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Aryabhata
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Biography
Name
While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus,JOURNAL, K. V. Sarma, Indian Journal of History of Science, 2001, 105â€“115, Ä€ryabhaá¹a: His name, time and provenance, 36, 4,weblink harv,weblink" title="web.archive.org/web/20100331152303weblink">weblink 31 March 2010, including Brahmagupta's references to him "in more than a hundred places by name". Furthermore, in most instances "Aryabhatta" would not fit the meter either.Time and place of birth
Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 years into the Kali Yuga, 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 Pataliputra (present day Patna, Bihar).Other hypothesis
BhÄskara I describes Aryabhata as ÄÅ›makÄ«ya, "one belonging to the AÅ›maka country." During the Buddha's time, a branch of the AÅ›maka people settled in the region between the Narmada and Godavari rivers in central India.It has been claimed that the aÅ›maka (Sanskrit for "stone") where Aryabhata originated may be the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala.BOOK, Menon, An Introduction to the History and Philosophy of Science,weblink 24 June 2012, Pearson Education India, 978-81-317-2890-1, 52â€“, This is based on the belief that Koá¹uá¹…á¹…allÅ«r was earlier known as Koá¹um-Kal-l-Å«r ("city of hard stones"); however, old records show that the city was actually Koá¹um-kol-Å«r ("city of strict governance"). Similarly, the fact that several commentaries on the Aryabhatiya have come from 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.{{citation | newspaper = The Hindu | url =weblink | title = Aryabhata lived in Ponnani? | date = June 25, 2007 | author = Radhakrishnan Kuttoor | deadurl = no | archiveurl =weblink" title="web.archive.org/web/20070701212700weblink">weblink | archivedate = 1 July 2007 | df = dmy-all }}Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is an abstraction, standing for a point on the equator at the same longitude as his Ujjayini.See: *{{Harvnb|Clark|1930}} *BOOK, 2000, Indian Astronomy: An Introduction, S. Balachandra Rao, Orient Blackswan, 978-81-7371-205-0, 82,weblink : "In Indian astronomy, the prime meridian is the great circle of the Earth passing through the north and south poles, UjjayinÄ« and Laá¹…kÄ, where Laá¹…kÄ was assumed to be on the Earth's equator."*BOOK, 2003, Ancient Indian Astronomy, L. Satpathy, Alpha Science Int'l Ltd., 978-81-7319-432-0, 200,weblink : "Seven cardinal points are then defined on the equator, one of them called Laá¹…kÄ, at the intersection of the equator with the meridional line through Ujjaini. This Laá¹…kÄ is, of course, a fanciful name and has nothing to do with the island of Sri Laá¹…kÄ."*BOOK, Classical Muhurta, Ernst Wilhelm, Kala Occult Publishers, 978-0-9709636-2-8, 44,weblink : "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.)"*BOOK, 2006, Pride of India: A Glimpse into India's Scientific Heritage, R.M. Pujari, Pradeep Kolhe, N. R. Kumar, SAMSKRITA BHARATI, 978-81-87276-27-2, 63,weblink *BOOK, 1989, The Surya Siddhanta: A Textbook of Hindu Astronomy, Ebenezer Burgess, Phanindralal Gangooly, Motilal Banarsidass Publ., 978-81-208-0612-2, 46,weblinkEducation
It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.BOOK, Cooke, Roger Cooke, History of Mathematics: A Brief Course, 1997, The Mathematics of the Hindus, 204, Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late 5th and the early 6th centuries at Kusumapura (Pataliutra, a village near the city of Patna) and wrote a book called Aryabhatiya., Both Hindu and Buddhist tradition, as well as BhÄskara I (CE 629), identify Kusumapura as PÄá¹aliputra, modern Patna. A verse mentions that Aryabhata was the head of an institution ({{IAST|kulapa}}) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, 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 Taregana, Bihar.WEB,weblink Get ready for solar eclipe, National Council of Science Museums, Ministry of Culture, Government of India, 9 December 2009, yes,weblink" title="web.archive.org/web/20110721162632weblink">weblink 21 July 2011,Works
Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost.His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya. It also contained a description of several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, and water clocks of at least two types, bow-shaped and cylindrical.JOURNAL, Ansari
, S.M.R.
, March 1977
, Aryabhata I, His Life and His Contributions
, Bulletin of the Astronomical Society of India
, 5
, 1
, 10â€“18
,weblink
, 2011-01-22
,weblink" title="web.archive.org/web/20071116013419weblink">weblink
, 16 November 2007
, harv, 1977BASI....5...10A,
A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf. 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 Persian scholar and chronicler of India, AbÅ« RayhÄn al-BÄ«rÅ«nÄ«., S.M.R.
, March 1977
, Aryabhata I, His Life and His Contributions
, Bulletin of the Astronomical Society of India
, 5
, 1
, 10â€“18
,weblink
, 2011-01-22
,weblink" title="web.archive.org/web/20071116013419weblink">weblink
, 16 November 2007
, harv, 1977BASI....5...10A,
Aryabhatiya
Direct details of Aryabhata's work are known only from the Aryabhatiya. The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name. His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). It is also occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in the text. It is written in the very terse style typical of sutra 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 pÄdas or chapters:- Gitikapada: (13 verses): large units of timeâ€”kalpa, manvantra, and yugaâ€”which present a cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There is also a table of sines (jya), given in a single verse. The duration of the planetary revolutions during a mahayuga is given as 4.32 million years.
- Ganitapada (33 verses): covering mensuration (ká¹£etra vyÄvahÄra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations (kuá¹á¹aka).
- Kalakriyapada (25 verses): different units of time and a method for determining the positions of planets for a given day, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week with names for the days of week.
- Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, node, shape of the earth, cause of day and night, rising of zodiacal signs on horizon, etc. In addition, some versions cite a few colophons added at the end, extolling the virtues of the work, etc.
Mathematics
Place value system and zero
The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients.BOOK, George. Ifrah
, A Universal History of Numbers: From Prehistory to the Invention of the Computer
, John Wiley & Sons
, London
, 1998
, However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.BOOK
, A Universal History of Numbers: From Prehistory to the Invention of the Computer
, John Wiley & Sons
, London
, 1998
, Dutta
, Bibhutibhushan
, Singh
, Avadhesh Narayan
, 1962
, History of Hindu Mathematics
, Asia Publishing House, Bombay
, 81-86050-86-8
, harv
,
, , Bibhutibhushan
, Singh
, Avadhesh Narayan
, 1962
, History of Hindu Mathematics
, Asia Publishing House, Bombay
, 81-86050-86-8
, harv
,
Approximation of Ï€
Aryabhata worked on the approximation for pi (Ï€), and may have come to the conclusion that Ï€ is irrational. In the second part of the Aryabhatiyam ({{IAST|gaá¹‡itapÄda}} 10), he writes:{{IAST|caturadhikaá¹ƒ Å›atamaá¹£á¹aguá¹‡aá¹ƒ dvÄá¹£aá¹£á¹istathÄ sahasrÄá¹‡Äm}} {{IAST|ayutadvayaviá¹£kambhasyÄsanno vá¹›ttapariá¹‡Ähaá¸¥.}}"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."BOOK, Geometry: Seeing, Doing, Understanding (Third Edition)
, Jacobs
, Harold R.
, 2003
, W.H. Freeman and Company
, New York
, 0-7167-4361-2
, 70,
This implies that the ratio of the circumference to the diameter is ((4 + 100) Ã— 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.It is speculated that Aryabhata used the word Äsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi (Ï€) was proved in Europe only in 1761 by Lambert.BOOK
, Jacobs
, Harold R.
, 2003
, W.H. Freeman and Company
, New York
, 0-7167-4361-2
, 70,
, S. Balachandra Rao
, Indian Mathematics and Astronomy: Some Landmarks
, Jnana Deep Publications
, First published 1994
, 1998
, Bangalore
, 81-7371-205-0
, After Aryabhatiya was translated into Arabic (c. 820 CE)this approximation was mentioned in Al-Khwarizmi's book on algebra., Indian Mathematics and Astronomy: Some Landmarks
, Jnana Deep Publications
, First published 1994
, 1998
, Bangalore
, 81-7371-205-0
Trigonometry
In Ganitapada 6, Aryabhata gives the area of a triangle as
{{IAST|tribhujasya phalaÅ›arÄ«raá¹ƒ samadalakoá¹Ä« bhujÄrdhasaá¹ƒvargaá¸¥}}
that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."BOOK
, Roger Cooke
, History of Mathematics: A Brief Course
, Wiley-Interscience
, 1997
, The Mathematics of the Hindus
, 0-471-18082-3
, 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.),
Aryabhata discussed the concept of sine in his work by the name of ardha-jya, which literally means "half-chord". For simplicity, people started calling it jya. When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba. However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; thence comes the English word sine.BOOK
, History of Mathematics: A Brief Course
, Wiley-Interscience
, 1997
, The Mathematics of the Hindus
, 0-471-18082-3
, 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.),
, Howard Eves
, An Introduction to the History of Mathematics
, Saunders College Publishing House, New York
, 1990
, 6
, 237
, , An Introduction to the History of Mathematics
, Saunders College Publishing House, New York
, 1990
, 6
, 237
Indeterminate equations
A problem of great interest to Indian mathematicians since ancient times has been to find integer solutions to Diophantine equations 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 Chinese remainder theorem.) This is an example from BhÄskara's commentary on Aryabhatiya:
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
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 Sulba Sutras, 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 {{IAST|kuá¹á¹aka}} (à¤•à¥à¤Ÿà¥à¤Ÿà¤•) method. Kuá¹á¹aka 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 algebra was called kuá¹á¹aka-gaá¹‡ita or simply kuá¹á¹aka.Amartya K Dutta, "Diophantine equations: The Kuttaka", Resonance, October 2002. Also see earlier overview: Mathematics in Ancient India {{webarchive|url=https://web.archive.org/web/20141102223752weblink |date=2 November 2014 }}.Algebra
In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes:BOOK, Carl B., Boyer, Carl Benjamin Boyer, A History of Mathematics, Second, John Wiley & Sons, Inc., 1991, 0-471-54397-7, 207, The Mathematics of the Hindus, "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 square of the sum of the series is the sum of the cubes.",
1^2 + 2^2 + cdots + n^2 = {n(n + 1)(2n + 1) over 6}
and
1^3 + 2^3 + cdots + n^3 = (1 + 2 + cdots + n)^2 (see squared triangular number)
Astronomy
Aryabhata's system of astronomy was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later writings on astronomy, which apparently proposed a second model (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, he seems to ascribe the apparent motions of the heavens to the Earth's rotation. He may have believed that the planet's orbits as elliptical rather than circular.J. J. O'Connor and E. F. Robertson, Aryabhata the Elder {{webarchive|url=https://www.webcitation.org/6Dxq5ms1u?url=http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Aryabhata_I.html |date=26 January 2013 }}, MacTutor History of Mathematics archive:Hayashi (2008), Aryabhata IMotions of the solar system
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.How Aryabhata got the earth's circumference right {{webarchive|url=https://web.archive.org/web/20170115063654weblink |date=15 January 2017 }} This is indicated in the first chapter of the Aryabhatiya, where he gives the number of rotations of the earth in a yuga,Aryabhatiya 1.3ab, see Plofker 2009, p. 111. and made more explicit in his gola chapter:[achalAni bhAni samapashchimagAni ... â€“ golapAda.9â€“10]. Translation from K. S. Shukla and K.V. Sarma, K. V. Ä€ryabhaá¹Ä«ya of Ä€ryabhaá¹a, New Delhi: Indian National Science Academy, 1976. Quoted in Plofker 2009.Aryabhata described a geocentric model of the solar system, in which theSun and Moon are each carried by epicycles. They in turn revolve aroundthe Earth. In this model, which is also found in the PaitÄmahasiddhÄnta (c. CE 425), the motions of the planets are each governed by two epicycles, a smaller manda (slow) and a larger Å›Ä«ghra (fast).BOOK, Pingree
, David
, David Pingree
, Astronomy in India
, Walker
, Christopher
, Astronomy before the Telescope
, 123â€“142
, British Museum Press
, London
, 1996
, 0-7141-1746-3
, harv
,
, pp. 127â€“9. The order of the planets in terms of distance from earth is taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms."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 planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.Otto Neugebauer, "The Transmission of Planetary Theories in Ancient and Medieval Astronomy," Scripta Mathematica, 22 (1956), pp. 165â€“192; reprinted in Otto Neugebauer, Astronomy and History: Selected Essays, New York: Springer-Verlag, 1983, pp. 129â€“156. {{ISBN|0-387-90844-7}} Another element in Aryabhata's model, the Å›Ä«ghrocca, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model.Hugh Thurston, Early Astronomy, New York: Springer-Verlag, 1996, pp. 178â€“189. {{ISBN|0-387-94822-8}}, David
, David Pingree
, Astronomy in India
, Walker
, Christopher
, Astronomy before the Telescope
, 123â€“142
, British Museum Press
, London
, 1996
, 0-7141-1746-3
, harv
,
Eclipses
Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as the pseudo-planetary lunar nodes), 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.38â€“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 Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration 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.Sidereal periods
Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds;BOOK, Helaine Selin, Helaine Selin, R.C.Gupta, Ä€ryabhaá¹a, Encyclopaedia of the history of science, technology, and medicine in non-western cultures,weblink 22 January 2011, 31 July 1997, Springer, 978-0-7923-4066-9, 72, the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days)Ansari, p. 13, Table 1 is an error of 3 minutes and 20 seconds over the length of a year (365.25636 days).Aryabhatiya , Mohan Apte, Pune, India, Rajhans Publications, 2009, p.25, {{ISBN|978-81-7434-480-9}}Heliocentrism
As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis. His model also gave corrections (the Å›Ä«gra 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 heliocentric model, in which the planets orbit the Sun,The concept of Indian heliocentrism has been advocated by B. L. van der Waerden, Das heliozentrische System in der griechischen, persischen und indischen Astronomie. Naturforschenden Gesellschaft in ZÃ¼rich. ZÃ¼rich:Kommissionsverlag Leeman AG, 1970.B.L. van der Waerden, "The Heliocentric System in Greek, Persian and Hindu Astronomy", in David A. King and George Saliba, ed., 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, Annals of the New York Academy of Science, 500 (1987), pp. 529â€“534.BOOK, Early Astronomy, Hugh Thurston, Springer Science+Business Media, Springer, 1996, 0-387-94822-8, 188, harv, though this has been rebutted.Noel Swerdlow, "Review: A Lost Monument of Indian Astronomy," Isis, 64 (1973): 239â€“243. It has also been suggested that aspects of Aryabhata's system may have been derived from an earlier, likely pre-Ptolemaic Greek, heliocentric model of which Indian astronomers were unaware,Though Aristarchus of Samos (3rd century BCE) is credited with holding an heliocentric theory, the version of Greek astronomy known in ancient India as the Paulisa Siddhanta makes no reference to such a theory. though the evidence is scant.Dennis Duke, "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models." Archive for History of Exact Sciences 59 (2005): 563â€“576, n. 4 WEB,weblink Archived copy, 2016-02-08, no,weblink" title="web.archive.org/web/20090318024632weblink">weblink 18 March 2009, dmy-all, . 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 Babylonian astronomical texts), and that Aryabhata's system was not explicitly heliocentric.BOOK, Kim Plofker, Mathematics in India, Princeton University Press, Princeton, NJ, 2009, 111, 0-691-12067-6,Legacy
(File:Aryabhata Satellite.jpg|thumb|300px|India's first satellite named after Aryabhata){{refimprove section|date=March 2017}}Aryabhata's work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age (c. 820 CE), was particularly influential. Some of his results are cited by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on its axis.His definitions of sine (jya), cosine (kojya), versine (utkrama-jya),and inverse sine (otkram jya) influenced the birth of trigonometry. He was also the first to specify sine and versine (1 âˆ’ cos x) tables, in 3.75Â° intervals from 0Â° to 90Â°, to an accuracy of 4 decimal places.In fact, modern names "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry text to Latin. He assumed that jiba was the Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).WEB, Online Etymology Dictionary,weblink Douglas Harper, 2001, 2007-07-14,weblink" title="web.archive.org/web/20070713125946weblink">weblink 13 July 2007, no, 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 (zijes). In particular, the astronomical tables in the work of the Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) and remained the most accurate ephemeris used in Europe for centuries.Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the basis of the Jalali calendar introduced in 1073 CE by a group of astronomers including Omar Khayyam,ENCYCLOPEDIA, Omar Khayyam, The Columbia Encyclopedia, May 2001, 6,weblink 2007-06-10, yes,weblink" title="web.archive.org/web/20071017002631weblink">weblink 17 October 2007, versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today. The dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta 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 Gregorian calendar.Aryabhatta Knowledge University (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.India's first satellite Aryabhata and the lunar crater Aryabhata are named in his honour. An Institute for conducting research in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) near Nainital, India. The inter-school Aryabhata Maths Competition is also named after him,NEWS, Maths can be fun,weblink The Hindu, 3 February 2006, 2007-07-06, no,weblink" title="web.archive.org/web/20071001091954weblink">weblink 1 October 2007, dmy-all, as is Bacillus aryabhata, a species of bacteria discovered in the stratosphere by ISRO scientists in 2009.WEB,weblink New Microorganisms Discovered In Earth's Stratosphere, ScienceDaily, 18 March 2009, no,weblink 1 April 2018, dmy-all, WEB, ISRO Press Release 16 March 2009,weblink ISRO, 24 June 2012, yes,weblink" title="web.archive.org/web/20120105065022weblink">weblink 5 January 2012,See also
- {{IAST|Ä€ryabhaá¹a numeration}}
- {{IAST|Ä€ryabhaá¹a's sine table}}
- Indian mathematics
- List of Indian mathematicians
References
{{Reflist|2}}Works cited
- BOOK
, Roger
, Cooke
, The History of Mathematics: A Brief Course
, Wiley-Interscience
, 1997
, 0-471-18082-3
, , Cooke
, The History of Mathematics: A Brief Course
, Wiley-Interscience
, 1997
, 0-471-18082-3
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, The {{IAST, Ä€ryabhaá¹Ä«ya, of {{IAST|Ä€ryabhaá¹a}}: An Ancient Indian Work on Mathematics and Astronomy
| last=Clark | first=Walter Eugene |authorlink=Walter Eugene Clark
| date=1930
| publisher=University of Chicago Press; reprint: Kessinger Publishing (2006)
| isbn=978-1-4254-8599-3
| url=https://archive.org/details/The_Aryabhatiya_of_Aryabhata_Clark_1930
| ref = harv
| postscript =
}} | last=Clark | first=Walter Eugene |authorlink=Walter Eugene Clark
| date=1930
| publisher=University of Chicago Press; reprint: Kessinger Publishing (2006)
| isbn=978-1-4254-8599-3
| url=https://archive.org/details/The_Aryabhatiya_of_Aryabhata_Clark_1930
| ref = harv
| postscript =
- Kak, Subhash C. (2000). 'Birth and Early Development of Indian Astronomy'. In ENCYCLOPEDIA
, Selin
, Helaine
, Helaine Selin
, 2000
, Astronomy Across Cultures: The History of Non-Western Astronomy
, Boston: Kluwer
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, 0-7923-6363-9
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, Helaine Selin
, 2000
, Astronomy Across Cultures: The History of Non-Western Astronomy
, Boston: Kluwer
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- Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Indian National Science Academy, 1976.
- JOURNAL
, Thurston
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, 1994
, Early Astronomy
, Springer-Verlag, New York
, harv
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External links
{{Commons category|Aryabhata}}- 1930 English translation of The Aryabhatiya in various formats at the Internet Archive.
- {{MacTutor Biography|id=Aryabhata_I}}
- ENCYCLOPEDIA, Thomas Hockey, Achar, Narahari, Ä€ryabhaá¹a I, The Biographical Encyclopedia of Astronomers, Springer, 2007, New York, 63,weblink 978-0-387-31022-0, etal, (PDF version)
- "Aryabhata and Diophantus' son", Hindustan Times Storytelling Science column, November 2004
- Surya Siddhanta translations
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