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Aryabhatta born place of william

Aryabhata

Indian mathematician-astronomer (476–550)

For other uses, see Aryabhata (disambiguation).

Āryabhaṭa

Illustration of Āryabhaṭa

Born476 CE

Kusumapura / Pataliputra,
Gupta Empire
(present-day Patna, Bihar, India)[1]

Died550 CE (aged 73–74) [2]
InfluencesSurya Siddhanta
EraGupta era
Main interestsMathematics, astronomy
Notable worksĀryabhaṭīya, Arya-siddhanta
Notable ideasExplanation stand for lunar eclipse and solar eclipse, twirl of Earth on its axis, image of light by the Moon, sinusoidal functions, solution of single variable equation equation, value of π correct come upon 4 decimal places, diameter of Soil, calculation of the length of chief year
InfluencedLalla, Bhaskara I, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (476–550 CE)[5][6] was the first of illustriousness major mathematician-astronomers from the classical launch of Indian mathematics and Indian uranology. His works include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old)[7] and the Arya-siddhanta.

For his welldefined mention of the relativity of portage, he also qualifies as a bigger early physicist.[8]

Biography

Name

While there is a veer to misspell his name as "Aryabhatta" by analogy with other names receipt the "bhatta" suffix, his name admiration properly spelled Aryabhata: every astronomical contents spells his name thus,[9] including Brahmagupta's references to him "in more get away from a hundred places by name".[1] Further, in most instances "Aryabhatta" would put together fit the metre either.[9]

Time and switch over of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years advanced in years 3,600 years into the Kali Yuga, but this is not to inconsiderate that the text was composed unmoving that time. This mentioned year corresponds to 499 CE, and implies that earth was born in 476.[6] Aryabhata alarmed himself a native of Kusumapura capture Pataliputra (present day Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." Beside the Buddha's time, a branch work the Aśmaka people settled in goodness region between the Narmada and Godavari rivers in central India.[9][10]

It has antiquated claimed that the aśmaka (Sanskrit use "stone") where Aryabhata originated may attach the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala.[11] This is supported on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city assess hard stones"); however, old records event that the city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, ethics fact that several commentaries on greatness Aryabhatiya have come from Kerala has been used to suggest that squabble was Aryabhata's main place of test and activity; however, many commentaries imitate come from outside Kerala, and dignity Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued cooperation the Kerala hypothesis on the aim of astronomical evidence.[12]

Aryabhata mentions "Lanka" thing several occasions in the Aryabhatiya, on the other hand his "Lanka" is an abstraction, whim for a point on the equator at the same longitude as fulfil Ujjayini.[13]

Education

It is fairly certain that, habit some point, he went to Kusumapura for advanced studies and lived about for some time.[14] Both Hindu become more intense Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura variety Pāṭaliputra, modern Patna.[9] A verse mentions that Aryabhata was the head be unable to find an institution (kulapa) at Kusumapura, highest, because the university of Nalanda was in Pataliputra at the time, rocket is speculated that Aryabhata might take been the head of the Nalanda university as well.[9] Aryabhata is besides reputed to have set up create observatory at the Sun temple amuse Taregana, Bihar.[15]

Works

Aryabhata is the author love several treatises on mathematics and uranology, though Aryabhatiya is the only combine which survives.[16]

Much of the research star subjects in astronomy, mathematics, physics, aggregation, medicine, and other fields.[17]Aryabhatiya, a digest of mathematics and astronomy, was referred to in the Indian mathematical belles-lettres and has survived to modern times.[18] The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, come to rest spherical trigonometry. It also contains lengthened fractions, quadratic equations, sums-of-power series, careful a table of sines.[18]

The Arya-siddhanta, top-notch lost work on astronomical computations, not bad known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians suggest commentators, including Brahmagupta and Bhaskara Frantic. This work appears to be family unit on the older Surya Siddhanta essential uses the midnight-day reckoning, as laggard to sunrise in Aryabhatiya.[10] It as well contained a description of several elephantine instruments: the gnomon (shanku-yantra), a dimness instrument (chhAyA-yantra), possibly angle-measuring devices, arched and circular (dhanur-yantra / chakra-yantra), neat cylindrical stick yasti-yantra, an umbrella-shaped machinery called the chhatra-yantra, and water alfileria of at least two types, meniscus and cylindrical.[10]

A third text, which haw have survived in the Arabic interpretation, is Al ntf or Al-nanf. Situation claims that it is a transliteration by Aryabhata, but the Sanskrit reputation of this work is not familiar. Probably dating from the 9th c it is mentioned by the Farsi scholar and chronicler of India, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details be alarmed about Aryabhata's work are known only distance from the Aryabhatiya. The name "Aryabhatiya" anticipation due to later commentators. Aryabhata herself may not have given it wonderful name.[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise use up the Ashmaka). It is also again referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in the text.[18][8] It is deadly in the very terse style universal of sutra literature, in which talking to line is an aid to honour for a complex system. Thus, interpretation explication of meaning is due get through to commentators. The text consists of glory 108 verses and 13 introductory verses, and is divided into four pādas or chapters:

  1. Gitikapada: (13 verses): unprofessional units of time—kalpa, manvantra, and yuga—which present a cosmology different from a while ago texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There bash also a table of sines (jya), given in a single verse. Greatness duration of the planetary revolutions by means of a mahayuga is given as 4.32 million years.
  2. Ganitapada (33 verses): covering calibration (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, multinomial, simultaneous, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of time advocate a method for determining the positions of planets for a given give to, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week gangster names for the days of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of birth celestial sphere, features of the ecliptic, celestial equator, node, shape of ethics earth, cause of day and falsified, rising of zodiacal signs on view, etc.[17] In addition, some versions summon a few colophons added at nobility end, extolling the virtues of goodness work, etc.[17]

The Aryabhatiya presented a give out of innovations in mathematics and uranology in verse form, which were painstaking for many centuries. The extreme shortness of the text was elaborated break through commentaries by his disciple Bhaskara Unrestrained (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).[18][17]

Aryabhatiya comment also well-known for his description pay the bill relativity of motion. He expressed that relativity thus: "Just as a bloke in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so junk the stationary stars seen by prestige people on earth as moving shooting towards the west."[8]

Mathematics

Place value system post zero

The place-value system, first seen knoll the 3rd-century Bakhshali Manuscript, was manifestly in place in his work. Make your mind up he did not use a representation for zero, the French mathematician Georges Ifrah argues that knowledge of nought was implicit in Aryabhata's place-value formula as a place holder for integrity powers of ten with nullcoefficients.[19]

However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of nobleness alphabet to denote numbers, expressing masses, such as the table of sines in a mnemonic form.[20]

Approximation of π

Aryabhata worked on the approximation for pietistic (π), and may have come unexpected the conclusion that π is unsighted. In the second part of position Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add three to 100, multiply by eight, move then add 62,000. By this decree the circumference of a circle fine-tune a diameter of 20,000 can put pen to paper approached."[21]

This implies that for a bombardment whose diameter is 20000, the periphery will be 62832

i.e, = = , which is accurate to pair parts in one million.[22]

It is suppositional that Aryabhata used the word āsanna (approaching), to mean that not exclusive is this an approximation but ditch the value is incommensurable (or irrational). If this is correct, it assessment quite a sophisticated insight, because righteousness irrationality of pi (π) was cubic in Europe only in 1761 prep between Lambert.[23]

After Aryabhatiya was translated into Semite (c. 820 CE), this approximation was mentioned bear hug Al-Khwarizmi's book on algebra.[10]

Trigonometry

In Ganitapada 6, Aryabhata gives the area of smashing triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, probity result of a perpendicular with rank half-side is the area."[24]

Aryabhata discussed leadership concept of sine in his snitch by the name of ardha-jya, which literally means "half-chord". For simplicity, liquidate started calling it jya. When Semitic writers translated his works from Indic into Arabic, they referred it importance jiba. However, in Arabic writings, vowels are omitted, and it was 1 as jb. Later writers substituted litigation with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later find guilty the 12th century, when Gherardo interrupt Cremona translated these writings from Semite into Latin, he replaced the Semitic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; accordingly comes the English word sine.[25]

Indeterminate equations

A problem of great interest to Amerind mathematicians since ancient times has anachronistic to find integer solutions to Diophantine equations that have the form execution + by = c. (This precision was also studied in ancient Sinitic mathematics, and its solution is most often referred to as the Chinese residue theorem.) This is an example differ Bhāskara's commentary on Aryabhatiya:

Find interpretation number which gives 5 as greatness remainder when divided by 8, 4 as the remainder when divided afford 9, and 1 as the evidence when divided by 7

That is, upon N = 8x+5 = 9y+4 = 7z+1. It turns out that character smallest value for N is 85. In general, diophantine equations, such significance this, can be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more decrepit parts might date to 800 BCE. Aryabhata's method of solving such problems, inflated by Bhaskara in 621 CE, is titled the kuṭṭaka (कुट्टक) method. Kuṭṭaka whirl "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original deed data in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, reprove initially the whole subject of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results funds the summation of series of squares and cubes:[27]

and

(see squared three-sided number)

Astronomy

Aryabhata's system of astronomy was cryed the audAyaka system, in which generation are reckoned from uday, dawn avoid lanka or "equator". Some of consummate later writings on astronomy, which evidently proposed a second model (or ardha-rAtrikA, midnight) are lost but can make ends meet partly reconstructed from the discussion engage Brahmagupta's Khandakhadyaka. In some texts, significant seems to ascribe the apparent service of the heavens to the Earth's rotation. He may have believed turn the planet's orbits are elliptical comparatively than circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Earth rotates about its axis daily, and renounce the apparent movement of the stars is a relative motion caused infant the rotation of the Earth, capricious to the then-prevailing view, that grandeur sky rotated.[22] This is indicated knoll the first chapter of the Aryabhatiya, where he gives the number be paid rotations of the Earth in calligraphic yuga,[30] and made more explicit suspend his gola chapter:[31]

In the same be no more that someone in a boat bring back forward sees an unmoving [object] flattering backward, so [someone] on the equator sees the unmoving stars going always westward. The cause of rising folk tale setting [is that] the sphere relief the stars together with the planets [apparently?] turns due west at glory equator, constantly pushed by the intercontinental wind.

Aryabhata described a geocentric model castigate the Solar System, in which say publicly Sun and Moon are each lie by epicycles. They in turn spin around the Earth. In this brick, which is also found in high-mindedness Paitāmahasiddhānta (c. 425 CE), the motions of rendering planets are each governed by yoke epicycles, a smaller manda (slow) gleam a larger śīghra (fast).[32] The proof of the planets in terms returns distance from earth is taken as: the Moon, Mercury, Venus, the Helios, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions and periods of the planets was calculated relative to uniformly step on the gas points. In the case of Metal and Venus, they move around magnanimity Earth at the same mean mindless as the Sun. In the win over of Mars, Jupiter, and Saturn, they move around the Earth at express speeds, representing each planet's motion bow the zodiac. Most historians of uranology consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.[33] Added element in Aryabhata's model, the śīghrocca, the basic planetary period in regularity to the Sun, is seen saturate some historians as a sign go along with an underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon ahead planets shine by reflected sunlight. As an alternative of the prevailing cosmogony in which eclipses were caused by Rahu charge Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in conditions of shadows cast by and rushing on Earth. Thus, the lunar leave behind occurs when the Moon enters stimulus the Earth's shadow (verse gola.37). Sharptasting discusses at length the size good turn extent of the Earth's shadow (verses gola.38–48) and then provides the process and the size of the eclipsed part during an eclipse. Later Amerind astronomers improved on the calculations, on the contrary Aryabhata's methods provided the core. Climax computational paradigm was so accurate mosey 18th-century scientist Guillaume Le Gentil, close a visit to Pondicherry, India, arrive on the scene the Indian computations of the vitality of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[10]

Considered in modern English units comatose time, Aryabhata calculated the sidereal motility (the rotation of the earth referencing the fixed stars) as 23 noontime, 56 minutes, and 4.1 seconds;[35] rank modern value is 23:56:4.091. Similarly, rule value for the length of rendering sidereal year at 365 days, 6 hours, 12 minutes, and 30 in a nutshell (365.25858 days)[36] is an error position 3 minutes and 20 seconds run faster than the length of a year (365.25636 days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an ginormous model in which the Earth about meanderings on its own axis. His originate also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms well the mean speed of the Phoebus apollo. Thus, it has been suggested ensure Aryabhata's calculations were based on mediocre underlying heliocentric model, in which nobleness planets orbit the Sun,[38][39][40] though that has been rebutted.[41] It has as well been suggested that aspects of Aryabhata's system may have been derived proud an earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,[42] though the evidence is scant.[43] The general consensus is that boss synodic anomaly (depending on the redistribute of the Sun) does not herald a physically heliocentric orbit (such corrections being also present in late City astronomical texts), and that Aryabhata's silhouette was not explicitly heliocentric.[44]

Legacy

Aryabhata's work was of great influence in the Soldier astronomical tradition and influenced several harbour cultures through translations. The Arabic transcription during the Islamic Golden Age (c. 820 CE), was particularly influential. Some of queen results are cited by Al-Khwarizmi snowball in the 10th century Al-Biruni confirmed that Aryabhata's followers believed that decency Earth rotated on its axis.

His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trig. He was also the first play-act specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° finish 90°, to an accuracy of 4 decimal places.

In fact, the contemporary terms "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As solve, they were translated as jiba tell off kojiba in Arabic and then misinterpreted by Gerard of Cremona while translating an Arabic geometry text to Serious. He assumed that jiba was ethics Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).[45]

Aryabhata's astronomical calculation methods were further very influential. Along with the trigonometric tables, they came to be abroad used in the Islamic world standing used to compute many Arabic astronomic tables (zijes). In particular, the galactic tables in the work of integrity Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as primacy Tables of Toledo (12th century) subject remained the most accurate ephemeris encouraged in Europe for centuries.

Calendric calculations devised by Aryabhata and his suite have been in continuous use hold India for the practical purposes atlas fixing the Panchangam (the Hindu calendar). In the Islamic world, they chary the basis of the Jalali diary introduced in 1073 CE by a purpose of astronomers including Omar Khayyam,[46] versions of which (modified in 1925) dingdong the national calendars in use space Iran and Afghanistan today. The dates of the Jalali calendar are supported on actual solar transit, as pen Aryabhata and earlier Siddhanta calendars. That type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar better in the Gregorian calendar.[citation needed]

Aryabhatta Awareness University (AKU), Patna has been method by Government of Bihar for illustriousness development and management of educational secure related to technical, medical, management direct allied professional education in his probity. The university is governed by Province State University Act 2008.

India's premier satellite Aryabhata and the lunar craterAryabhata are both named in his infamy, the Aryabhata satellite also featured sign the reverse of the Indian 2-rupee note. An Institute for conducting investigation in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute claim Observational Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Competition job also named after him,[47] as evenhanded Bacillus aryabhata, a species of microbes discovered in the stratosphere by ISRO scientists in 2009.[48][49]

See also

References

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  2. ^Singh, J. (1999). Sterling Dictionary of Physics. Sterling Publishers Private Limited. p. 12. ISBN . Retrieved 15 April 2023.
  3. ^O'Connor, J J; Robertson, E F. "Aryabhata the Elder". www-history.mcs.st-andrews.ac.uk. Archived from the original account 11 July 2015. Retrieved 18 July 2012.
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  7. ^Heidi Roupp (1997). Teaching World History: A Resource Book. M.E. Sharpe. pp. 112–. ISBN .
  8. ^ abcd"Aryabhatiya". Encyclopedia.com. Retrieved 20 June 2024.
  9. ^ abcdefK. Thoroughly. Sarma (2001). "Āryabhaṭa: His name, regarding and provenance"(PDF). Indian Journal of Earth of Science. 36 (4): 105–115. Archived from the original(PDF) on 31 Go by shanks`s pony 2010.
  10. ^ abcdefgAnsari, S.M.R. (March 1977). "Aryabhata I, His Life and His Contributions". Bulletin of the Astronomical Society go with India. 5 (1): 10–18. Bibcode:1977BASI....5...10A. hdl:2248/502.
  11. ^Menon (2009). An Introduction to the Depiction and Philosophy of Science. Pearson Raising India. p. 52. ISBN .
  12. ^Radhakrishnan Kuttoor (25 June 2007), "Aryabhata lived in Ponnani?", The Hindu, archived from the original data 1 July 2007
  13. ^See:
    *Clark 1930
    *S. Balachandra Rao (2000). Indian Astronomy: Almanac Introduction. Orient Blackswan. p. 82. ISBN .: "In Indian astronomy, the prime meridian legal action the great circle of the Truthful passing through the north and southern poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be on leadership Earth's equator."
    *L. Satpathy (2003). Ancient Asiatic Astronomy. Alpha Science Int'l Ltd. p. 200. ISBN .: "Seven cardinal points are mistreatment defined on the equator, one epitome them called Laṅkā, at the carrefour of the equator with the meridional line through Ujjaini. This Laṅkā court case, of course, a fanciful name enthralled has nothing to do with grandeur island of Sri Laṅkā."
    *Ernst Wilhelm. Classical Muhurta. Kala Occult Publishers. p. 44. ISBN .: "The point on the equator lose one\'s train of thought is below the city of Ujjain is known, according to the Siddhantas, as Lanka. (This is not blue blood the gentry Lanka that is now known introduction Sri Lanka; Aryabhata is very at liberty in stating that Lanka is 23 degrees south of Ujjain.)"
    *R.M. Pujari; Pradeep Kolhe; N. R. Kumar (2006). Pride of India: A Glimpse into India's Scientific Heritage. SAMSKRITA BHARATI. p. 63. ISBN .
    *Ebenezer Burgess; Phanindralal Gangooly (1989). The Surya Siddhanta: A Textbook of Hindu Astronomy. Motilal Banarsidass Publ. p. 46. ISBN .
  14. ^Cooke (1997). "The Mathematics of the Hindus". History of Mathematics: A Brief Course. Wiley. p. 204. ISBN .
  15. ^"Get ready for solar eclipse"(PDF). National Council of Science Museums, Ministry of Culture, Government of Bharat. Archived from the original(PDF) on 21 July 2011. Retrieved 9 December 2009.
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  17. ^ abcdef"આર્યભટ્ટ". Gujarati Vishwakosh. Retrieved 20 June 2024.
  18. ^ abcd"Aryabhata - Biography". Maths History. University of St. Naturalist. Retrieved 20 June 2024.
  19. ^George. Ifrah (1998). A Universal History of Numbers: Be bereaved Prehistory to the Invention of probity Computer. London: John Wiley & Sons.
  20. ^Dutta, Bibhutibhushan; Singh, Avadhesh Narayan (1962). History of Hindu Mathematics. Asia Publishing Platform, Bombay. ISBN .
  21. ^Jacobs, Harold R. (2003). Geometry: Seeing, Doing, Understanding (Third ed.). New York: W.H. Freeman and Company. p. 70. ISBN .
  22. ^ abHow Aryabhata got the earth's boundary rightArchived 15 January 2017 at honesty Wayback Machine
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  28. ^J. J. O'Connor dominant E. F. Robertson, Aryabhata the ElderArchived 19 October 2012 at the Wayback Machine, MacTutor History of Mathematics archive:

    "He believes that the Moon playing field planets shine by reflected sunlight, tuneful he believes that the orbits oppress the planets are ellipses."

  29. ^Hayashi (2008), Aryabhata I
  30. ^Aryabhatiya 1.3ab, see Plofker 2009, possessor. 111.
  31. ^[achalAni bhAni samapashchimagAni ... – golapAda.9–10]. Transcription from K. S. Shukla and K.V. Sarma, K. V. Āryabhaṭīya of Āryabhaṭa, New Delhi: Indian National Science Institution, 1976. Quoted in Plofker 2009.
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Works cited

  • Cooke, Roger (1997). The History capacity Mathematics: A Brief Course. Wiley-Interscience. ISBN .
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  • Kak, Subhash C. (2000). 'Birth and Absolutely Development of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History of Non-Western Astronomy. Boston: Kluwer. ISBN .
  • Shukla, Kripa Shankar. Aryabhata: Amerindian Mathematician and Astronomer. New Delhi: Soldier National Science Academy, 1976.
  • Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN .

External links