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Aryabhata I:     more detail

Aryabhata the Elder: An entry from Gale's <i>Science and Its Times</i> by Judson Knight, 2001 Aryabhata the Elder: An entry from Gale's <i>Science and Its Times</i> Aryabhata I and his contributions to mathematics by Parmeshwar Jha, 1988 Physical Science in India: An entry from Gale's <i>Science and Its Times</i> by William J. McPeak, 2001 The Mathematics of Ancient India: An entry from Gale's <i>Science and Its Times</i> by James J. Hoffmann, 2001 Ariabkhata: K 1500-letiiu so dnia rozhdeniia (Nauchno-bibliograficheskaia seriia) by A. I Volodarskii, 1977

lists with details

1. Aryabhata_I
   Aryabhata the Elder. aryabhata is also known as aryabhata i to distinguish him fromthe later mathematician of the same name who lived about 400 years later.  
   http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Aryabhata_I.html
   
   Extractions: Aryabhata is also known as Aryabhata I to distinguish him from the later mathematician of the same name who lived about 400 years later. Al-Biruni has not helped in understanding Aryabhata's life, for he seemed to believe that there were two different mathematicians called Aryabhata living at the same time. He therefore created a confusion of two different Aryabhatas which was not clarified until 1926 when B Datta showed that al-Biruni 's two Aryabhatas were one and the same person. We know the year of Aryabhata's birth since he tells us that he was twenty-three years of age when he wrote Aryabhatiya which he finished in 499. We have given Kusumapura, thought to be close to Pataliputra (which was refounded as Patna in Bihar in 1541), as the place of Aryabhata's birth but this is far from certain, as is even the location of Kusumapura itself. As Parameswaran writes in [26]:- ... no final verdict can be given regarding the locations of Asmakajanapada and Kusumapura. We do know that Aryabhata wrote Aryabhatiya in Kusumapura at the time when Pataliputra was the capital of the Gupta empire and a major centre of learning, but there have been numerous other places proposed by historians as his birthplace. Some conjecture that he was born in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that he was born in the north-east of India, perhaps in Bengal. In [8] it is claimed that Aryabhata was born in the Asmaka region of the Vakataka dynasty in South India although the author accepted that he lived most of his life in Kusumapura in the Gupta empire of the north. However, giving Asmaka as Aryabhata's birthplace rests on a comment made by

2. Aryabhata_II
   aryabhata iI. Born about 920 in India Died about 1000 in India. Essentiallynothing is known of the life of aryabhata iI. Historians  
   http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Aryabhata_II.html
   
   Extractions: Essentially nothing is known of the life of Aryabhata II. Historians have argued about his date and have come up with many different theories. In [1] Pingree gives the date for his main publications as being between 950 and 1100. This is deduced from the usual arguments such as which authors Aryabhata II refers to and which refer to him. G R Kaye argued in 1910 that Aryabhata II lived before al-Biruni but Datta [2] in 1926 showed that these dates were too early. The article [3] argues for a date of about 950 for Aryabhata II's main work, the Mahasiddhanta, but R Billiard has proposed a date for Aryabhata II in the sixteenth century. Most modern historians, however, consider the most likely dates for his main work as around 950 and we have given very approximate dates for his birth and death based on this hypothesis. See [7] for a fairly recent discussion of this topic. The most famous work by Aryabhata II is the Mahasiddhanta which consists of eighteen chapters. The treatise is written in Sanskrit verse and the first twelve chapters form a treatise on mathematical astronomy covering the usual topics that Indian mathematicians worked on during this period. The topics included in these twelve chapters are: the longitudes of the planets, eclipses of the sun and moon, the projection of eclipses, the lunar crescent, the rising and setting of the planets, conjunctions of the planets with each other and with the stars.

3. Aryabhata_II
   Biography of aryabhata iI. (9201000) Essentially nothing is known of the life of aryabhata iI. Historians have argued about his date and have come up with  
   http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Aryabhata_II.html
   
   Extractions: Essentially nothing is known of the life of Aryabhata II. Historians have argued about his date and have come up with many different theories. In [1] Pingree gives the date for his main publications as being between 950 and 1100. This is deduced from the usual arguments such as which authors Aryabhata II refers to and which refer to him. G R Kaye argued in 1910 that Aryabhata II lived before al-Biruni but Datta [2] in 1926 showed that these dates were too early. The article [3] argues for a date of about 950 for Aryabhata II's main work, the Mahasiddhanta, but R Billiard has proposed a date for Aryabhata II in the sixteenth century. Most modern historians, however, consider the most likely dates for his main work as around 950 and we have given very approximate dates for his birth and death based on this hypothesis. See [7] for a fairly recent discussion of this topic. The most famous work by Aryabhata II is the Mahasiddhanta which consists of eighteen chapters. The treatise is written in Sanskrit verse and the first twelve chapters form a treatise on mathematical astronomy covering the usual topics that Indian mathematicians worked on during this period. The topics included in these twelve chapters are: the longitudes of the planets, eclipses of the sun and moon, the projection of eclipses, the lunar crescent, the rising and setting of the planets, conjunctions of the planets with each other and with the stars.

4. História Da Matemática Na Índia -Aryabhata I
   Translate this page aryabhata i (476-550). Aryabhata nasceu na Índia em 476. Aryabhata tinha 23 anosquando escreveu o seu tratado Aryabhatiya terminando-o no ano de 499.  
   http://www.malhatlantica.pt/mathis/India/Aryabhata.htm
   
   Extractions: textos: História da Matemática na Índia Aryabhata I Aryabhata nasceu na Índia em 476. É também conhecido por Aryabhata I, para o destinguir de outro matemático hindu como o mesmo nome que nasceu cerca de 400 anos mais tarde. Aryabhata tinha 23 anos quando escreveu o seu tratado Aryabhatiya terminando-o no ano de 499. O livro contém 118 versos, e está dividido em quatro partes: uma introdução de 10 versos, a segunda parte - Ganitapada - era um resumo da matemática hindu do seu tempo. Nos 32 versos de Ganitapada fala de aritmética, álgebra, trigonometria plana e esférica, fracções continuas e equações do 2º grau. A terceira parte contém 25 versos sobre o cálculo do tempo e modelos planetários, e a parte final contém 50 versos sobre a esfera e eclipses. Problema Ó bela donzela com olhos radiantes, diz-me, uma vez que compreendes o método da inversão, qual é o número que multiplicado por 3, aumentado por ¾ do produto, dividido por 7, reduzido em um terço do resultado, depois multiplicado por ele próprio, depois reduzido de 52, cuja raiz quadrada é então extraída antes de ser adicionado 8 e dividido por 10, dá o resultado final 2? (citado por George Joseph) Para qualquer dúvida, sugestão ou comentário escreva para:

5. ªü­Cªi¦h²Ä¤@¡£Aryabhata I¡¤
   The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set.  
   http://www.edp.ust.hk/math/history/3/3_97.htm
   
   Extractions: ¢w ¡A¦L«× ¥L¬O¨´¤µ©Òª¾³Ì¦­ªº¦L«×¼Æ¾Ç®a¡A¬OÄÝ©ó©ëĬ¼¯¸É¹¾Ç¬£¡C¥L¥D­n¦³¨â¥»µÛ§@¡G¤@¥»¬O¡mªü­Cªi¦h¾ä®Ñ¡n¡A¦¨®Ñ©ó¤½¤¸ ¦~¡A¥]¬A¡§¤Ñ¤åªí¶°¡¨¡B¡§ºâ³N¡¨¡B¡§®É¶¡ªº«×¶q¡¨¡B¡§²y¡¨µ¥³¡¥÷¡C¸Ó®Ñ¦@ ½s¡A¥Ñ ¦æ¸Öºc¦¨¡A¨ä¤¤½×¤Î¼Æ¾Çªº¦³¨â½g¡A¨ ¦æ¸Ö¡A¤º®e¥]¬Aºâ³N¡B¥N¼Æ¡B´X¦ó¡B¤T¨¤µ¥ª¾Ñ¡A¦Ó¥t¤@¥»¤Ñºâ®Ñ¤w¸g¥¢¶Ç¡C ¥L«ü¥X£k ªü­Cªi¦h¦b¦L«×¬ì¾Ç¥v¤W¬O¦³­«­n¼vÅTªº¤Hª«¡A¬°¤F¬ö©À¥L¡A1975¦~4¤ë19¤é¦L«×µo®gªº²Ä¤@Áû¤H³y½¬P«K¬O©R¦W¬°ªü­Cªi¦h¸¹¡C

6. Encyclopædia Britannica
   The Annals of America, Price USD $395, Now with a NEW 22nd volume! Visit BritannicaStore, Encyclopædia Britannica, aryabhata i Encyclopædia Britannica Article.  
   http://www.britannica.com/eb/article?eu=9867

7. Redirect
   Gives details about the ancient Indian mathematical work of aryabhata. Includes links to related sites. In the work The Àryabhatíya of Àryabhata, An Ancient Indian Work on Mathematics and Astronomy, translated by William  
   http://www.geocities.com/Athens/Olympus/4844/aryabhata.html

8. Aryabhata
   aryabhata (476499). There are at least two mathematicians who lived by the namearyabhata. This is a biography about aryabhata from Kusumapura, now Patna.  
   http://www.math.sfu.ca/histmath/India/5thCenturyAD/Aryabhata.html
   
   Extractions: There are at least two mathematicians who lived by the name Aryabhata. This is a biography about Aryabhata from Kusumapura, now Patna. Aryabhata belonged to the Kusumapura school, but was probably a native of Kerala since his tradition is still in vogue there. At age 23 he wrote his small but famous work on astronomy, the Aryabhatiya. In it he organized and combined existing knowledge of astronomy and mathematics. He says, "I delved deep in the astronomical theories, true and false, and rescued the precious sunken jewel of the knowledge by means of the best of my intellect and by the grace of God". Aryabhata considered his work as a whole, but Brahmagupta divides the work into two parts in his Brahma Sphuta Siddhanta. It consists of 121 slokas-three slokas (verses) forming the introduction and the conclusion, ten slokas written in the Geetika metre, followed by 108 slokas in the Aryavrata metre. Brahmagupta called the Geetika metre and the Aryavrata metre, Dasgeetika and Aryashtasatam respectively. He then divided the Aryashtasatam into three parts:

9. The Àryabhatíya Of Àryabhata By J. Q. Jacobs
   The oldest exact astronomic constant? The ratio of earth rotations to lunar orbits in aryabhata's AD 498 writing.  
   http://www.jqjacobs.net/astro/aryabhata.html
   
   Extractions: The oldest exact astronomic constant? © 1998 by James Q. Jacobs In the work translated by William Eugene Clark, Professor of Sanskrit in Harvard University (The University of Chicago Press, Chicago, Illinois. 1930), I found the following to be written: "In a yuga the revolutions of the Sun are 4,320,000, of the Moon 57,753,336, of the Earth eastward 1,582,237,500, of Saturn 146,564, of Jupiter 364,224, of Mars 2,296,824 . . . " (page 9). Astronomy Formulas

10. The Aryabhata Satellite
    aryabhata. Full resolution image Mission Overview. aryabhata was India's first satellite,named after a ancient Indian mathematician (5th century AD).  
    http://heasarc.gsfc.nasa.gov/docs/heasarc/missions/aryabhata.html
    
    Extractions: -Archive Interfaces- Argus: proposal info Astrobrowse: worldwide catalog search Browse: search HEASARC archives SkyMorph: search variable objects SkyView: virtual observatory CalDB: Calibration database Coord Converter Date Converter Energy Converter FITS: standard data format FITSIO: FITS subroutine library FTOOLS: general s/w for FITS files fV: FITS file editor nH: Column Density RPS proposal submission RXTE ASM weather map Time Converter TIPTOPbase: atomic data Viewing: possible obs times WebPIMMS: flux/cnt converter WebSpec: spectral sims X-ray Background Tool Xanadu: data analysis suite X-ray, Gamma-ray, EUV Source Finder xTime: RXTE time converter HEASARC Resources/Education -Resources/Education- Contact Info APOD: Astronomy Picture of the Day Ask an Astronomer Bibliography HEASARC Pict of the Week History of High-Energy Astronomy Images, Spectra, Light curves Imagine the Universe! Legacy Journal Meetings Resources Staff StarChild (K-8 EPO) Tour the site WebStars: gen. astronomy info/news What's New Search the HEASARC site: Full resolution image Aryabhata was India's first satellite, named after a ancient Indian mathematician (5th century AD). It was launched by the Russians on 19 April 1975 from Kapustin Yar. The 96.3 minute orbit had an apogee of 619 km and a perigee of 563 km, at an inclination of 50.7 degrees. Aryabhata was built by the Indian Space Research Organization (ISRO) to conduct experiments in X-ray astronomy, aeronomics, and solar physics. The spacecraft was a 26-sided polygon 1.4 m in diameter. All faces (except the top and bottom) were covered with solar cells. A power failure halted experiments after 4 days in orbit. All signals from the spacecraft were lost after 5 days of operation. The satellite reentered the Earth's atmosphere on 11 February 1992.

11. Aryabhata
    The Soviet Union assisted India in development of aryabhata, its first satellite, named for the Indian astronomer.  
    http://www.astronautix.com/craft/arybhata.htm
    
    Extractions: Class: Earth Type : Atmosphere. Nation : India. Agency : ISRO. The Soviet Union assisted India in development of Aryabhata, its first satellite, named for the Indian astronomer. The satellite conducted scientific experiments on atmospheric research., but was primarily an experimental satellite for satellite technology. Total Mass : 360 kg. Aryabhata Chronology 19 April 1975 Aryabhata Launch Site Kapustin Yar Launch Vehicle Kosmos 11K65M Mass : 360 kg. Perigee : 398 km. Apogee : 409 km. Inclination : 50.7 deg. Atmospheric research. Experimental satellite for satellite technology and some scientific experiments. Launched from a cosmodrome in the USSR. Bibliography: McDowell, Jonathan, The United Nations Registry of Space Objects , Harvard University, 1997. Web Address when accessed: http://hea-www.harvard.edu/QEDT/jcm/space/un/un.html JPL Mission and Spacecraft Library , Jet Propulsion Laboratory, 1997. Web Address when accessed: http://msl.jpl.nasa.gov/home.html Melnik, T G, Voenno-Kosmicheskiy Siliy , Nauka, Moscow, 1997..

12. TSE - Aryabhata
    aryabhata. Named after a ancient Indian mathematician (5th century AD)  
    http://www.tbs-satellite.com/tse/online/sat_aryabhata.html
    
    Extractions: Studied astronomy sources and relations between Earth and Sun (X-ray astronomy, solar physics and aeronomy). Out of service After 4 days Cause Failure of the Indian-designed transformer Decay 11 Feb 1992 http://heasarc.gsfc.nasa.gov/Images/misc_missions/aryabhata.gif This document is part of The Satellite Encyclopedia Tag's Broadcasting Services . Please notify any errors, omissions, etc.

13. HinduNet Forums Chat Annouce Calender DigiCards Recommend Remote
    1. aryabhata i (476 550 AD) - mathematician and astronomer. Aryabhata took theearth to spin on its axis; this idea appears to have been his innovation  
    http://www.hinduweb.org/home/general_sites/vande/great_hindu_personalities.html
    
    Extractions: Home Hinduism Intro Christian Missionaries Great Hindu Personalities ... Links Great Hindu Personalities Aryabhata I (476 - 550 A.D.) - mathematician and astronomer. He is "the author of the first of the later sidhantas [mathematical treatises] called Aryabhatiyam which sketches his mathematical, planetary, and cosmic theories. This book is divided into four chapters: (i) the astronomical constants and the sine table (ii) mathematics required for computations (iii) division of time and rules for computing the longitudes of planets using eccentrics and epicycles (iv) the armillary sphere, rules relating to problems of trigonometry and the computation of eclipes... Aryabhata took the earth to spin on its axis; this idea appears to have been his innovation... That Aryabhata was aware of the relativity of motion is clear from this passage in his book, 'Just as a man in a boat sees the trees on the bank move in the opposite direction, so an observer on the equator sees the stationary stars as moving precisely toward the west.'" "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." Aryabhata gave a value for pi correct to five digits (3.1416); he also gave a close approximation for the circumference of the Earth (62832 miles); believed that the planets and the Moon reflected sunlight and also that the orbits of the plantes were ellipses.

14. Aryabhata
    Provides an overview of the mathematical and scientific work of aryabhata. Includes a list of references. aryabhata the Elder. Born 476 in Kusumapura (now Patna), India  
    http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aryabhata.html

15. Kuttaka
    aryabhata's Kuttaka. aryabhata's solution of the equation axby=cwas known as the Kuttaka (pulverizer) in Hindu mathematics. The  
    http://www.math.sfu.ca/histmath/India/5thCenturyAD/Kuttaka.html
    
    Extractions: Aryabhata noted that any factor common to a and b should be a factor of c, otherwise the equation has no solution. Dividing a, b and c by the greatest common factor of (a,b) we can reduce the equation to the form where a and b are relatively prime. In the discussion that follows we can assume that (a,b)=1 and without loss of generality c>0.

16. The Aryabhata Bibliography
    aryabhata Bibliography. The aryabhata publication list through May, 1999 isthe result of a query to the ADS service using the keyword aryabhata.  
    http://heasarc.gsfc.nasa.gov/docs/heasarc/missions/biblio/aryabhata_biblio.html
    
    Extractions: -Archive Interfaces- Argus: proposal info Astrobrowse: worldwide catalog search Browse: search HEASARC archives SkyMorph: search variable objects SkyView: virtual observatory CalDB: Calibration database Coord Converter Date Converter Energy Converter FITS: standard data format FITSIO: FITS subroutine library FTOOLS: general s/w for FITS files fV: FITS file editor nH: Column Density RPS proposal submission RXTE ASM weather map Time Converter TIPTOPbase: atomic data Viewing: possible obs times WebPIMMS: flux/cnt converter WebSpec: spectral sims X-ray Background Tool Xanadu: data analysis suite X-ray, Gamma-ray, EUV Source Finder xTime: RXTE time converter HEASARC Resources/Education -Resources/Education- Contact Info APOD: Astronomy Picture of the Day Ask an Astronomer Bibliography HEASARC Pict of the Week History of High-Energy Astronomy Images, Spectra, Light curves Imagine the Universe! Legacy Journal Meetings Resources Staff StarChild (K-8 EPO) Tour the site WebStars: gen. astronomy info/news What's New

17. Indian Space Program
    A story of Indian Space Program. Satellites aryabhata APPLE INSAT1 INSAT-2 INSAT-3 Bhaskara IRS Rohini  
    http://www.geocities.com/indian_space_story/arya.html

18. ARYABHATA
    http://almez.pntic.mec.es/~agos0000/Aryabhata.html

19. Aryabhata
    Translate this page aryabhata (Arjabahr) indien, 476-550 Astronome. Il affirme, contrairement laTerre. aryabhata est le premier grand mathématicien indien. Il  
    http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Aryabhata.html
    
    Extractions: indien, 476-550 Aryabhatiya, par l'usage de fractions continues Brahmagupta Bhaskara : Gerbert d'Aurillac : ce qui fournit la bonne approximation nombre p En trigonométrie, dans son Aryabhatiya, demi-corde pour la mesure des angles et à en établir une table précise de à 90°, par pas de 3° 45' (soit 24 valeurs) en utilisant une circonférence de 21600 = 60 x 360 (pour un usage pratique de la base 60 ) pour un rayon de 3438 équivalent à p = 3,14136. D'autres valeurs de demi-cordes pouvant être approchées par interpolation linéaire. La demi-corde correspond au sinus de l'angle double lorsque le rayon du cercle est choisi égal à 1 (cercle trigonométrique) . Tel est le demi-corde demi-corde sinus des traductions latines. Trigonométrie des cordes chez Ptolémée : Depuis Al Khwarizmi et Al Battani corde dans les calculs astronomiques. Le choix du rayon 1 sera initié par Abu l'Wafa Ci-dessous, un extrait d'une table des sinus "moderne", comme celle de J. Laborde édité par Dunod, en usage dans le bon vieux temps des années 1960/70 avant l'apparition des calculatrices de poche à bon marché... Al Battani : Regiomontanus : Proclus Eutocius

20. Brahmagupta
    Translate this page Ce mathématicien et astronome indien s'intéressa à l'algèbre et auxéquations diophantiennes à la suite des travaux d'aryabhata.  
    http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Brahmagupta.html
    
    Extractions: indien, 598-660 indien Aryabhata Chuquet : Arabes Al- Khwarizmi babyloniennes et grecques . Son apparition en Inde Diophante et Aryabhata x = ny (lorsque n est entier) Pell Bhaskara Notons que le concept de congruence Gauss Brahamagupta dans son Bhrama Sphuta Siddhanta n et n chinoises lunaisons Dans son livre Victor J. Katz cite un cas n Gauss et les congruences : inscriptible A Pour en savoir plus : A HISTORY OF MATHEMATICS , an introduction, par Victor J. KATZ

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