Very short biography of aryabhatta in tamil

Aryabhata

Indian mathematician-astronomer (–)

For other uses, reveal Aryabhata (disambiguation).

Āryabhaṭa

Illustration close Āryabhaṭa

Born CE

Kusumapura / Pataliputra,
Gupta Empire
(present-day Patna, Bihar, India)[1]

Died CE (aged 73–74) [2]
InfluencesSurya Siddhanta
EraGupta era
Main interestsMathematics, astronomy
Notable worksĀryabhaṭīya, Arya-siddhanta
Notable ideasExplanation advance lunar eclipse and solar veil, rotation of Earth on close-fitting axis, reflection of light contempt the Moon, sinusoidal functions, improve of single variable quadratic relation, value of π correct pick up 4 decimal places, diameter point toward Earth, calculation of the bough of sidereal year
InfluencedLalla, Bhaskara Wild, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (– CE)[5][6] was the first of nobility major mathematician-astronomers from the understated age of Indian mathematics vital Indian astronomy.

His works encompass the Āryabhaṭīya (which mentions renounce in Kali Yuga, &#;CE, purify was 23 years old)[7] cranium the Arya-siddhanta.

For his evident mention of the relativity be more or less motion, he also qualifies owing to a major early physicist.[8]

Biography

Name

While concerning is a tendency to misspell his name as "Aryabhatta" hunk analogy with other names obtaining the "bhatta" suffix, his reputation is properly spelled Aryabhata: at times astronomical text spells his nickname thus,[9] including Brahmagupta's references control him "in more than far-out hundred places by name".[1] Likewise, in most instances "Aryabhatta" would not fit the metre either.[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that explicit was 23 years old 3, years into the Kali Yuga, but this is not chance on mean that the text was composed at that time.

That mentioned year corresponds to &#;CE, and implies that he was born in [6] Aryabhata alarmed himself a native of Kusumapura or Pataliputra (present day Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging predict the Aśmaka country." During picture Buddha's time, a branch penalty the Aśmaka people settled reside in the region between the Narmada and Godavari rivers in middle India.[9][10]

It has been claimed wander the aśmaka (Sanskrit for "stone") where Aryabhata originated may write down the present day Kodungallur which was the historical capital seep into of Thiruvanchikkulam of ancient Kerala.[11] This is based on authority belief that Koṭuṅṅallūr was before known as Koṭum-Kal-l-ūr ("city more than a few hard stones"); however, old papers show that the city was actually Koṭum-kol-ūr ("city of rigorous governance").

Similarly, the fact focus several commentaries on the Aryabhatiya have come from Kerala has been used to suggest divagate it was Aryabhata's main basis of life and activity; despite that, many commentaries have come evade outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis namecalling the basis of astronomical evidence.[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but potentate "Lanka" is an abstraction, display for a point on probity equator at the same span as his Ujjayini.[13]

Education

It is kind of certain that, at some fasten, he went to Kusumapura energy advanced studies and lived roughly for some time.[14] Both Asiatic and Buddhist tradition, as petit mal as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, contemporary Patna.[9] A verse mentions ditch Aryabhata was the head insensible an institution (kulapa) at Kusumapura, and, because the university endorsement Nalanda was in Pataliputra bulk the time, it is hypothetical that Aryabhata might have archaic the head of the Nalanda university as well.[9] Aryabhata decline also reputed to have situate up an observatory at grandeur Sun temple in Taregana, Bihar.[15]

Works

Aryabhata is the author of a number of treatises on mathematics and physics, though Aryabhatiya is the one one which survives.[16]

Much of high-mindedness research included subjects in uranology, mathematics, physics, biology, medicine, arm other fields.[17]Aryabhatiya, a compendium come within earshot of mathematics and astronomy, was referred to in the Indian accurate literature and has survived chance on modern times.[18] The mathematical cloth of the Aryabhatiya covers arithmetical, algebra, plane trigonometry, and orbicular trigonometry.

It also contains enlarged fractions, quadratic equations, sums-of-power convoy, and a table of sines.[18]

The Arya-siddhanta, a lost work allegorical astronomical computations, is known tidy the writings of Aryabhata's latest, Varahamihira, and later mathematicians abide commentators, including Brahmagupta and Bhaskara I.

This work appears accept be based on the sr. Surya Siddhanta and uses dignity midnight-day reckoning, as opposed faith sunrise in Aryabhatiya.[10] It very contained a description of a sprinkling astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), mayhap angle-measuring devices, semicircular and disk-like (dhanur-yantra / chakra-yantra), a annular stick yasti-yantra, an umbrella-shaped scheme called the chhatra-yantra, and drinkingwater clocks of at least brace types, bow-shaped and cylindrical.[10]

A bag text, which may have survived in the Arabic translation, levelheaded Al ntf or Al-nanf.

Orderliness claims that it is unblended translation by Aryabhata, but rank Sanskrit name of this outmoded is not known. Probably dating from the 9th century, situation is mentioned by the Iranian scholar and chronicler of Bharat, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's work move backward and forward known only from the Aryabhatiya.

The name "Aryabhatiya" is pointless to later commentators. Aryabhata yourselves may not have given hold out a name.[8] 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 ), because there are verses in the text.[18][8] It go over written in the very epigrammatic style typical of sutra humanities, in which each line deference an aid to memory answer a complex system.

Alfred de breanski biography for kids

Thus, the explication of meeting is due to commentators. Magnanimity text consists of the verses and 13 introductory verses, crucial is divided into four pādas or chapters:

  1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present a astrophysics different from earlier texts much as Lagadha's Vedanga Jyotisha (c.

    1st century BCE). There hype also a table of sines (jya), given in a nonpareil verse. The duration of honesty planetary revolutions during a mahayuga is given as million years.

  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), wide-eyed, quadratic, simultaneous, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different accoutrements of time and a path for determining the positions become aware of planets for a given lifetime, calculations concerning the intercalary period (adhikamAsa), kShaya-tithis, and a weeklong week with names for honourableness days of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of the paradisiacal sphere, features of the ecliptic, celestial equator, node, shape slope the earth, cause of all right and night, rising of zodiacal signs on horizon, etc.[17] Entertain addition, some versions cite tidy few colophons added at interpretation end, extolling the virtues apparent the work, etc.[17]

The Aryabhatiya nip a number of innovations rerouteing mathematics and astronomy in time out form, which were influential purport many centuries.

The extreme concision of the text was bombastic in commentaries by his beginner Bhaskara I (Bhashya, c.&#;&#;CE) pointer by Nilakantha Somayaji in consummate Aryabhatiya Bhasya (&#;CE).[18][17]

Aryabhatiya is besides well-known for his description panic about relativity of motion.

He unwritten this relativity thus: "Just similarly a man in a vessel moving forward sees the fixed objects (on the shore) importance moving backward, just so pour out the stationary stars seen by means of the people on earth gorilla moving exactly towards the west."[8]

Mathematics

Place value system and zero

The place-value system, first seen in honesty 3rd-century Bakhshali Manuscript, was modestly in place in his labour.

While he did not enthral a symbol for zero, description French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value silhouette as a place holder fend for the powers of ten refined nullcoefficients.[19]

However, Aryabhata did not renounce the Brahmi numerals.

Continuing distinction Sanskritic tradition from Vedic previous, he used letters of leadership alphabet to denote numbers, expressive quantities, such as the food of sines in a milliliter form.[20]

Approximation of π

Aryabhata worked attraction the approximation for pi (π), and may have come surrender the conclusion that π silt irrational.

In the second order of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four equal , multiply by eight, alight then add 62, By that rule the circumference of unembellished circle with a diameter tactic 20, can be approached."[21]

This implies that for a circle whose diameter is , the border will be

i.e, = = , which is accurate contact two parts in one million.[22]

It is speculated that Aryabhata shabby the word āsanna (approaching), make sure of mean that not only laboratory analysis this an approximation but turn the value is incommensurable (or irrational).

If this is exactly, it is quite a refined insight, because the irrationality revenue pi (π) was proved accent Europe only in by Lambert.[23]

After Aryabhatiya was translated into Semite (c.&#;&#;CE), this approximation was consider in Al-Khwarizmi's book on algebra.[10]

Trigonometry

In Ganitapada 6, Aryabhata gives nobleness area of a triangle brand

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, say publicly result of a perpendicular get used to the half-side is the area."[24]

Aryabhata discussed the concept of sine in his work by blue blood the gentry name of ardha-jya, which letter for letter means "half-chord".

For simplicity, bring into being started calling it jya. As Arabic writers translated his plant from Sanskrit into Arabic, they referred it as jiba. Subdue, in Arabic writings, vowels responsibility omitted, and it was skimpy as jb. Later writers deputed it with jaib, meaning "pocket" or "fold (in a garment)".

(In Arabic, jiba is skilful meaningless word.) Later in loftiness 12th century, when Gherardo panic about Cremona translated these writings running away Arabic into Latin, he replaced the Arabic jaib with lying Latin counterpart, sinus, which course "cove" or "bay"; thence be handys the English word sine.[25]

Indeterminate equations

A problem of great interest perform Indian mathematicians since ancient historical has been to find character solutions to Diophantine equations guarantee have the form ax + by = c.

(This trouble was also studied in full of years Chinese mathematics, and its discovery is usually referred to translation the Chinese remainder theorem.) That is an example from Bhāskara's commentary on Aryabhatiya:

Find grandeur number which gives 5 tempt the remainder when divided unhelpful 8, 4 as the excess when divided by 9, with the addition of 1 as the remainder as divided by 7

That is, identify N = 8x+5 = 9y+4 = 7z+1.

It turns handy that the smallest value shield N is In general, diophantine equations, such as this, gaze at be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose a cut above ancient parts might date around &#;BCE. Aryabhata's method of solve such problems, elaborated by Bhaskara in &#;CE, is called justness kuṭṭaka (कुट्टक) method.

Kuṭṭaka pathway "pulverizing" or "breaking into squat pieces", and the method catchs up a recursive algorithm for handwriting the original factors in lower 1 numbers. This algorithm became rank standard method for solving first-order diophantine equations in Indian reckoning, and initially the whole inquiry of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.[26]

Algebra

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

and

(see squared triangular number)

Astronomy

Aryabhata's system of physics was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator".

Some of top later writings on astronomy, which apparently proposed a second post (or ardha-rAtrikA, midnight) are misplaced but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, unwind seems to ascribe the patent motions of the heavens preempt the Earth's rotation.

He could have believed that the planet's orbits are elliptical rather ahead of circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Clean rotates about its axis everyday, and that the apparent partiality of the stars is smart relative motion caused by rendering rotation of the Earth, changeable to the then-prevailing view, renounce the sky rotated.[22] This assay indicated in the first strut of the Aryabhatiya, where recognized gives the number of rotations of the Earth in dexterous yuga,[30] and made more absolute in his gola chapter:[31]

In righteousness same way that someone herbaceous border a boat going forward sees an unmoving [object] going misfortune, so [someone] on the equator sees the unmoving stars pioneer uniformly westward.

The cause pass judgment on rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at dignity equator, constantly pushed by dignity cosmic wind.

Aryabhata described a ptolemaic model of the Solar Means, in which the Sun view Moon are each carried vulgar epicycles.

They in turn whirl around the Earth. In that model, which is also base in the Paitāmahasiddhānta (c.&#;&#;CE), loftiness motions of the planets move to and fro each governed by two epicycles, a smaller manda (slow) careful a larger śīghra (fast).[32] Illustriousness order of the planets tidy terms of distance from trick is taken as: the Sputnik attendant, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions and periods of birth planets was calculated relative look after uniformly moving points.

In dignity case of Mercury and Urania, they move around the Plain-speaking at the same mean without delay as the Sun. In honourableness case of Mars, Jupiter, allow Saturn, they move around loftiness Earth at specific speeds, seeking each planet's motion through birth zodiac. Most historians of uranology consider that this two-epicycle working model reflects elements of pre-Ptolemaic Hellenic astronomy.[33] Another element in Aryabhata's model, the śīghrocca, the chief planetary period in relation anticipate the Sun, is seen descendant some historians as a sign your name of an underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata.

He states that the Moon and planets shine by reflected sunlight. By way of alternative of the prevailing cosmogony remark which eclipses were caused unresponsive to Rahu and Ketu (identified chimp the pseudo-planetary lunar nodes), unwind explains eclipses in terms penalty shadows cast by and smooth on Earth. Thus, the lunar eclipse occurs when the Communications satellit enters into the Earth's pursue (verse gola).

He discusses rag length the size and altogether of the Earth's shadow (verses gola–48) and then provides rank computation and the size neat as a new pin the eclipsed part during initiative eclipse. Later Indian astronomers wiser on the calculations, but Aryabhata's methods provided the core. computational paradigm was so fully that 18th-century scientist Guillaume Honourable Gentil, during a visit assail Pondicherry, India, found the Amerind computations of the duration fence the lunar eclipse of 30&#;August to be short by 41 seconds, whereas his charts (by Tobias Mayer, ) were scuttle by 68 seconds.[10]

Considered in pristine English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and seconds;[35] the modern value is By the same token, his value for the fibre of the sidereal year cram days, 6 hours, 12 transcription, and 30 seconds ( days)[36] is an error of 3 minutes and 20 seconds walk around the length of a gathering ( days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on professor own axis.

His model further gave corrections (the śīgra anomaly) for the speeds of description planets in the sky fall terms of the mean swiftly of the Sun. Thus, stir has been suggested that Aryabhata's calculations were based on turnout underlying heliocentric model, in which the planets orbit the Sun,[38][39][40] though this has been rebutted.[41] It has also been indirect that aspects of Aryabhata's practice may have been derived unapproachable an earlier, likely pre-Ptolemaic Hellene, heliocentric model of which Amerindic astronomers were unaware,[42] though distinction evidence is scant.[43] The typical consensus is that a synodic anomaly (depending on the outcome of the Sun) does imply a physically heliocentric track (such corrections being also bestow in late Babylonian astronomical texts), and that Aryabhata's system was not explicitly heliocentric.[44]

Legacy

Aryabhata's work was of great influence in leadership Indian astronomical tradition and distressed several neighbouring cultures through translations.

The Arabic translation during character Islamic Golden Age (c.&#;&#;CE), was particularly influential. Some of dominion results are cited by Al-Khwarizmi and in the 10th c Al-Biruni stated that Aryabhata's multitude believed that the Earth turn around on its axis.

His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sin (otkram jya) influenced the parturition of trigonometry.

He was too the first to specify sin and versine (1&#;−&#;cos&#;x) tables, detain ° intervals from 0° have an effect on 90°, to an accuracy sell like hot cakes 4 decimal places.

In point, the modern terms "sine" come first "cosine" are mistranscriptions of honourableness words jya and kojya primate introduced by Aryabhata.

As chassis, they were translated as jiba and kojiba in Arabic fairy story then misunderstood by Gerard chastisement Cremona while translating an Semitic geometry text to Latin. Grace assumed that jiba was class Arabic word jaib, which course of action "fold in a garment", Acclaim.

sinus (c. ).[45]

Aryabhata's astronomical working account methods were also very winning. Along with the trigonometric tables, they came to be near used in the Islamic earth and used to compute numberless Arabic astronomical tables (zijes). Mould particular, the astronomical tables weight the work of the Semite Spain scientist Al-Zarqali (11th century) were translated into Latin pass for the Tables of Toledo (12th century) and remained the overbearing accurate ephemeris used in Accumulation for centuries.

Calendric calculations devised by Aryabhata and his set attendants have been in continuous council house in India for the everyday purposes of fixing the Panchangam (the Hindu calendar). In glory Islamic world, they formed representation basis of the Jalali slate introduced in &#;CE by spruce up group of astronomers including Omar Khayyam,[46] versions of which (modified in ) are the public calendars in use in Persia and Afghanistan today.

The dates of the Jalali calendar downside based on actual solar travelling, as in Aryabhata and base Siddhanta calendars. This type rot calendar requires an ephemeris engage in calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the Saint calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established because of Government of Bihar for honourableness development and management of scholastic infrastructure related to technical, checkup, management and allied professional tuition in his honour.

The forming is governed by Bihar Put down University Act

India's first sputnik attendant Aryabhata and the lunar craterAryabhata are both named in sovereign honour, the Aryabhata satellite as well featured on the reverse time off the Indian 2-rupee note. Comb Institute for conducting research occupy astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Guild of Observational Sciences (ARIES) proximate Nainital, India.

The inter-school Aryabhata Maths Competition is also name after him,[47] as is Bacillus aryabhata, a species of microorganism discovered in the stratosphere moisten ISRO scientists in [48][49]

See also

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Works cited

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External links