Please read: A personal appeal from Wikipedia founder Jimmy WalesAryabhata From Wikipedia, the free encyclopedia Jump to: navigation, search For other uses, see Aryabhata (disambiguation). Statue of Aryabhata on the grounds of IUCAA, Pune. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist's conception. Aryabhata (IAST: Āryabhaṭa; Sanskrit: आयरभटः) (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and 1 Name o 1. in most instances "Aryabhatta" does not fit the metre either.3 Mensuration and trigonometry o 3. His most famous works are the Aryabhatiya (499 CE.1 Aryabhatiya 3 Mathematics o 3.[2] Furthermore.4 Heliocentrism 5 Legacy 6 See also 7 References o 7. when he was 23 years old) and the Arya-siddhanta.4 Other hypotheses 2 Works o 2. his name is properly spelled Aryabhata: every astronomical text spells his name thus.1 Place value system and zero o 3.[1] including Brahmagupta's references to him "in more than a hundred places by name".Indian astronomy.2 Birth o 1. Contents [hide] • • • • • • • 1 Biography o 1.2 Approximation of pi o 3.1 Other references 8 External links • [edit] Biography [edit] Name While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix.4 Indeterminate equations o 3.[1] [edit] Birth .2 Eclipses o 4.3 Sidereal periods o 4.1 Motions of the solar system o 4.5 Algebra 4 Astronomy o 4.3 Work o 1. The mathematical part of the Aryabhatiya covers arithmetic. which would put them further north. "one belonging to the aśmaka country. and implies that he was born in 476 CE. he went to Kusumapura for advanced studies and that he lived there for some time.Aryabhata mentions in the Aryabhatiya that it was composed 3.[6] Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya. Aryabhata is believed to have been born there. V. and a table of sines. a branch of the Aśmaka people settled in the region between the Narmada and Godavari rivers in central India. is known through the writings of Aryabhata's contemporary. standing for a point on the equator at the same longitude as his Ujjayini. a compendium of mathematics and astronomy. Sarma. This work appears to be based on the older Surya Siddhanta and uses the midnight-day reckoning. during the Buddha's time. early Buddhist texts describe Ashmaka as being further south. a lost work on astronomical computations. some of which are lost. when he was 23 years old. It also contains continued fractions. The only information comes from Bhāskara I.[1][3] However. algebra.[4] Both Hindu and Buddhist tradition. today the South Gujarat–North Maharashtra region. Aryabhatiya. as well as Bhāskara I (CE 629).[1] Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana. His major work. but K.[1] A verse mentions that Aryabhata was the head of an institution (kulapa) at Kusumapura. at some point. modern Patna. disagreed[1] and pointed out several errors in this hypothesis.[5] [edit] Other hypotheses It was suggested that Aryabhata may have been from Kerala. while other texts describe the Ashmakas as having fought Alexander.[3] [edit] Work It is fairly certain that. quadratic equations. This corresponds to 499 CE. as opposed to sunrise in . it is speculated that Aryabhata might have been the head of the Nalanda university as well. but his "Lanka" is an abstraction. because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory. an authority on Kerala's astronomical tradition. and spherical trigonometry.[7] [edit] Works Aryabhata is the author of several treatises on mathematics and astronomy. Bihar. who describes Aryabhata as āśmakīya. identify Kusumapura as Pāṭaliputra. was extensively referred to in the Indian mathematical literature and has survived to modern times." It is widely attested that. sums-of-power series. and.600 years into the Kali Yuga. in dakshinapath or the Deccan. The Arya-siddhanta. and later mathematicians and commentators. Varahamihira. plane trigonometry. including Brahmagupta and Bhaskara I.[1] Aryabhata provides no information about his place of birth. and water clocks of at least two types. which were influential for many centuries. is Al ntf or Al-nanf. extolling the virtues of the work. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya. Aryabhata himself may not have given it a name. some versions cite a few colophons added at the end. It is also occasionally referred to as Arya-shatas-aShTa (literally. it is mentioned by the Persian scholar and chronicler of India. quadratic. kShaya-tithis. It is written in the very terse style typical of sutra literature. node. and indeterminate equations (kuTTaka) 3. shape of the earth. cause of day and night. His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka).[3] [edit] Aryabhatiya Direct details of Aryabhata's work are known only from the Aryabhatiya. etc. (1465 CE). etc.Aryabhatiya. Thus. 4. bow-shaped and cylindrical. gnomon / shadows (shanku-chhAyA). a cylindrical stick yasti-yantra. It also contained a description of several astronomical instruments: the gnomon (shanku-yantra). a shadow instrument (chhAyA-yantra). and yuga—which present a cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (ca. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra). Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere.[3] A third text. The duration of the planetary revolutions during a mahayuga is given as 4. Probably dating from the 9th century. The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form. an umbrella-shaped device called the chhatra-yantra. given in a single verse.32 million years. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya. In addition. but the Sanskrit name of this work is not known. possibly anglemeasuring devices. calculations concerning the intercalary month (adhikamAsa). simple. Abū Rayhān al-Bīrūnī. Gitikapada: (13 verses): large units of time—kalpa. 2. The text consists of the 108 verses and 13 introductory verses. rising of zodiacal signs on horizon. simultaneous. features of the ecliptic. arithmetic and geometric progressions. because there are 108 verses in the text. and a seven-day week with names for the days of week. and is divided into four pādas or chapters: 1. The name "Aryabhatiya" is due to later commentators. manvantra. in which each line is an aid to memory for a complex system. semicircular and circular (dhanur-yantra / chakra-yantra). Aryabhata's 108). [edit] Mathematics . Kalakriyapada (25 verses): different units of time and a method for determining the positions of planets for a given day. ca. the explication of meaning is due to commentators. It claims that it is a translation by Aryabhata. celestial equator. There is also a table of sines (jya). 1st century BCE). which may have survived in the Arabic translation. Literally. For simplicity.000 can be approached. it is quite a sophisticated insight.[11] After Aryabhatiya was translated into Arabic (ca. they referred it as jiba. 820 CE) this approximation was mentioned in Al-Khwarizmi's book on algebra.[9] [edit] Approximation of pi Aryabhata worked on the approximation for pi (π). However. he writes: caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ. expressing quantities. Later writers . When Arabic writers translated his works from Sanskrit into Arabic.[3] [edit] Mensuration and trigonometry In Ganitapada 6. and it was abbreviated as jb. to mean that not only is this an approximation but that the value is incommensurable (or irrational). and then add 62. was clearly in place in his work. he used letters of the alphabet to denote numbers. Aryabhata gives the area of a triangle as tribhujasya phalashariram samadalakoti bhujardhasamvargah that translates to: "for a triangle. such as the table of sines in a mnemonic form. Aryabhata did not use the Brahmi numerals. In the second part of the Aryabhatiyam (gaṇitapāda 10)."[12] Aryabhata discussed the concept of sine in his work by the name of ardha-jya. because the irrationality of pi was proved in Europe only in 1761 by Lambert. it means "half-chord". If this is correct. people started calling it jya. the result of a perpendicular with the half-side is the area. multiply by eight. vowels are omitted. which is accurate to five significant figures. While he did not use a symbol for zero.000. Continuing the Sanskritic tradition from Vedic times. first seen in the 3rd century Bakhshali Manuscript. in Arabic writings."[10] This implies that the ratio of the circumference to the diameter is ((4+100)×8+62000)/20000 = 62832/20000 = 3.[edit] Place value system and zero The place-value system. 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[8] However.1416. It is speculated that Aryabhata used the word āsanna (approaching). and may have come to the conclusion that π is irrational. By this rule the circumference of a circle with a diameter of 20. "Add four to 100. 4 as the remainder when divided by 9. elaborated by Bhaskara in 621 CE. and 1 as the remainder when divided by 7 That is. which means "cove" or "bay". meaning "cove" or "bay. he replaced the Arabic jiab with its Latin counterpart. and the method involves a recursive algorithm for writing the original factors in smaller numbers. dawn at lanka or "equator"." (In Arabic. 2006.[13] [edit] Indeterminate equations A problem of great interest to Indian mathematicians since ancient times has been to find integer solutions to equations that have the form ax + by = c. a topic that has come to be known as diophantine equations. [edit] Algebra In Aryabhatiya Aryabhata provided elegant results for the summation of series of squares and cubes:[15] and [edit] Astronomy Aryabhata's system of astronomy was called the audAyaka system. when Gherardo of Cremona translated these writings from Arabic into Latin. diophantine equations.[14] The diophantine equations are of interest in cryptology. Some of his later writings on astronomy. In general. And after that. This is an example from Bhāskara's commentary on Aryabhatiya: Find the number which gives 5 as the remainder when divided by 8. is the standard method for solving first-order diophantine equations and is often referred to as the Aryabhata algorithm. sinus.substituted it with jiab. whose more ancient parts might date to 800 BCE. and the RSA Conference. Aryabhata's method of solving such problems is called the kuṭṭaka (कुटक) method. In some texts. which apparently proposed a second model (or ardha-rAtrikA. find N = 8x+5 = 9y+4 = 7z+1. midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's khanDakhAdyaka. Kuttaka means "pulverizing" or "breaking into small pieces". can be notoriously difficult. such as this. the sinus became sine in English. It turns out that the smallest value for N is 85. he seems to ascribe the apparent motions of the heavens . focused on the kuttaka method and earlier work in the Sulvasutras. in which days are reckoned from uday. jiba is a meaningless word. Today this algorithm.) Later in the 12th century. They were discussed extensively in ancient Vedic text Sulba Sutras. In the case of Mars. the motions of the planets are each governed by two epicycles. He also treated the planet's orbits as elliptical rather than circular. the lunar eclipse occurs when the moon enters into the Earth's shadow (verse gola. just so are the stationary stars seen by the people in Lanka (or on the equator) as moving exactly towards the west. he explains eclipses in terms of shadows cast by and falling on Earth. and the asterisms. Sri Lanka) is here a reference point on the equator. [18] The order of the planets in terms of distance from earth is taken as: the Moon. and Saturn. which is also found in the Paitāmahasiddhānta (ca. constantly moves westwards at Lanka. CE 425). [16][17] [edit] Motions of the solar system Aryabhata appears to have believed that the earth rotates about its axis. Thus. Instead of the prevailing cosmogony in which eclipses were caused by pseudo-planetary nodes Rahu and Ketu."[3] The positions and periods of the planets was calculated relative to uniformly moving points. This is indicated in the statement.9] But the next verse describes the motion of the stars and planets as real movements: "The cause of their rising and setting is due to the fact that the circle of the asterisms. the basic planetary period in relation to the Sun." [achalAni bhAni samapashchimagAni – golapAda. . Mars. Aryabhata described a geocentric model of the solar system. Mercury.[19] Another element in Aryabhata's model. They in turn revolve around the Earth. which was the equivalent of the reference meridian for astronomical calculations. representing each planet's motion through the zodiac.to the Earth's rotation. He discusses at length the size and extent of the Earth's shadow (verses gola. Saturn. in which the Sun and Moon are each carried by epicycles. is seen by some historians as a sign of an underlying heliocentric model. together with the planets driven by the provector wind. but Aryabhata's methods provided the core. they move around the Earth at the same speed as the Sun.37).[20] [edit] Eclipses Aryabhata states that the Moon and planets shine by reflected sunlight. In this model. the Sun. Later Indian astronomers improved on the calculations. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy. Jupiter.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Venus. Jupiter. the śīghrocca. which describes the movement of the stars as a relative motion caused by the rotation of the earth: "Like a man in a boat moving forward sees the stationary objects as moving backward. a smaller manda (slow) and a larger śīghra (fast). they move around the Earth at specific speeds. In the case of Mercury and Venus. Lanka (lit. referring to Lanka ." As mentioned above. 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. The notion of sidereal time was known in most other astronomical systems of the time. The Arabic translation during the Islamic Golden Age (ca. whereas his charts (by Tobias Mayer. was particularly influential."[26] However. 820 CE).091." Thus. van der Waerden's book as "show[ing] a complete misunderstanding of Indian planetary theory [that] is flatly contradicted by every word of Aryabhata's description. whose exact computation is not known in modern units but his estimate had an error of around 5–10%.2% smaller than the actual value of 40. 1752) were long by 68 seconds. L. This approximation was a significant improvement over the computation by Greek mathematician Eratosthenes (c. in which the planets orbit the Sun.[citation needed] [edit] Heliocentrism As mentioned. found the Indian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds.968. Aryabhata claimed that the Earth turns on its own axis. the modern value is 23:56:4. Similarly. of which he was unaware. his value for the length of the sidereal year at 365 days.His computational paradigm was so accurate that 18th century scientist Guillaume Le Gentil. and 4. .0167 kilometres. [edit] Legacy Aryabhata's work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations.[27] Though Aristarchus of Samos (3rd century BCE) is credited with holding an heliocentric theory. The planetary orbits were also given with respect to the Sun and he also states: "Whoever knows this Dasagitika Sutra which describes the movements of the Earth and the planets in the sphere of the asterisms passes through the paths of the planets and asterisms and goes to the higher Brahman.[21][22] [edit] Sidereal periods Considered in modern English units of time. 6 hours. 12 minutes.075. India.1 seconds. it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model. 56 minutes.[23][24][25] A detailed rebuttal to this heliocentric interpretation is in a review that describes B.[3] Aryabhata's computation of the Earth's circumference as 39. and 30 seconds is an error of 3 minutes and 20 seconds over the length of a year. the version of Greek astronomy known in ancient India as the Paulisa Siddhanta makes no reference to such a theory. 200 BCE). and some elements of his planetary epicyclic models rotate at the same speed as the motion of the Earth around the Sun.0582 kilometres was only 0. during a visit to Pondicherry. Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours. some concede that Aryabhata's system stems from an earlier heliocentric model. but this computation was likely the most accurate of the period. 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). Although dates were difficult to compute. The inter-school Aryabhata Maths Competition is also named after him.[31] [edit] See also • • • Āryabhaṭa numeration Aryabhatiya Aryabhata's sine table [edit] References 1. to an accuracy of 4 decimal places. sinus (c. astrophysics and atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) near Nainital.His definitions of sine (jya). 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 was also the first to specify sine and versine (1 − cos x) tables. they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables (zijes). which means "fold in a garment".75° intervals from 0° to 90°. modern names "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. time and provenance". In particular. versine (utkrama-jya). Indian Journal of History of Science 36 (4): 105–115. 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 c. . This type of calendar requires an ephemeris for calculating dates. and inverse sine (otkram jya) influenced the birth of trigonometry. In the Islamic world. India's first satellite Aryabhata and the lunar crater Aryabhata are named in his honour. they formed the basis of the Jalali calendar introduced in 1073 CE by a group of astronomers including Omar Khayyam. India. An Institute for conducting research in astronomy. "Āryabhaṭa: His name. seasonal errors were less in the Jalali calendar than in the Gregorian calendar.1150).[28] Aryabhata's astronomical calculation methods were also very influential. ^ a b c d e f g K. a species of bacteria discovered by ISRO scientists in 2009. L. as in Aryabhata and earlier Siddhanta calendars. Sarma (2001). cosine (kojya). As mentioned. He assumed that jiba was the Arabic word jaib.) and remained the most accurate ephemeris used in Europe for centuries. The dates of the Jalali calendar are based on actual solar transit. in 3. V.[29] versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today.[30] as is Bacillus aryabhata. Along with the trigonometric tables. In fact. at the intersection of the equator with the meridional line through Ujjaini. http://books. (This is not the Lanka that is now known as Sri Lanka. "The Mathematics of the Hindus". however. Kumar (2006).google.dli. http://www.google. one hypothesis was that aśmaka (Sanskrit for "stone") may be the region in Kerala that is now known as Koṭuṅṅallūr. (March 1977). many commentaries have come from outside Kerala. ^ a b c d e f g Ansari.net/2248/502. a fanciful name and has nothing to do with the island of Sri Laṅkā. http://books.2. p. ISBN 9780970963628. Satpathy (2003).com/? .new. p.com/?id=fAsFAAAAMAAJ&pg=PA392&dq=aryabhata.google. Balachandra Rao (2000). This Laṅkā is. a village near the city of Patna) and wrote a book called Aryabhatiya. the fact that several commentaries on the Aryabhatiya have come from Kerala were used to suggest that it was Aryabhata's main place of life and activity. http://books. pp. Kala Occult Publishers. N. Retrieved 2007-07-21. 63. "Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late fifth and the early sixth centuries at Kusumapura (Pataliutra. the prime meridian is the great circle of the Earth passing through the north and south poles. p. Journal of the Royal Asiatic Society of Greatb Britain and Ireland. where Laṅkā was assumed to be on the Earth's equator. http://hdl." *L. Pujari.M. Aryabhata is very clear in stating that Lanka is 23 degrees south of Ujjain. S. however. and Bhaskaracharya". Brahmagupta.: "Seven cardinal points are then defined on the equator. Pride of India: A Glimpse into India's Scientific Heritage. 44.google. as Lanka.handle. National Council of Science Museums. SAMSKRITA BHARATI. one of them called Laṅkā.com/? id=N3DE3GAyqcEC&pg=PA82&dq=lanka. Retrieved 9 December 2009.in/docs/Get%20ready%20for %20Solar%20eclipse. 82. Indian Astronomy: An Introduction. of course. according to the Siddhantas.com/? id=nh6jgEEqqkkC&pg=PA200&dq=lanka. ^ Cooke (1997). R." ^ "Get ready for solar eclipe". 4. 204. and the Aryasiddhanta was completely unknown in Kerala. ^ For instance. ^ See: *Clark 1930 *S.in/rawdataupload/upload/insa/INSA_1/20005b67_105. Pradeep Kolhe. "Brief Notes on the Age and Authenticity of the Works of Aryabhata.com/? id=3zMPFJy6YygC&pg=PA44&dq=lanka. 6. Bulletin of the Astronomical Society of India 5 (1): 10–18. ISBN 9788173712050.google. His Life and His Contributions". based on the belief that it was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"). "Aryabhata I. ISBN 9788173194320.. 3. http://ncsm. 392. Classical Muhurta. http://books. Ujjayinī and Laṅkā.pdf. Ancient Indian Astronomy. ^ Bhau Daji (1865). Orient Blackswan. Bhattotpala. Ministry of Culture. Varahamihira. old records show that the city was actually Koṭum-kol-ūr ("city of strict governance").gov." *Ernst Wilhelm.: "In Indian astronomy. 7. 5. http://books. Alpha Science Int'l Ltd. Similarly.p df.: "The point on the equator that is below the city of Ujjain is known.ernet. See Sarma for details.M. p. p.)" *R.R. 200. Government of India. ISBN 9788187276272. 237. Ifrah (1998). J. O'Connor and E. Geometry: Seeing. The sixth part of the product of three quantities consisting of the number of terms.com/?id=W0Uo__iizwC&pg=PA46&dq=lanka. Singh. Indian Mathematics and Astronomy: Some Landmarks. October 2002. 8. Jnana Deep Publications.).)" 13." Scripta Mathematica. 1996. and twice the number of terms plus one is the sum of the squares. ^ Roger Cooke (1997. New York: W. pp.. ISBN 0471180823. "Astronomy in India". Avadhesh Narayan (1962). Early Astronomy. http://books. incredibly he believes that the orbits of the planets are ellipses. 9. An Introduction to the History of Mathematics (6 ed."" 16. 22 (1956). Wiley-Interscience. Carl B. F. Freeman and Company. London: British Museum Press. p. Bombay. The square of the sum of the series is the sum of the cubes. "The Mathematics of the Hindus". Harold R. pp. Aryabhata I 18. John Wiley & Sons. Astronomy before the Telescope. 127–9. ISBN 81-86050-86-8 (reprint) 10.H. (1991).google. 123–142. New York: SpringerVerlag. p. ISBN 0-387-90844-7 20. Resonance. (2003). History of Hindu Mathematics. ^ Boyer. Balachandra Rao (1994/1998). 11. reprinted in Otto Neugebauer. Aryabhata the Elder.id=sEX11ZyjLpYC&pg=PA63&dq=lanka. 178– 189. ^ Pingree. History of Mathematics: A Brief Course. "The Transmission of Planetary Theories in Ancient and Medieval Astronomy. A History of Mathematics (Second ed. ISBN 81-7371-205-0. 70. Astronomy and History: Selected Essays. 207. *Ebenezer Burgess. 46. ^ Hayashi (2008). New York. ^ S. 15. Doing. In Walker. Motilal Banarsidass Publ. Understanding (Third Edition). A Universal History of Numbers: From Prehistory to the Invention of the Computer. David (1996). ^ Howard Eves (1990). 14. "The Mathematics of the Hindus". Bibhutibhushan. Saunders College Publishing House. 12. p.. ^ Otto Neugebauer. MacTutor History of Mathematics archive: "He believes that the Moon and planets shine by reflected sunlight. ^ Dutta. ^ Hugh Thurston. 165–192.). Phanindralal Gangooly (1989). p. the number of terms plus one. ^ Jacobs. Inc. ^ George. ISBN 0-7141-1746-3 pp.). ISBN 9788120806122. pp. Robertson. ISBN 0-387-94822-8 . ISBN 0471543977. Christopher. ""He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. pp. "Diophantine equations: The Kuttaka". ^ Amartya K Dutta. John Wiley & Sons. Asia Publishing House. 19. 1983. Also see earlier overview: Mathematics in Ancient India. ^ J. (He claimed that the volume was half the height times the area of the base. 129–156." 17. The Surya Siddhanta: A Textbook of Hindu Astronomy. "Aryabhata gave the correct rule for the area of a triangle and an incorrect rule for the volume of a pyramid. New York: Springer-Verlag. Clark. 2009. ISRO. 30. Subhash C. ISBN 0471180823. ^ The concept of Indian heliocentrism has been advocated by B. "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models. Retrieved 2007-07-06. Aryabhata: Indian Mathematician and Astronomer. 1976." Isis. Zürich:Kommissionsverlag Leeman AG. New Delhi: Indian National Science Academy. 24. ^ Noel Swerdlow. Springer-Verlag. Retrieved 2007-07-14.etymonline. retrieved 24th January.com/yw/2006/02/03/stories/2006020304520600. retrieved 24th November. 25. Roger (1997). Springer. http://www. 'Birth and Early Development of Indian Astronomy'. 4 [1]. The Āryabhaṭīya of Āryabhaṭa: An Ancient Indian Work on Mathematics and Astronomy. ISBN 0387948228 26.com/. ^ "Maths can be fun". 529–534. reprint: Kessinger Publishing (2006). NASA.). ISBN 0-38794107-X [edit] External links . 64 (1973): 239–243. The Columbia Encyclopedia (6 ed. The History of Mathematics: A Brief Course. Kennedy. 31. ISBN 978-1425485993. 12th December. ^ Dennis Duke. 3 February 2006. van der Waerden. 188. "Online Etymology Dictionary". persischen und indischen Astronomie. http://www. L.hindu.. [edit] Other references • • • • • Cooke. 23. "The Heliocentric System in Greek.org/details/The_Aryabhatiya_of_Aryabhata_Clark_1930 Kak.html. ^ "Omar Khayyam". ISBN 0-7923-6363-9 Shukla. Walter Eugene (1930). ^ B. 2004. "Review: A Lost Monument of Indian Astronomy. ^ "JSC NES School Measures Up". Astronomy Across Cultures: The History of Non-Western Astronomy. New York. Retrieved 2007-06-10. 1970. 2010. n. van der Waerden. Kripa Shankar. (1994).bartleby. http://www. 2001-05. H. p. pp. Persian and Hindu Astronomy". Helaine (2000). (2000). University of Chicago Press. ^ "The Round Earth". 500 (1987). 29. 28. The Hindu. 27. Thurston." Archive for History of Exact Sciences 59 (2005): 563–576. Das heliozentrische System in der griechischen. ^ Douglas Harper (2001). 2008. 16. Annals of the New York Academy of Science. From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. NASA. ^ Discovery of New Microorganisms in the Stratosphere. 11th April. Naturforschenden Gesellschaft in Zürich. 22.htm.com/65/om/OmarKhay. in David A. King and George Saliba. ed.21. WileyInterscience. Early Astronomy.L. 2006. S. ^ Hugh Thurston (1996). Boston: Kluwer. Mar. http://www.archive. Early Astronomy. In Selin. Roy · Sharadchandra Shankar Shrikhande · Navin M. Nov 2004 http://www.. A..The Aryabhatiya of Aryabhata English Translation O'Connor. Ray-Chaudhuri · Sarvadaman Chowla · Narendra Karmarkar · Prasanta Chandra Modern Mahalanobis · Jayant Narlikar · Vijay Kumar Patodi · Srinivasa Ramanujan · Calyampudi Radhakrishna Rao · S.scribd. Delhi) Babylonian mathematics · Greek mathematics · Islamic mathematics Treatises Centers Influences .uk/Biographies/Aryabhata_I. Singhi · Mathukumalli V.org/ (Surya Siddhanta translations) [hide][hide] v•d•e Indian mathematics Ancient Apastamba · Baudhayana · Katyayana · Manava · Pāṇini · Pingala · Yajnavalkya Aryabhata I · Aryabhata II · Bhāskara I · Bhāskara II · Melpathur Narayana Bhattathiri · Brahmadeva · Brahmagupta · Brihaddeshi · Halayudha · Jyesthadeva · Madhava of Sangamagrama · Mahavira · Mahendra Suri · Classical Munishvara · Narayana Pandit · Parameshvara · Achyuta Pisharati · Jagannatha Samrat · Nilakantha Somayaji · Śrīpati · Sridhara · Gangesha Upadhyaya · Varahamihira · Sankara Mathematicians Variar · Virasena Shreeram Shankar Abhyankar · A.ac. "Aryabhata". http://www-history.standrews.htm http://www. Subbarao · S. Aryabhata and Diophantus' son.html. Edmund F. K. Hindustan Times Storytelling Science column.com/2007/06/25/stories/2007062558250400. MacTutor History of Mathematics archive.hindu. Krishnaswami Ayyangar · Raj Chandra Bose · Satyendra Nath Bose · Harish-Chandra · Subrahmanyan Chandrasekhar · D.mcs. Robertson. N. Srinivasa Varadhan Aryabhatiya · Bakhshali manuscript · Brahmasphutasiddhanta · Karanapaddhati · Maha-Siddhanta · Paulisa Siddhanta · Paitamaha Siddhanta · Romaka Siddhanta · Sadratnamala · Śulba Sūtras · Surya Siddhanta · Tantrasamgraha · Vasishtha Siddhanta · Veṇvāroha · Yuktibhasa · Yavanajataka Jantar Mantar (Jaipur) · Kerala school of astronomy and mathematics · Ujjain · Yantra Mantra (Jaipur.wilbourhall. John J. R.• • • • • http://www.com/doc/20912413/The-Aryabhatiya-of-Aryabhata-EnglishTranslation . University of St Andrews. wikipedia.Influenced Chinese mathematics · Islamic mathematics · European mathematics Retrieved from "http://en.org/wiki/Aryabhata" Categories: 476 births | 550 deaths | 5th-century mathematicians | 6th-century mathematicians | Indian astronomers | Indian mathematicians | Medieval astronomers | People from Bihar Hidden categories: Articles containing Sanskrit language text | All articles with unsourced statements | Articles with unsourced statements from May 2010 | Articles with inconsistent citation formats Personal tools • Log in / create account Namespaces • • Article Discussion Variants Views • • • Actions Search þÿ Read Edit View history Navigation • • • • • • Main page Contents Featured content Current events Random article Donate Interaction • • Help About Wikipedia . • • • Toolbox • • • • • • Community portal Recent changes Contact Wikipedia What links here Related changes Upload file Special pages Permanent link Cite this page Print/export • • • Create a book Download as PDF Printable version Languages • • • • • • • • • • • • • • • • • • • • • • • • • • العربية বাংলা Català Corsu Deutsch Español Français ગુજરાતી िहनदी Bahasa Indonesia Íslenska Italiano עברית ಕನಡ ನ Қазақша Kreyòl ayisyen മലയാളം मराठी Bahasa Melayu Nederlands नेपाली 日本語 Norsk (bokmål) پنجابی Piemontèis Polski . .• • • • • • • • • • • • • • Português Русский संसकृत Slovenščina Suomi Svenska தமிழ் తలుగు Türkçe Українська اردو Winaray This page was last modified on 18 November 2010 at 20:50. 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