biography of tagore

8/11/2019 Biography Of Tagore

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BiographyName

While there is a tendency to misspell his name as "Aryabhatta" byanalogy with other names having the "bhatta"suffix, his name isproperly spelled Aryabhata: every astronomical text spells his namethus,[6]includingBrahmagupta's references to him "in more than ahundred places by name".[7]Furthermore, in most instances"Aryabhatta" does not fit the metre either.[6]

Time and place of birthAryabhata mentions in the Aryabhatiya that it was composed 3,600years into theKali Yuga,when he was 23 years old. This correspondsto 499 CE, and implies that he was born in 476.[4]

Aryabhata provides no information about his place of birth. The onlyinformation comes fromBhskara I,who describes Aryabhataas makya, "one belonging to theamaka country." During theBuddha's time, a branch of the Amaka people settled in the region

between theNarmada andGodavari rivers in central India;Aryabhata is believed to have been born there.[6][8]
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Other hypotheses

It has been claimed that the amaka (Sanskrit for "stone") whereAryabhata originated may be the present dayKodungallur whichwas the historical capital city ofThiruvanchikkulam of ancientKerala.[9]This is based on the belief that Kouallr was earlierknown as Koum-Kal-l-r ("city of hard stones"); however, old recordsshow that the city was actually Koum-kol-r ("city of strictgovernance"). Similarly, the fact that several commentaries on the

Aryabhatiya have come from Kerala has been used to suggest that itwas Aryabhata's main place of life and activity; however, manycommentaries have come from outside Kerala, and theAryasiddhanta was completely unknown in Kerala.[6]

Aryabhata mentions "Lanka" on several occasions inthe Aryabhatiya, but his "Lanka" is an abstraction, standing for apoint on the equator at the same longitude as hisUjjayini.[10]

EducationIt is fairly certain that, at some point, he went to Kusumapura foradvanced studies and lived there for some time.[11]Both Hindu andBuddhist tradition, as well asBhskara I (CE 629), identifyKusumapura asPaliputra,modernPatna.[6]A verse mentions thatAryabhata was the head of an institution (kulapa) at Kusumapura,and, because the university ofNalanda was in Pataliputra at thetime and had an astronomical observatory, it is speculated thatAryabhata might have been the head of the Nalanda university as

well.[6]Aryabhata is also reputed to have set up an observatory at theSun temple inTaregana,Bihar.[12]
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WorksAryabhata is the author of several treatisesonmathematics andastronomy,some of which are lost.

His major work, Aryabhatiya, a compendium of mathematics andastronomy, was extensively referred to in the Indian mathematicalliterature and has survived to modern times. The mathematical partof the Aryabhatiya coversarithmetic,algebra,plane trigonometry,andspherical trigonometry.It also containscontinuedfractions,quadratic equations,sums-of-power series, and atable of

sines.The Arya-siddhanta, a lost work on astronomical computations, isknown through the writings of Aryabhata'scontemporary,Varahamihira,and later mathematicians andcommentators, includingBrahmagupta andBhaskara I.This workappears to be based on the olderSurya Siddhanta and uses themidnight-day reckoning, as opposed to sunrise in Aryabhatiya. It alsocontained a description of several astronomical instruments:thegnomon (shanku-yantra), a shadow instrument (chhAyA-yantra),

possibly angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, anumbrella-shaped device called the chhatra-yantra, andwater clocks ofat least two types, bow-shaped and cylindrical.[8]A third text, whichmay have survived in theArabic translation, is Al ntf or Al-nclaimsthat it is a translation by Aryabhata, but the Sanskrit name of thiswork is not known.

Probably dating from the 9th century, it is mentionedbythePersian scholar and chronicler of IndianAbRayhn al-Brn.[8]
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AryabhatiyaMain article:Aryabhatiya

Direct details of Aryabhata's work are known only fromthe Aryabhatiya. The name "Aryabhatiya" is due to latercommentators. Aryabhata himself may not have given it a name. HisdiscipleBhaskara I calls it Ashmakatantra (or the treatise from theAshmaka). It is also occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in thetext. It is written in the very terse style typical ofsutra literature, inwhich each line is an aid to memory for a complex system. Thus, theexplication of meaning is due to commentators. The text consists ofthe 108 verses and 13 introductory verses, and is divided intofour pdas or chapters:

1. Gitikapada: (13 verses): large units of timekalpa, manvantra,and yugawhich present a cosmology different from earlier

texts such as Lagadha'sVedanga Jyotisha (c. 1st century BCE).There is also a table of sines (jya), given in a single verse. Theduration of the planetary revolutions during a mahayuga isgiven as 4.32 million years.

2. Ganitapada (33 verses): covering mensuration (ketravyvahra), arithmetic and geometric progressions,gnomon/shadows (shanku-chhAyA), simple,quadratic,simultaneous,andindeterminate equations

3. Kalakriyapada (25 verses): different units of time and a method

for determining the positions of planets for a given day,
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calculations concerning the intercalary month(adhikamAsa), kShaya-tithis, and a seven-day week with namesfor the days of week.

4.Golapada (50 verses): Geometric/trigonometric aspects of

thecelestial sphere,features of theecliptic,celestial equator,node, shape of the earth, cause of day and night, risingofzodiacal signs on horizon, etc. In addition, some versions citea fewcolophons added at the end, extolling the virtues of thework, etc.

The Aryabhatiya presented a number of innovations in mathematicsand astronomy in verse form, which were influential for manycenturies. The extreme brevity of the text was elaborated incommentaries by his disciple Bhaskara I (Bhashya, c. 600 CE) and

byNilakantha Somayaji in his Aryabhatiya Bhasya, (1465 CE).

MathematicsPlace value system and zero

Theplace-value system, first seen in the 3rd-centuryBakhshaliManuscript,was clearly in place in his work. While he did not use a

symbol forzero,the French mathematicianGeorges Ifrah argues thatknowledge of zero was implicit in Aryabhata'splace-value system as aplace holder for the powers of ten withnullcoefficients[13]

However, Aryabhata did not use the Brahmi numerals. ContinuingtheSanskritic tradition fromVedic times,he used letters of thealphabet to denote numbers, expressing quantities, such as the table ofsines in amnemonicform.[14]
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Approximation of

Aryabhata worked on the approximation forpi ( ), and may havecome to the conclusion that is irrational. In the second part ofthe Aryabhatiyam (gaitapda 10), he writes:

caturadhikam atamaaguam dvaistathsahasrmayutadvayavikambhasysanno vttapariha."Add four to 100, multiply by eight, and then add 62,000. By this rulethe circumference of a circle with a diameter of 20,000 can beapproached."

[15]

This implies that the ratio of the circumference to the diameter is((4 + 100) 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate

to fivesignificant figures.

It is speculated that Aryabhata used the word sanna (approaching),to mean that not only is this an approximation but that the value isincommensurable (orirrational). If this is correct, it is quite asophisticated insight, because the irrationality of pi was proved inEurope only in 1761 byLambert.[16]

After Aryabhatiya was translated intoArabic (c. 820 CE) thisapproximation was mentioned inAl-Khwarizmi's book on

algebra.[8]TrigonometryIn Ganitapada 6, Aryabhata gives the area of a triangle as

tribhujasya phalashariram samadalakoti bhujardhasamvargah

that translates to: "for a triangle, the result of a perpendicularwith the half-side is the area."[17]

Aryabhata discussed the concept ofsine in his work by the nameofardha-jya,which literally means "half-chord". For simplicity,people started calling itjya.When Arabic writers translated hisworks fromSanskrit into Arabic, they referred it as jiba. However,in Arabic writings, vowels are omitted, and it was abbreviatedas jb. Later writers substituted it with jaib, meaning "pocket" or"fold (in a garment)". (In Arabic, jiba is a meaningless word.) Laterin the 12th century, whenGherardo of Cremona translated thesewritings from Arabic into Latin, he replaced the Arabic jaib withits Latin counterpart, sinus, which means "cove" or "bay"; thencecomes the English sine. Alphabetic code has been used by him todefine a set of increments. If we use Aryabhacalculate the value ofsin(30) (corresponding to hasjha) which is 1719/3438 = 0.5; the value
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(seesquared triangular

number AstronomyAryabhata's system of astronomy was called

the audAyaka system, in which days are reckonedfrom uday, dawn at lanka or "equator". Some of his laterwritings on astronomy, which apparently proposed asecond model (or ardha-rAtrikA, midnight) are lost butcan be partly reconstructed from the discussioninBrahmagupta'skhanDakhAdyaka. In some texts, heseems to ascribe the apparent motions of the heavens totheEarth's rotation.He may have believed that theplanet's orbits aselliptical rather than circular.[21][22]

Motions of the solar system

Aryabhata correctly insisted that the earth rotates aboutits axis daily, and that the apparent movement of thestars is a relative motion caused by the rotation of theearth, contrary to the then-prevailing view, that the skyrotated. This is indicated in the first chapter ofthe Aryabhatiya, where he gives the number of rotations

of the earth in ayuga,[23]and made more explicit inhis gola chapter:[24]

In the same way that someone in a boat goingforward sees an unmoving [object] going backward,so [someone] on the equator sees the unmoving starsgoing uniformly westward. The cause of rising andsetting [is that] the sphere of the stars together withthe planets [apparently?] turns due west at theequator, constantly pushed by the cosmic wind.

Aryabhata described ageocentric model of the solarsystem, in which the Sun and Moon are each carriedbyepicycles.They in turn revolve around the Earth. Inthis model, which is also found inthe Paitmahasiddhnta (c. CE 425), the motions of theplanets are each governed by two epicycles, asmaller manda (slow) and a largerghra (fast).[25]Theorder of the planets in terms of distance from earth is

taken as: theMoon,Mercury,Venus,theSun,Mars,Jupiter,Saturn,and theasterisms."[8]
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The positions and periods of the planets was calculatedrelative to uniformly moving points. In the case ofMercury and Venus, they move around the Earth at thesame mean speed as the Sun. In the case of Mars, Jupiter,

and Saturn, they move around the Earth at specificspeeds, representing each planet's motion through thezodiac. Most historians of astronomy consider that thistwo-epicycle model reflects elements of pre-PtolemaicGreek astronomy.[26]Another element inAryabhata's model, theghrocca, the basic planetaryperiod in relation to the Sun, is seen by some historians asa sign of an underlyingheliocentric model.[27]

Eclipses

Solar and lunar eclipses were scientifically explained byAryabhata. He states that theMoon and planets shine byreflected sunlight. Instead of the prevailing cosmogony inwhich eclipses were caused by pseudo-planetarydemonsRahu andKetu,he explains eclipses in terms ofshadows cast by and falling on Earth. These will onlyoccur when the earth-moon orbital plane intersects the

earth-sun orbital plane, at points calledlunar nodes.Thus,the lunar eclipse occurs when the moon enters into theEarth's shadow (verse gola.37). He discusses at length thesize and extent of the Earth's shadow (verses gola.3848)and then provides the computation and the size of theeclipsed part during an eclipse. Later Indian astronomersimproved on the calculations, but Aryabhata's methodsprovided the core. His computational paradigm was soaccurate that 18th-century scientistGuillaume Le Gentil,

during a visit to Pondicherry, India, found the Indiancomputations of the duration of thelunar eclipseof 30August 1765 to be short by 41 seconds, whereas his charts(by Tobias Mayer, 1752) were long by 68 seconds.[8]

Sidereal periods

Considered in modern English units of time, Aryabhatacalculated thesidereal rotation (the rotation of the earthreferencing the fixed stars) as 23 hours, 56 minutes, and

4.1 seconds;[28]

the modern value is 23:56:4.091. Similarly, hisvalue for the length of thesidereal year at 365 days, 6
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hours, 12 minutes, and 30 seconds (365.25858 days)[29]is anerror of 3 minutes and 20 seconds over the length of ayear (365.25636 days).

Heliocentrism

As mentioned, Aryabhata advocated an astronomicalmodel in which the Earth turns on its own axis. His modelalso gave corrections (the gra anomaly) for the speeds ofthe planets in the sky in terms of the mean speed of thesun. Thus, it has been suggested that Aryabhata'scalculations were based on anunderlyingheliocentric model, in which the planets orbitthe Sun,[30][31][32]though this has been rebutted.[33]It has also

been suggested that aspects of Aryabhata's system mayhave been derived from an earlier, likely pre-PtolemaicGreek,heliocentric model of which Indianastronomers were unaware,[34]though the evidence isscant.[35]The general consensus is that a synodic anomaly(depending on the position of the sun) does not imply aphysically heliocentric orbit (such corrections being alsoAryabhata's system was not explicitly heliocentric.[36]

Legacy

India's first satellite named after Aryabhata

Aryabhata's work was of great influence in the Indian

astronomical tradition and influenced severalneighbouring cultures through translations.
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TheArabic translation during theIslamic Golden Age (c.820 CE), was particularly influential. Some of his resultsare cited byAl-Khwarizmi and in the 10th centuryAl-Biruni stated that Aryabhata's followers believed that the

Earth rotated on its axis.His definitions ofsine (jya), cosine (kojya), versine(utkrama-jya), and inverse sine (otkram jya) influencedthe birth oftrigonometry.He was also the first to specifysine andversine (1 cos x) tables, in 3.75 intervals from 0to 90, to an accuracy of 4 decimal places.

In fact, modern names "sine" and "cosine" aremistranscriptions of the words jya and kojya asintroduced by Aryabhata. As mentioned, they weretranslated as jiba and kojiba in Arabic and thenmisunderstood byGerard of Cremona while translating anArabic geometry text toLatin.He assumed that jiba wasthe Arabic word jaib, which means "fold in a garment",L. sinus (c. 1150).[37]

Aryabhata's astronomical calculation methods were alsovery influential. Along with the trigonometric tables, theycame to be widely used in the Islamic world and used +

to compute manyArabic astronomical tables (zijes). Inparticular, the astronomical tables in the work oftheArabic Spain scientistAl-Zarqali (11th century) weretranslated into Latin as theTables of Toledo (12th century)and remained the most accurateephemeris used inEurope for centuries.

Calendric calculations devised by Aryabhata and hisfollowers have been in continuous use in India for thepractical purposes of fixing thePanchangam (theHinducalendar). In the Islamic world, they formed the basis oftheJalali calendar introduced in 1073 CE by a group ofastronomers includingOmar Khayyam,[38]versions ofwhich (modified in 1925) are the national calendars in useinIran andAfghanistan today. The dates of the Jalalicalendar are based on actual solar transit, as inAryabhata and earlierSiddhanta calendars. This type ofcalendar requires an ephemeris for calculating dates.Although dates were difficult to compute, seasonal errors
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were less in the Jalali calendar than in theGregoriancalendar.

Aryabhatta Knowledge University (AKU), Patna has

been established by Government of Bihar for thedevelopment and management of educationalinfrastructure related to technical, medical, managementand allied professional education in his honour. Theuniversity is governed by Bihar State University Act2008.

India's first satelliteAryabhata and thelunarcraterAryabhata are named in his honour. An Institutefor conducting research in astronomy, astrophysics and

atmospheric sciences is theAryabhatta Research Instituteof Observational Sciences (ARIES) near Nainital, India.The inter-schoolAryabhata Maths Competition is alsonamed after him,[39]as is Bacillus aryabhata, a species ofbacteria discovered byISRO scientists in 2009.[40]
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