, Inc. p.
2592:
Dutta, Bibhutibhushan; Singh, Avadhesh Narayan (1962).
1814:
Aryabhatta Research Institute of Observational Sciences
835:
736:
on horizon, etc. In addition, some versions cite a few
509:, and later mathematicians and commentators, including
389:
Aryabhata mentions "Lanka" on several occasions in the
2868:. Translation from K. S. Shukla and K.V. Sarma, K. V.
1764:). In the Islamic world, they formed the basis of the
644:(c. 1st century BCE). There is also a table of sines (
4300:
Ramanujan Institute for Advanced Study in Mathematics
4045:
3372:: An Ancient Indian Work on Mathematics and Astronomy
3172:. Princeton, NJ: Princeton University Press. p.
2235:
1245:
1132:
928:
904:
883:
855:
caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
1969:
Britannica Educational Publishing (15 August 2010).
1378:. He may have believed that the planet's orbits are
1914:. Sterling Publishers Private Limited. p. 12.
557:of at least two types, bow-shaped and cylindrical.
2889:. London: British Museum Press. pp. 123–142.
2841:
2693:
2662:
2391:
2359:The Surya Siddhanta: A Textbook of Hindu Astronomy
2268:
2082:
2080:
2078:
2076:
1935:
1327:
1225:
934:
914:
889:
3458:
3419:New Delhi: Indian National Science Academy, 1976.
2645:How Aryabhata got the earth's circumference right
1941:
1745:(11th century) were translated into Latin as the
942:, which is accurate to two parts in one million.
4317:
2940:, New York: Springer-Verlag, 1996, pp. 178–189.
2665:Indian Mathematics and Astronomy: Some Landmarks
2356:Ebenezer Burgess; Phanindralal Gangooly (1989).
2335:R.M. Pujari; Pradeep Kolhe; N. R. Kumar (2006).
1011:. When Arabic writers translated his works from
441:Aryabhata is the author of several treatises on
425:) at Kusumapura, and, because the university of
3417:Aryabhata: Indian Mathematician and Astronomer.
2640:
2638:
2073:
1972:The Britannica Guide to Numbers and Measurement
1816:(ARIES) near Nainital, India. The inter-school
1348:Aryabhata's system of astronomy was called the
3196:
2920:New York: Springer-Verlag, 1983, pp. 129–156.
1749:(12th century) and remained the most accurate
1385:
945:It is speculated that Aryabhata used the word
776:
323:that he was 23 years old 3,600 years into the
186:solution of single variable quadratic equation
3539:
3048:
2726:An Introduction to the History of Mathematics
2576:
2176:Bulletin of the Astronomical Society of India
1962:
1713:while translating an Arabic geometry text to
801:as a place holder for the powers of ten with
560:A third text, which may have survived in the
517:. This work appears to be based on the older
44:Statue depicting Aryabhata on the grounds of
3487:The Biographical Encyclopedia of Astronomers
2859:Aryabhatiya 1.3ab, see Plofker 2009, p. 111.
2635:
1975:. The Rosen Publishing Group. pp. 97–.
1682:. He was also the first to specify sine and
1476:. Another element in Aryabhata's model, the
280:, 499 CE, he was 23 years old) and the
3455:in various formats at the Internet Archive.
3165:
2753:, October 2002. Also see earlier overview:
2723:
2687:
2290:
2124:
2052:
2025:
2021:
2019:
1995:
863:ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
4067:Kerala school of astronomy and mathematics
3546:
3532:
3515:Storytelling Science column, November 2004
3336:The History of Mathematics: A Brief Course
2957:R.C.Gupta (31 July 1997). "Āryabhaṭa". In
2591:
2130:"Āryabhaṭa: His name, time and provenance"
1824:, a species of bacteria discovered in the
1050:
834:Aryabhata worked on the approximation for
668:), arithmetic and geometric progressions,
314:
38:
2956:
2950:
2312:
2169:
2167:
2165:
2163:
2161:
2159:
2157:
2002:. Pearson Education India. pp. 95–.
1887:
1621:Learn how and when to remove this message
381:which was the historical capital city of
16:Indian mathematician-astronomer (476–550)
4295:Homi Bhabha Centre for Science Education
3485:. In Thomas Hockey; et al. (eds.).
3422:
2362:. Motilal Banarsidass Publ. p. 46.
2297:. Alpha Science Int'l Ltd. p. 200.
2046:
2016:
1563:
3470:MacTutor History of Mathematics Archive
2918:Astronomy and History: Selected Essays,
2881:
2830:MacTutor History of Mathematics archive
2469:
2215:. Pearson Education India. p. 52.
2120:
2118:
2116:
2114:
2112:
2110:
2056:Teaching World History: A Resource Book
549:, an umbrella-shaped device called the
4318:
3553:
3231:(6 ed.). May 2001. Archived from
3150:: CS1 maint: archived copy as title (
2696:History of Mathematics: A Brief Course
2667:. Bangalore: Jnana Deep Publications.
2619:Geometry: Seeing, Doing, Understanding
2616:
2394:History of Mathematics: A Brief Course
2319:. Kala Occult Publishers. p. 44.
2236:Radhakrishnan Kuttoor (25 June 2007),
2173:
2154:
1989:
1883:
1881:
1879:
1725:, which means "fold in a garment", L.
960:After Aryabhatiya was translated into
785:system, first seen in the 3rd-century
190:value of π correct to 4 decimal places
3527:
3480:
3393:
3353:
3332:
3115:Archive for History of Exact Sciences
2775:
2541:
2539:
2537:
2535:
2533:
2505:
2503:
2501:
2499:
2497:
2495:
2382:
2263:
2208:
2202:
2029:Ancient Indian Leaps into Mathematics
1907:
826:
3104:makes no reference to such a theory.
2817:J. J. O'Connor and E. F. Robertson,
2740:"Diophantine equations: The Kuttaka"
2137:Indian Journal of History of Science
2107:
1946:. www-history.mcs.st-andrews.ac.uk.
1709:in Arabic and then misunderstood by
1603:adding citations to reliable sources
1574:
1504:(identified as the pseudo-planetary
1023:. Later writers substituted it with
3820:Subbayya Sivasankaranarayana Pillai
1876:
1519:
993:Aryabhata discussed the concept of
626:: (13 verses): large units of time—
344:
13:
4280:Institute of Mathematical Sciences
3489:. New York: Springer. p. 63.
3305:"ISRO Press Release 16 March 2009"
3293:from the original on 1 April 2018.
3132:from the original on 18 March 2009
2530:
2492:
1352:, in which days are reckoned from
14:
4387:
4346:6th-century Indian mathematicians
4341:5th-century Indian mathematicians
4290:Harish-Chandra Research Institute
3800:K. R. Parthasarathy (probabilist)
3442:
3263:. 3 February 2006. Archived from
3205:from the original on 13 July 2007
2596:. Asia Publishing House, Bombay.
2470:Elgarøy, Øystein (18 June 2024),
2341:. SAMSKRITA BHARATI. p. 63.
2272:Indian Astronomy: An Introduction
1950:from the original on 11 July 2015
1015:into Arabic, they referred it as
915:{\displaystyle 62832 \over 20000}
576:scholar and chronicler of India,
409:(CE 629), identify Kusumapura as
2581:. London: John Wiley & Sons.
2275:. Orient Blackswan. p. 82.
1996:Bharati Ray (1 September 2009).
1579:
1535:
1399:, and made more explicit in his
455:is the only one which survives.
3509:"Aryabhata and Diophantus' son"
3289:. ScienceDaily. 18 March 2009.
3279:
3247:
3217:
3190:
3159:
3107:
3084:
3071:
3042:
3029:
3016:
2990:
2981:
2930:
2904:
2875:
2862:
2853:
2811:
2781:"The Mathematics of the Hindus"
2769:
2732:
2717:
2690:"The Mathematics of the Hindus"
2681:
2656:
2610:
2585:
2570:
2463:
2431:
2376:
2254:
2229:
2026:B. S. Yadav (28 October 2010).
1942:O'Connor, J J; Robertson, E F.
1820:is also named after him, as is
1792:Aryabhatta Knowledge University
1590:needs additional citations for
1055:A problem of great interest to
971:
654:is given as 4.32 million years.
196:, calculation of the length of
178:reflection of light by the Moon
4356:6th-century Indian astronomers
4351:5th-century Indian astronomers
4275:Chennai Mathematical Institute
3644:Melpathur Narayana Bhattathiri
3326:
3098:known in ancient India as the
2887:Astronomy before the Telescope
2059:. M.E. Sharpe. pp. 112–.
1911:Sterling Dictionary of Physics
1901:
1753:used in Europe for centuries.
1316:
1291:
1214:
1199:
1196:
1184:
1071:'s commentary on Aryabhatiya:
771:
753:, c. 600 CE) and by
583:
1:
3427:. Springer-Verlag, New York.
3199:"Online Etymology Dictionary"
2439:"Get ready for solar eclipse"
2388:The Mathematics of the Hindus
2238:"Aryabhata lived in Ponnani?"
1870:
1865:List of Indian mathematicians
1554:Babylonian astronomical texts
373:It has been claimed that the
274:(which mentions that in 3600
252:) was the first of the major
174:rotation of Earth on its axis
4376:People from the Gupta Empire
4265:Indian Statistical Institute
3519:Surya Siddhanta translations
2756:Mathematics in Ancient India
2663:S. Balachandra Rao (1998) .
2594:History of Hindu Mathematics
2143:(4): 105–115. Archived from
1343:
1039:with its Latin counterpart,
400:
293:
7:
4285:Indian Institute of Science
4270:Bhaskaracharya Pratishthana
4148:A. A. Krishnaswamy Ayyangar
4113:Shankar Balakrishna Dikshit
4040:Hindu–Arabic numeral system
3368:
3362:
2269:S. Balachandra Rao (2000).
1851:
1842:
1835:
1818:Aryabhata Maths Competition
1487:
1386:Motions of the Solar System
1087:
1067:.) This is an example from
999:in his work by the name of
982:
862:
854:
844:
793:, the French mathematician
777:Place value system and zero
420:
240:
10:
4392:
4371:6th-century Indian writers
3780:Subrahmanyan Chandrasekhar
2617:Jacobs, Harold R. (2003).
1999:Different Types of History
1678:) influenced the birth of
1110:
587:
319:Aryabhata mentions in the
260:from the classical age of
21:Aryabhata (disambiguation)
18:
4255:
4219:
4193:
4097:
4059:
4025:
3862:
3790:Veeravalli S. Varadarajan
3757:
3616:
3570:
3561:
3229:The Columbia Encyclopedia
3117:59 (2005): 563–576, n. 4
3002:
2557:University of St. Andrews
1559:
1337:squared triangular number
1065:Chinese remainder theorem
370:rivers in central India.
225:
203:
160:
146:
132:
122:
117:
107:
102:
98:
90:
56:
37:
30:
4206:Henry Thomas Colebrooke
3795:S. R. Srinivasa Varadhan
3481:Achar, Narahari (2007).
3475:University of St Andrews
3449:1930 English translation
2967:. Springer. p. 72.
2870:Āryabhaṭīya of Āryabhaṭa
2786:A History of Mathematics
2294:Ancient Indian Astronomy
2032:. Springer. p. 88.
1797:India's first satellite
1686:(1 − cos
1645:and in the 10th century
533:), a shadow instrument (
436:
356:, "one belonging to the
268:. His works include the
3679:Mādhava of Saṅgamagrāma
3415:Shukla, Kripa Shankar.
3197:Douglas Harper (2001).
2824:19 October 2012 at the
2762:2 November 2014 at the
2745:2 November 2014 at the
2650:15 January 2017 at the
2547:"Aryabhata - Biography"
1637:translation during the
1569:India's first satellite
1051:Indeterminate equations
716:(50 verses): Geometric/
545:), a cylindrical stick
352:describes Aryabhata as
315:Time and place of birth
298:
3339:. Wiley-Interscience.
3307:. ISRO. Archived from
3049:Hugh Thurston (1996).
2987:Ansari, p. 13, Table 1
2838:
2700:. Wiley-Interscience.
2577:George. Ifrah (1998).
1853:Āryabhaṭa's sine table
1572:
1416:Aryabhata described a
1414:
1382:rather than circular.
1329:
1227:
1123:of squares and cubes:
936:
935:{\displaystyle 3.1416}
916:
891:
872:
660:(33 verses): covering
480:spherical trigonometry
4361:Scientists from Patna
3890:Brāhmasphuṭasiddhānta
3423:Thurston, H. (1994).
3333:Cooke, Roger (1997).
3081:, 64 (1973): 239–243.
2834:
2477:Store norske leksikon
1944:"Aryabhata the Elder"
1674:), and inverse sine (
1571:named after Aryabhata
1567:
1405:
1330:
1228:
1061:Diophantine equations
1057:Indian mathematicians
937:
917:
892:
850:
4166:T. A. Saraswati Amma
3877:Bakhshali manuscript
3845:Kannan Soundararajan
3461:Robertson, Edmund F.
3355:Clark, Walter Eugene
3169:Mathematics in India
3166:Kim Plofker (2009).
3092:Aristarchus of Samos
2724:Howard Eves (1990).
2688:Roger Cooke (1997).
2291:L. Satpathy (2003).
2053:Heidi Roupp (1997).
1844:Āryabhaṭa numeration
1832:scientists in 2009.
1721:was the Arabic word
1599:improve this article
1432:(slow) and a larger
1243:
1130:
968:'s book on algebra.
926:
901:
890:{\displaystyle \pi }
881:
787:Bakhshali Manuscript
578:Abū Rayhān al-Bīrūnī
182:sinusoidal functions
94:550 CE (aged 73–74)
19:For other uses, see
4366:Scholars from Bihar
4336:Indian cosmologists
4242:Islamic mathematics
4201:Walter Eugene Clark
3995:Vasishtha Siddhanta
3967:Siddhānta Shiromani
3946:Paitamaha Siddhanta
3825:Tilak Raj Prabhakar
3770:Satyendra Nath Bose
3765:Srinivasa Ramanujan
3719:Nilakantha Somayaji
3459:O'Connor, John J.;
2913:Scripta Mathematica
2819:Aryabhata the Elder
2516:Gujarati Vishwakosh
2188:1977BASI....5...10A
1897:. pp. 392–406.
1810:Indian 2-rupee note
1652:His definitions of
1510:Guillaume Le Gentil
1099:algebra was called
1033:Gherardo of Cremona
755:Nilakantha Somayaji
488:quadratic equations
484:continued fractions
482:. It also contains
103:Academic background
3734:Gangesha Upadhyaya
3555:Indian mathematics
3401:. Boston: Kluwer.
3255:"Maths can be fun"
3235:on 17 October 2007
1908:Singh, J. (1999).
1860:Indian mathematics
1822:Bacillus aryabhata
1786:Gregorian calendar
1717:. He assumed that
1639:Islamic Golden Age
1573:
1426:Paitāmahasiddhānta
1325:
1223:
932:
908:
887:
799:place-value system
759:Aryabhatiya Bhasya
724:, features of the
476:plane trigonometry
262:Indian mathematics
4313:
4312:
4119:Sudhakara Dvivedi
3939:Paulisa Siddhanta
3858:
3857:
3714:Jagannatha Samrat
3709:Achyuta Pisharati
3496:978-0-387-31022-0
3382:978-1-4254-8599-3
3311:on 5 January 2012
3267:on 1 October 2007
3183:978-0-691-12067-6
3101:Paulisa Siddhanta
3012:978-81-7434-480-9
2974:978-0-7923-4066-9
2738:Amartya K Dutta,
2398:. Wiley. p.
2369:978-81-208-0612-2
2348:978-81-87276-27-2
2326:978-0-9709636-2-8
2316:Classical Muhurta
2304:978-81-7319-432-0
2282:978-81-7371-205-0
2222:978-81-317-2890-1
2150:on 31 March 2010.
2066:978-1-56324-420-9
2039:978-0-8176-4694-3
2009:978-81-317-1818-6
1982:978-1-61530-218-5
1921:978-81-7359-124-2
1711:Gerard of Cremona
1631:
1630:
1623:
1526:sidereal rotation
1221:
1092:(कुट्टक) method.
912:
827:Approximation of
730:celestial equator
608:Arya-shatas-aShTa
383:Thiruvanchikkulam
229:
228:
4383:
3953:Romaka Siddhanta
3835:Akshay Venkatesh
3805:M. S. Narasimhan
3775:P.C. Mahalanobis
3568:
3567:
3548:
3541:
3534:
3525:
3524:
3500:
3477:
3438:
3412:
3386:
3371:
3365:
3350:
3321:
3320:
3318:
3316:
3301:
3295:
3294:
3283:
3277:
3276:
3274:
3272:
3251:
3245:
3244:
3242:
3240:
3221:
3215:
3214:
3212:
3210:
3194:
3188:
3187:
3163:
3157:
3155:
3149:
3141:
3139:
3137:
3131:
3124:
3111:
3105:
3088:
3082:
3075:
3069:
3068:
3046:
3040:
3033:
3027:
3020:
3014:
3004:
2994:
2988:
2985:
2979:
2978:
2954:
2948:
2934:
2928:
2908:
2902:
2900:
2879:
2873:
2866:
2860:
2857:
2851:
2847:Hayashi (2008),
2845:
2839:
2815:
2809:
2808:
2773:
2767:
2736:
2730:
2729:
2721:
2715:
2714:
2699:
2685:
2679:
2678:
2660:
2654:
2642:
2633:
2632:
2614:
2608:
2607:
2589:
2583:
2582:
2574:
2568:
2567:
2565:
2563:
2543:
2528:
2527:
2525:
2523:
2507:
2490:
2488:
2487:
2485:
2467:
2461:
2460:
2458:
2456:
2450:
2443:
2435:
2429:
2428:
2397:
2380:
2374:
2373:
2352:
2330:
2308:
2286:
2258:
2252:
2251:
2246:, archived from
2233:
2227:
2226:
2206:
2200:
2199:
2171:
2152:
2151:
2149:
2134:
2122:
2105:
2104:
2102:
2100:
2093:Encyclopedia.com
2084:
2071:
2070:
2050:
2044:
2043:
2023:
2014:
2013:
1993:
1987:
1986:
1966:
1960:
1959:
1957:
1955:
1939:
1933:
1932:
1930:
1928:
1905:
1899:
1898:
1885:
1856:
1847:
1747:Tables of Toledo
1626:
1619:
1615:
1612:
1606:
1583:
1575:
1520:Sidereal periods
1376:Earth's rotation
1334:
1332:
1331:
1326:
1324:
1323:
1287:
1286:
1268:
1267:
1255:
1254:
1232:
1230:
1229:
1224:
1222:
1217:
1179:
1174:
1173:
1155:
1154:
1142:
1141:
1090:
985:
941:
939:
938:
933:
921:
919:
918:
913:
903:
896:
894:
893:
888:
865:
857:
848:10), he writes:
847:
761:(1465 CE).
722:celestial sphere
666:kṣetra vyāvahāra
641:Vedanga Jyotisha
564:translation, is
423:
345:Other hypothesis
266:Indian astronomy
243:
42:
28:
27:
4391:
4390:
4386:
4385:
4384:
4382:
4381:
4380:
4316:
4315:
4314:
4309:
4257:
4251:
4215:
4189:
4160:C. T. Rajagopal
4107:Bapudeva Sastri
4099:
4093:
4055:
4035:Brahmi numerals
4027:
4021:
3981:Surya Siddhanta
3854:
3830:Manjul Bhargava
3753:
3612:
3557:
3552:
3513:Hindustan Times
3497:
3453:The Aryabhatiya
3445:
3435:
3425:Early Astronomy
3409:
3390:Kak, Subhash C.
3383:
3347:
3329:
3324:
3314:
3312:
3303:
3302:
3298:
3285:
3284:
3280:
3270:
3268:
3253:
3252:
3248:
3238:
3236:
3223:
3222:
3218:
3208:
3206:
3195:
3191:
3184:
3164:
3160:
3143:
3142:
3135:
3133:
3129:
3122:
3120:"Archived copy"
3118:
3112:
3108:
3096:Greek astronomy
3089:
3085:
3076:
3072:
3065:
3057:. p. 188.
3051:Early Astronomy
3047:
3043:
3034:
3030:
3021:
3017:
2995:
2991:
2986:
2982:
2975:
2955:
2951:
2938:Early Astronomy
2936:Hugh Thurston,
2935:
2931:
2909:
2905:
2897:
2880:
2876:
2867:
2863:
2858:
2854:
2846:
2842:
2833:
2826:Wayback Machine
2816:
2812:
2801:
2774:
2770:
2764:Wayback Machine
2747:Wayback Machine
2737:
2733:
2722:
2718:
2708:
2686:
2682:
2675:
2661:
2657:
2652:Wayback Machine
2643:
2636:
2629:
2615:
2611:
2604:
2590:
2586:
2575:
2571:
2561:
2559:
2545:
2544:
2531:
2521:
2519:
2509:
2508:
2493:
2483:
2481:
2468:
2464:
2454:
2452:
2451:on 21 July 2011
2448:
2441:
2437:
2436:
2432:
2410:
2381:
2377:
2370:
2353:
2349:
2332:
2327:
2313:Ernst Wilhelm.
2310:
2305:
2288:
2283:
2266:
2261:
2259:
2255:
2234:
2230:
2223:
2207:
2203:
2172:
2155:
2147:
2132:
2123:
2108:
2098:
2096:
2086:
2085:
2074:
2067:
2051:
2047:
2040:
2024:
2017:
2010:
1994:
1990:
1983:
1967:
1963:
1953:
1951:
1940:
1936:
1926:
1924:
1922:
1906:
1902:
1886:
1877:
1873:
1838:
1766:Jalali calendar
1627:
1616:
1610:
1607:
1596:
1584:
1562:
1538:
1522:
1490:
1474:Greek astronomy
1388:
1350:audAyaka system
1346:
1319:
1315:
1282:
1278:
1263:
1259:
1250:
1246:
1244:
1241:
1240:
1180:
1178:
1169:
1165:
1150:
1146:
1137:
1133:
1131:
1128:
1127:
1113:
1053:
974:
927:
924:
923:
902:
899:
898:
882:
879:
878:
867:
859:
832:
815:tradition from
779:
774:
720:aspects of the
619:s or chapters:
592:
586:
519:Surya Siddhanta
439:
403:
347:
317:
301:
296:
164:Explanation of
112:Surya Siddhanta
86:
72:
68:
61:
52:
33:
24:
17:
12:
11:
5:
4389:
4379:
4378:
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4181:
4175:
4169:
4163:
4157:
4151:
4145:
4140:
4134:
4131:P. C. Sengupta
4128:
4122:
4116:
4110:
4103:
4101:
4095:
4094:
4092:
4091:
4069:
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4057:
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4037:
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4029:
4023:
4022:
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4019:
4012:
4005:
3998:
3991:
3988:Tantrasamgraha
3984:
3977:
3970:
3963:
3956:
3949:
3942:
3935:
3928:
3921:
3914:
3911:Karanapaddhati
3907:
3900:
3897:Ganita Kaumudi
3893:
3886:
3879:
3874:
3866:
3864:
3860:
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3856:
3855:
3853:
3852:
3847:
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3837:
3832:
3827:
3822:
3817:
3815:Harish-Chandra
3812:
3810:C. S. Seshadri
3807:
3802:
3797:
3792:
3787:
3782:
3777:
3772:
3767:
3761:
3759:
3755:
3754:
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3751:
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3744:Sankara Variar
3741:
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3711:
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3611:
3610:
3605:
3600:
3595:
3590:
3585:
3580:
3574:
3572:
3565:
3563:Mathematicians
3559:
3558:
3551:
3550:
3543:
3536:
3528:
3522:
3521:
3516:
3506:
3495:
3478:
3456:
3444:
3443:External links
3441:
3440:
3439:
3433:
3420:
3413:
3407:
3397:, ed. (2000).
3395:Selin, Helaine
3387:
3381:
3351:
3345:
3328:
3325:
3323:
3322:
3296:
3278:
3246:
3225:"Omar Khayyam"
3216:
3189:
3182:
3158:
3106:
3083:
3070:
3063:
3041:
3028:
3015:
2989:
2980:
2973:
2949:
2929:
2903:
2895:
2883:Pingree, David
2874:
2861:
2852:
2840:
2810:
2799:
2777:Boyer, Carl B.
2768:
2731:
2716:
2706:
2680:
2673:
2655:
2634:
2627:
2609:
2602:
2584:
2569:
2529:
2491:
2480:(in Norwegian)
2462:
2430:
2408:
2375:
2368:
2347:
2325:
2303:
2281:
2253:
2250:on 1 July 2007
2228:
2221:
2209:Menon (2009).
2201:
2153:
2106:
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2065:
2045:
2038:
2015:
2008:
1988:
1981:
1961:
1934:
1920:
1900:
1874:
1872:
1869:
1868:
1867:
1862:
1857:
1848:
1837:
1834:
1762:Hindu calendar
1629:
1628:
1587:
1585:
1578:
1561:
1558:
1537:
1534:
1521:
1518:
1489:
1486:
1387:
1384:
1371:Khandakhadyaka
1345:
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1322:
1318:
1314:
1311:
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1305:
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1112:
1109:
1101:kuṭṭaka-gaṇita
1077:
1076:
1052:
1049:
988:
987:
973:
970:
931:
911:
907:
886:
831:
825:
778:
775:
773:
770:
742:
741:
734:zodiacal signs
711:
697:
655:
588:Main article:
585:
582:
551:chhatra-yantra
503:Arya-siddhanta
496:table of sines
438:
435:
402:
399:
346:
343:
316:
313:
300:
297:
295:
292:
227:
226:
223:
222:
205:
201:
200:
192:, diameter of
162:
158:
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148:
144:
143:
134:
133:Main interests
130:
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124:
120:
119:
115:
114:
109:
105:
104:
100:
99:
96:
95:
92:
88:
87:
62:
58:
54:
53:
43:
35:
34:
31:
15:
9:
6:
4:
3:
2:
4388:
4377:
4374:
4372:
4369:
4367:
4364:
4362:
4359:
4357:
4354:
4352:
4349:
4347:
4344:
4342:
4339:
4337:
4334:
4332:
4329:
4327:
4324:
4323:
4321:
4306:
4303:
4301:
4298:
4296:
4293:
4291:
4288:
4286:
4283:
4281:
4278:
4276:
4273:
4271:
4268:
4266:
4263:
4262:
4260:
4254:
4248:
4245:
4243:
4240:
4238:
4235:
4233:
4230:
4228:
4225:
4224:
4222:
4220:Other regions
4218:
4212:
4211:David Pingree
4209:
4207:
4204:
4202:
4199:
4198:
4196:
4192:
4185:
4182:
4179:
4176:
4173:
4170:
4167:
4164:
4161:
4158:
4155:
4152:
4149:
4146:
4144:
4141:
4138:
4135:
4132:
4129:
4126:
4125:M. Rangacarya
4123:
4120:
4117:
4114:
4111:
4108:
4105:
4104:
4102:
4098:Historians of
4096:
4089:
4085:
4081:
4077:
4073:
4072:Jantar Mantar
4070:
4068:
4065:
4064:
4062:
4058:
4052:
4049:
4047:
4043:
4041:
4038:
4036:
4033:
4032:
4030:
4024:
4018:
4017:
4013:
4011:
4010:
4006:
4004:
4003:
3999:
3997:
3996:
3992:
3990:
3989:
3985:
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3978:
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3975:
3971:
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3838:
3836:
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3828:
3826:
3823:
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3816:
3813:
3811:
3808:
3806:
3803:
3801:
3798:
3796:
3793:
3791:
3788:
3786:
3783:
3781:
3778:
3776:
3773:
3771:
3768:
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3762:
3760:
3756:
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3717:
3715:
3712:
3710:
3707:
3705:
3702:
3700:
3697:
3695:
3692:
3690:
3689:Mahendra Sūri
3687:
3685:
3682:
3680:
3677:
3675:
3672:
3670:
3667:
3665:
3662:
3660:
3657:
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3645:
3642:
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3606:
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3530:
3529:
3526:
3520:
3517:
3514:
3510:
3507:
3504:
3498:
3492:
3488:
3484:
3483:"Āryabhaṭa I"
3479:
3476:
3472:
3471:
3466:
3462:
3457:
3454:
3450:
3447:
3446:
3436:
3434:0-387-94107-X
3430:
3426:
3421:
3418:
3414:
3410:
3408:0-7923-6363-9
3404:
3400:
3396:
3391:
3388:
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3373:
3370:
3364:
3356:
3352:
3348:
3346:0-471-18082-3
3342:
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3331:
3330:
3310:
3306:
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3292:
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3282:
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3250:
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3121:
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3110:
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3097:
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3074:
3066:
3064:0-387-94822-8
3060:
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3032:
3025:
3019:
3013:
3009:
3005:
3000:
2993:
2984:
2976:
2970:
2966:
2965:
2960:
2959:Helaine Selin
2953:
2947:
2946:0-387-94822-8
2943:
2939:
2933:
2927:
2926:0-387-90844-7
2923:
2919:
2915:
2914:
2907:
2898:
2896:0-7141-1746-3
2892:
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2856:
2850:
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2837:
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2814:
2807:
2802:
2800:0-471-54397-7
2796:
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2757:
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2709:
2707:0-471-18082-3
2703:
2698:
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2684:
2676:
2674:81-7371-205-0
2670:
2666:
2659:
2653:
2649:
2646:
2641:
2639:
2630:
2628:0-7167-4361-2
2624:
2620:
2613:
2605:
2603:81-86050-86-8
2599:
2595:
2588:
2580:
2573:
2558:
2554:
2553:
2552:Maths History
2548:
2542:
2540:
2538:
2536:
2534:
2518:
2517:
2512:
2506:
2504:
2502:
2500:
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2478:
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2440:
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2427:
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2421:
2417:
2411:
2409:9780471180821
2405:
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2138:
2131:
2127:
2121:
2119:
2117:
2115:
2113:
2111:
2095:
2094:
2089:
2088:"Aryabhatiya"
2083:
2081:
2079:
2077:
2068:
2062:
2058:
2057:
2049:
2041:
2035:
2031:
2030:
2022:
2020:
2011:
2005:
2001:
2000:
1992:
1984:
1978:
1974:
1973:
1965:
1949:
1945:
1938:
1923:
1917:
1913:
1912:
1904:
1896:
1895:
1890:
1884:
1882:
1880:
1875:
1866:
1863:
1861:
1858:
1855:
1854:
1849:
1846:
1845:
1840:
1839:
1833:
1831:
1827:
1823:
1819:
1815:
1811:
1807:
1804:
1800:
1795:
1793:
1789:
1787:
1783:
1779:
1775:
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1767:
1763:
1759:
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1650:
1648:
1644:
1640:
1636:
1625:
1622:
1614:
1604:
1600:
1594:
1593:
1588:This section
1586:
1582:
1577:
1576:
1570:
1566:
1557:
1555:
1551:
1547:
1543:
1536:Heliocentrism
1533:
1531:
1530:sidereal year
1527:
1517:
1515:
1514:lunar eclipse
1511:
1507:
1503:
1499:
1495:
1485:
1483:
1479:
1475:
1469:
1467:
1463:
1459:
1455:
1451:
1447:
1443:
1439:
1435:
1431:
1427:
1423:
1419:
1413:
1411:
1404:
1402:
1398:
1394:
1383:
1381:
1377:
1373:
1372:
1367:
1363:
1362:ardha-rAtrikA
1359:
1355:
1351:
1338:
1320:
1312:
1309:
1306:
1303:
1300:
1297:
1294:
1288:
1283:
1279:
1275:
1272:
1269:
1264:
1260:
1256:
1251:
1247:
1239:
1238:
1237:
1218:
1211:
1208:
1205:
1202:
1193:
1190:
1187:
1181:
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1170:
1166:
1162:
1159:
1156:
1151:
1147:
1143:
1138:
1134:
1126:
1125:
1124:
1122:
1118:
1108:
1106:
1102:
1097:
1096:
1091:
1089:
1083:
1074:
1073:
1072:
1070:
1066:
1062:
1058:
1048:
1046:
1042:
1038:
1034:
1030:
1026:
1022:
1018:
1014:
1010:
1009:
1004:
1003:
998:
997:
991:
986:
984:
979:
978:
977:
969:
967:
963:
958:
956:
952:
948:
943:
929:
909:
905:
884:
875:
871:
868:
866:
864:
858:
856:
849:
846:
841:
837:
830:
824:
822:
818:
814:
809:
807:
804:
800:
796:
795:Georges Ifrah
792:
788:
784:
769:
766:
762:
760:
756:
752:
747:
739:
735:
731:
727:
723:
719:
718:trigonometric
715:
712:
709:
705:
701:
700:Kalakriyapada
698:
695:
691:
690:indeterminate
687:
683:
679:
675:
671:
667:
663:
659:
656:
653:
649:
648:
643:
642:
637:
633:
629:
625:
622:
621:
620:
618:
613:
609:
605:
604:Ashmakatantra
601:
597:
591:
581:
579:
575:
571:
567:
563:
558:
556:
552:
548:
544:
543:chakra-yantra
540:
539:dhanur-yantra
536:
535:chhAyA-yantra
532:
531:shanku-yantra
528:
524:
520:
516:
512:
508:
504:
499:
497:
493:
489:
485:
481:
477:
473:
469:
465:
461:
456:
454:
453:
448:
444:
434:
432:
428:
424:
422:
416:
412:
408:
398:
396:
392:
387:
384:
380:
376:
371:
369:
365:
361:
360:
355:
351:
342:
340:
336:
333:(present day
332:
328:
327:
322:
312:
310:
306:
291:
288:
286:
285:
279:
278:
273:
272:
267:
263:
259:
255:
254:mathematician
251:
247:
242:
237:
233:
224:
221:
217:
213:
209:
206:
202:
199:
198:sidereal year
195:
191:
187:
183:
179:
175:
171:
170:solar eclipse
167:
166:lunar eclipse
163:
161:Notable ideas
159:
156:
152:
149:
147:Notable works
145:
142:
138:
135:
131:
128:
125:
121:
118:Academic work
116:
113:
110:
106:
101:
97:
93:
89:
84:
80:
76:
73:(present-day
71:
66:
63:Kusumapura /
59:
55:
51:
47:
41:
36:
29:
26:
22:
4258:institutions
4178:K. S. Shukla
4150:(1892– 1953)
4016:Yavanajataka
4014:
4007:
4000:
3993:
3986:
3979:
3974:Śulba Sūtras
3972:
3965:
3960:Sadratnamala
3958:
3951:
3944:
3937:
3930:
3923:
3916:
3909:
3904:Kanakkusaram
3902:
3895:
3888:
3881:
3869:
3739:Varāhamihira
3704:Parameshvara
3659:Govindasvāmi
3629:Āryabhaṭa II
3623:
3486:
3468:
3452:
3424:
3416:
3398:
3359:
3335:
3313:. Retrieved
3309:the original
3299:
3281:
3269:. Retrieved
3265:the original
3258:
3249:
3237:. Retrieved
3233:the original
3228:
3219:
3207:. Retrieved
3192:
3168:
3161:
3134:. Retrieved
3109:
3099:
3086:
3078:
3073:
3050:
3044:
3036:
3031:
3023:
3018:
2997:Aryabhatiya
2996:
2992:
2983:
2963:
2952:
2937:
2932:
2917:
2911:
2906:
2886:
2877:
2869:
2864:
2855:
2848:
2843:
2835:
2813:
2804:
2785:
2771:
2755:
2750:
2734:
2725:
2719:
2711:
2695:
2683:
2664:
2658:
2618:
2612:
2593:
2587:
2578:
2572:
2560:. Retrieved
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4180:(1918–2007)
4174:(1918–1992)
4168:(1918–2000)
4162:(1903–1978)
4156:(1901–1954)
4154:A. N. Singh
4139:(1888–1958)
4137:B. B. Datta
4133:(1876–1962)
4127:(1861–1916)
4121:(1855–1910)
4115:(1853–1898)
4109:(1821–1900)
4100:mathematics
4044:Symbol for
4028:innovations
3925:Lokavibhaga
3871:Aryabhatiya
3669:Jyeṣṭhadeva
3654:Brahmagupta
3639:Bhāskara II
3624:Āryabhaṭa I
3608:Yajnavalkya
3503:PDF version
3465:"Aryabhata"
3363:Āryabhaṭīya
3327:Works cited
2849:Aryabhata I
2472:"Aryabhata"
2424:Aryabhatiya
2126:K. V. Sarma
1778:Afghanistan
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1671:utkrama-jya
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331:Pataliputra
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271:Āryabhaṭīya
258:astronomers
246:Aryabhata I
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3694:Munishvara
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3649:Brahmadeva
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3583:Baudhayana
3136:8 February
2901:pp. 127–9.
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1871:References
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1464:, and the
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4080:New Delhi
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413:, modern
401:Education
326:Kali Yuga
294:Biography
284:siddhanta
277:Kali Yuga
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241:Āryabhaṭa
232:Aryabhata
155:siddhanta
141:astronomy
127:Gupta era
32:Āryabhaṭa
4088:Varanasi
4046:zero (0)
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