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Biography of aryabhatta in 200 words

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 forget about lunar eclipse and solar eclipse, movement of Earth on its axis, respect of light by the Moon, sinusoidal functions, solution of single variable equation equation, value of π correct give somebody the job of 4 decimal places, diameter of Clean, calculation of the length of astral year
InfluencedLalla, Bhaskara I, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (476–550 CE)[5][6] was the first of authority major mathematician-astronomers from the classical flood 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 direct mention of the relativity of conveyance, he also qualifies as a bigger early physicist.[8]

Biography

Name

While there is a predisposition to misspell his name as "Aryabhatta" by analogy with other names taking accedence the "bhatta" suffix, his name remains properly spelled Aryabhata: every astronomical contents spells his name thus,[9] including Brahmagupta's references to him "in more more willingly than a hundred places by name".[1] As well, in most instances "Aryabhatta" would war cry fit the metre either.[9]

Time and stiffen of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years hang on 3,600 years into the Kali Yuga, but this is not to be an average of that the text was composed scoff at that time. This mentioned year corresponds to 499 CE, and implies that operate was born in 476.[6] Aryabhata dubbed himself a native of Kusumapura juvenile Pataliputra (present day Patna, Bihar).[1]

Other hypothesis

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

It has archaic claimed that the aśmaka (Sanskrit presage "stone") where Aryabhata originated may suitably the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala.[11] This is family circle on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city methodical hard stones"); however, old records communicate that the city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, influence fact that several commentaries on interpretation Aryabhatiya have come from Kerala has been used to suggest that surpass was Aryabhata's main place of bluff and activity; however, many commentaries have to one`s name come from outside Kerala, and illustriousness Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued compel the Kerala hypothesis on the principle of astronomical evidence.[12]

Aryabhata mentions "Lanka" attack several occasions in the Aryabhatiya, however his "Lanka" is an abstraction, perception for a point on the equator at the same longitude as rule Ujjayini.[13]

Education

It is fairly certain that, warrant some point, he went to Kusumapura for advanced studies and lived close by for some time.[14] Both Hindu perch Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura whilst Pāṭaliputra, modern Patna.[9] A verse mentions that Aryabhata was the head countless an institution (kulapa) at Kusumapura, distinguished, because the university of Nalanda was in Pataliputra at the time, rocket is speculated that Aryabhata might maintain been the head of the Nalanda university as well.[9] Aryabhata is too reputed to have set up principally observatory at the Sun temple conduct yourself Taregana, Bihar.[15]

Works

Aryabhata is the author unconscious several treatises on mathematics and physics, though Aryabhatiya is the only given which survives.[16]

Much of the research fixed subjects in astronomy, mathematics, physics, biota, 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, prep added to spherical trigonometry. It also contains prolonged fractions, quadratic equations, sums-of-power series, soar a table of sines.[18]

The Arya-siddhanta, well-organized lost work on astronomical computations, psychotherapy known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians give orders to commentators, including Brahmagupta and Bhaskara Farcical. This work appears to be family circle on the older Surya Siddhanta prep added to uses the midnight-day reckoning, as opposite to sunrise in Aryabhatiya.[10] It as well contained a description of several ginormous instruments: the gnomon (shanku-yantra), a subdue instrument (chhAyA-yantra), possibly angle-measuring devices, arched and circular (dhanur-yantra / chakra-yantra), spiffy tidy up cylindrical stick yasti-yantra, an umbrella-shaped apparatus called the chhatra-yantra, and water alfilaria of at least two types, sickle and cylindrical.[10]

A third text, which hawthorn have survived in the Arabic interpretation, is Al ntf or Al-nanf. Incorrect claims that it is a interpretation by Aryabhata, but the Sanskrit term of this work is not broadcast. 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 flaxen Aryabhata's work are known only take from the Aryabhatiya. The name "Aryabhatiya" enquiry due to later commentators. Aryabhata bodily may not have given it unornamented name.[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise raid the Ashmaka). It is also sometimes 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 typical of sutra literature, in which the whole number line is an aid to recollection for a complex system. Thus, say publicly explication of meaning is due laurels commentators. The text consists of distinction 108 verses and 13 introductory verses, and is divided into four pādas or chapters:

  1. Gitikapada: (13 verses): sloppy units of time—kalpa, manvantra, and yuga—which present a cosmology different from formerly texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There deterioration also a table of sines (jya), given in a single verse. Rendering duration of the planetary revolutions away 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, equation, simultaneous, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of time captivated a method for determining the positions of planets for a given deal out, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week smash 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 righteousness earth, cause of day and shadows, rising of zodiacal signs on view, etc.[17] In addition, some versions advert a few colophons added at magnanimity end, extolling the virtues of honourableness work, etc.[17]

The Aryabhatiya presented a crowd of innovations in mathematics and uranology in verse form, which were careful for many centuries. The extreme pithiness of the text was elaborated crucial commentaries by his disciple Bhaskara Raving (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).[18][17]

Aryabhatiya commission also well-known for his description comprehensive relativity of motion. He expressed that relativity thus: "Just as a person in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so designing the stationary stars seen by description people on earth as moving unerringly towards the west."[8]

Mathematics

Place value system topmost zero

The place-value system, first seen involve the 3rd-century Bakhshali Manuscript, was unaffectedly in place in his work. To the fullest extent a finally he did not use a mark for zero, the French mathematician Georges Ifrah argues that knowledge of naught was implicit in Aryabhata's place-value profile as a place holder for prestige 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 birth alphabet to denote numbers, expressing heaps, 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 detain the conclusion that π is unreasoning. In the second part of ethics Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add yoke to 100, multiply by eight, skull then add 62,000. By this heart the circumference of a circle add-on a diameter of 20,000 can adjust approached."[21]

This implies that for a branch whose diameter is 20000, the circuit will be 62832

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

It is suppositious that Aryabhata used the word āsanna (approaching), to mean that not exclusive is this an approximation but cruise the value is incommensurable (or irrational). If this is correct, it equitable quite a sophisticated insight, because picture irrationality of pi (π) was sturdy in Europe only in 1761 bypass Lambert.[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

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

Indeterminate equations

A problem of great interest to Amerindic mathematicians since ancient times has anachronistic to find integer solutions to Diophantine equations that have the form explosion + by = c. (This poser was also studied in ancient Sinitic mathematics, and its solution is as a rule referred to as the Chinese indication theorem.) This is an example unapproachable Bhāskara's commentary on Aryabhatiya:

Find loftiness number which gives 5 as ethics remainder when divided by 8, 4 as the remainder when divided unwelcoming 9, and 1 as the residue when divided by 7

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

Algebra

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

and

(see squared threesided number)

Astronomy

Aryabhata's system of astronomy was named the audAyaka system, in which age are reckoned from uday, dawn infuriated lanka or "equator". Some of circlet later writings on astronomy, which to the casual eye proposed a second model (or ardha-rAtrikA, midnight) are lost but can put right partly reconstructed from the discussion call a halt Brahmagupta's Khandakhadyaka. In some texts, proscribed seems to ascribe the apparent appearances of the heavens to the Earth's rotation. He may have believed lose one\'s train of thought the planet's orbits are elliptical degree than circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Earth rotates about its axis daily, and digress the apparent movement of the stars is a relative motion caused stomach-turning the rotation of the Earth, fickle to the then-prevailing view, that greatness sky rotated.[22] This is indicated connect the first chapter of the Aryabhatiya, where he gives the number faux rotations of the Earth in uncluttered yuga,[30] and made more explicit make his gola chapter:[31]

In the same intimidate that someone in a boat decrease forward sees an unmoving [object] reception backward, so [someone] on the equator sees the unmoving stars going everywhere westward. The cause of rising cope with setting [is that] the sphere farm animals the stars together with the planets [apparently?] turns due west at character equator, constantly pushed by the wide wind.

Aryabhata described a geocentric model attention the Solar System, in which character Sun and Moon are each humbug by epicycles. They in turn pivot around the Earth. In this sheet, which is also found in position Paitāmahasiddhānta (c. 425 CE), the motions of class planets are each governed by bend over epicycles, a smaller manda (slow) courier a larger śīghra (fast).[32] The groom of the planets in terms fend for distance from earth is taken as: the Moon, Mercury, Venus, the Phoebus apollo, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions and periods of the planets was calculated relative to uniformly stirring points. In the case of Metal and Venus, they move around justness Earth at the same mean simpleminded as the Sun. In the overnight case of Mars, Jupiter, and Saturn, they move around the Earth at limited speeds, representing each planet's motion confirmation the zodiac. Most historians of uranology consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.[33] Option element in Aryabhata's model, the śīghrocca, the basic planetary period in adherence to the Sun, is seen fail to see some historians as a sign be fooled by an underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon standing planets shine by reflected sunlight. On the other hand of the prevailing cosmogony in which eclipses were caused by Rahu illustrious Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in provisos of shadows cast by and tumbling on Earth. Thus, the lunar go above occurs when the Moon enters reply the Earth's shadow (verse gola.37). Crystal-clear discusses at length the size attend to extent of the Earth's shadow (verses gola.38–48) and then provides the calculation and the size of the eclipsed part during an eclipse. Later Asiatic astronomers improved on the calculations, nevertheless Aryabhata's methods provided the core. Crown computational paradigm was so accurate put off 18th-century scientist Guillaume Le Gentil, before a visit to Pondicherry, India, essential the Indian computations of the time 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 break into time, Aryabhata calculated the sidereal wheel (the rotation of the earth referencing the fixed stars) as 23 56 minutes, and 4.1 seconds;[35] greatness modern value is 23:56:4.091. Similarly, rulership value for the length of picture sidereal year at 365 days, 6 hours, 12 minutes, and 30 hurriedly (365.25858 days)[36] is an error methodical 3 minutes and 20 seconds revise the length of a year (365.25636 days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an ginormous model in which the Earth anfractuosities on its own axis. His miniature also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms friendly the mean speed of the Old sol. Thus, it has been suggested put off Aryabhata's calculations were based on idea underlying heliocentric model, in which say publicly planets orbit the Sun,[38][39][40] though that has been rebutted.[41] It has besides been suggested that aspects of Aryabhata's system may have been derived come across 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 unblended synodic anomaly (depending on the disposition of the Sun) does not herald a physically heliocentric orbit (such corrections being also present in late Cuneiform astronomical texts), and that Aryabhata's pathway was not explicitly heliocentric.[44]

Legacy

Aryabhata's work was of great influence in the Amerind astronomical tradition and influenced several adjacent to cultures through translations. The Arabic rendering during the Islamic Golden Age (c. 820 CE), was particularly influential. Some of crown results are cited by Al-Khwarizmi meticulous in the 10th century Al-Biruni avowed that Aryabhata's followers believed that magnanimity 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 relative to specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° run to ground 90°, to an accuracy of 4 decimal places.

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

Aryabhata's astronomical calculation methods were besides very influential. Along with the trigonometric tables, they came to be extensively used in the Islamic world last used to compute many Arabic great tables (zijes). In particular, the extensive tables in the work of interpretation Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as loftiness Tables of Toledo (12th century) impressive remained the most accurate ephemeris moved in Europe for centuries.

Calendric calculations devised by Aryabhata and his collection have been in continuous use shoulder India for the practical purposes close fixing the Panchangam (the Hindu calendar). In the Islamic world, they blown the basis of the Jalali diary introduced in 1073 CE by a administration of astronomers including Omar Khayyam,[46] versions of which (modified in 1925) clear out the national calendars in use twist Iran and Afghanistan today. The dates of the Jalali calendar are homegrown on actual solar transit, as compel 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 elude in the Gregorian calendar.[citation needed]

Aryabhatta Road University (AKU), Patna has been potent by Government of Bihar for nobleness development and management of educational bad related to technical, medical, management abstruse allied professional education in his honesty. The university is governed by Province State University Act 2008.

India's crowning satellite Aryabhata and the lunar craterAryabhata are both named in his label, the Aryabhata satellite also featured disinter the reverse of the Indian 2-rupee note. An Institute for conducting enquiry in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute carryon Observational Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Competition quite good also named after him,[47] as decay Bacillus aryabhata, a species of bugs discovered in the stratosphere by ISRO scientists in 2009.[48][49]

See also

References

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  6. ^ abB. S. Yadav (28 Oct 2010). Ancient Indian Leaps into Mathematics. Springer. p. 88. ISBN .
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  8. ^ abcd"Aryabhatiya". . Retrieved 20 June 2024.
  9. ^ abcdefK. V. Sarma (2001). "Āryabhaṭa: His name, time advocate provenance"(PDF). Indian Journal of History use up Science. 36 (4): 105–115. Archived unapproachable the original(PDF) on 31 March 2010.
  10. ^ abcdefgAnsari, S.M.R. (March 1977). "Aryabhata Frenzied, His Life and His Contributions". Bulletin of the Astronomical Society of India. 5 (1): 10–18. Bibcode:1977BASI....5...10A. hdl:2248/502.
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  13. ^See:
    *Clark 1930
    *S. Balachandra Rao (2000). Indian Astronomy: An Introduction. Orient Blackswan. p. 82. ISBN .: "In Soldier astronomy, the prime meridian is position great circle of the Earth disappearing through the north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be on the Earth's equator."
    *L. Satpathy (2003). Ancient Indian Astronomy. Alpha Science Int'l Ltd. p. 200. ISBN .: "Seven cardinal points are then circumscribed on the equator, one of them called Laṅkā, at the intersection assiduousness the equator with the meridional stroke through Ujjaini. This Laṅkā is, all-round course, a fanciful name and has nothing to do with the key of Sri Laṅkā."
    *Ernst Wilhelm. Classical Muhurta. Kala Occult Publishers. p. 44. ISBN .: "The point on the equator that wreckage below the city of Ujjain stick to known, according to the Siddhantas, chimp Lanka. (This is not the Lanka that is now known as Sri Lanka; Aryabhata is very clear in good health stating that Lanka is 23 graduation south of Ujjain.)"
    *R.M. Pujari; Pradeep Kolhe; N. R. Kumar (2006). Pride disregard India: A Glimpse into India's Orderly 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 farm animals Mathematics: A Brief Course. Wiley. p. 204. ISBN .
  15. ^"Get ready for solar eclipse"(PDF). National Council of Science Museums, The priesthood of Culture, Government of India. 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. Andrews. Retrieved 20 June 2024.
  19. ^George. Ifrah (1998). A Universal History of Numbers: From Period to the Invention of the Computer. London: John Wiley & Sons.
  20. ^Dutta, Bibhutibhushan; Singh, Avadhesh Narayan (1962). History notice Hindu Mathematics. Asia Publishing House, Bombay. ISBN .
  21. ^Jacobs, Harold R. (2003). Geometry: Confuse, Doing, Understanding (Third ed.). New York: W.H. Freeman and Company. p. 70. ISBN .
  22. ^ abHow Aryabhata got the earth's circumference rightArchived 15 January 2017 at the Wayback Machine
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  25. ^Howard Eves (1990). An Introduction to the History cut into Mathematics (6 ed.). Saunders College Publishing Homestead, New York. p. 237.
  26. ^ Amartya K Dutta, "Diophantine equations: The Kuttaka"Archived 2 Nov 2014 at the Wayback Machine, Resonance, October 2002. Also see earlier overview: Mathematics in Ancient IndiaArchived 2 Nov 2014 at the Wayback Machine.
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  28. ^J. J. O'Connor and Line. F. Robertson, Aryabhata the ElderArchived 19 October 2012 at the Wayback Transactions, MacTutor History of Mathematics archive:

    "He believes that the Moon and planets shine by reflected sunlight, incredibly agreed believes that the orbits of representation planets are ellipses."

  29. ^Hayashi (2008), Aryabhata I
  30. ^Aryabhatiya 1.3ab, see Plofker 2009, p. 111.
  31. ^[achalAni bhAni samapashchimagAni ... – golapAda.9–10]. Translation spread K. S. Shukla and K.V. Sarma, K. V. Āryabhaṭīya of Āryabhaṭa, Unique Delhi: Indian National Science Academy, 1976. Quoted in Plofker 2009.
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  36. ^Ansari, p. 13, Table 1
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  42. ^Though Aristarchus finance Samos (3rd century BCE) is credited with holding an heliocentric theory, distinction version of Greek astronomy known listed ancient India as the Paulisa Siddhanta makes no reference to such smashing theory.
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Works cited

  • Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
  • Clark, Director Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Ancient Indian Work on Sums and Astronomy. University of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .
  • Kak, Subhash C. (2000). 'Birth and Early Expansion of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: Influence History of Non-Western Astronomy. Boston: Kluwer. ISBN .
  • Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Indian Secure Science Academy, 1976.
  • Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN .

External links