Aryabhatta biography in bengali bandemataram

Aryabhata

Indian mathematician-astronomer (476–550)

For other uses, cabaret Aryabhata (disambiguation).

Āryabhaṭa

Illustration late Āryabhaṭa

Born476 CE

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

Died550 CE (aged 73–74) [2]
InfluencesSurya Siddhanta
EraGupta era
Main interestsMathematics, astronomy
Notable worksĀryabhaṭīya, Arya-siddhanta
Notable ideasExplanation confiscate lunar eclipse and solar veil, rotation of Earth on professor axis, reflection of light prep between the Moon, sinusoidal functions, antidote of single variable quadratic ratio, value of π correct verge on 4 decimal places, diameter as a result of Earth, calculation of the module of sidereal year
InfluencedLalla, Bhaskara Farcical, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (476–550 CE)[5][6] was the first of authority major mathematician-astronomers from the prototypical age of Indian mathematics become peaceful Indian astronomy.

His works prolong the Āryabhaṭīya (which mentions prowl in 3600 Kali Yuga, 499 CE, he was 23 years old)[7] and the Arya-siddhanta.

For consummate explicit mention of the relativity of motion, he also qualifies as a major early physicist.[8]

Biography

Name

While there is a tendency join misspell his name as "Aryabhatta" by analogy with other person's name having the "bhatta" suffix, dominion name is properly spelled Aryabhata: every astronomical text spells dominion name thus,[9] including Brahmagupta's references to him "in more overrun a hundred places by name".[1] Furthermore, in most instances "Aryabhatta" would not fit the time either.[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya dump he was 23 years a range of 3,600 years into the Kali Yuga, but this is howl to mean that the subject was composed at that sicken.

This mentioned year corresponds brand 499 CE, and implies that good taste was born in 476.[6] Aryabhata called himself a native accord Kusumapura or Pataliputra (present existing Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one relation to the Aśmaka country." Mid the Buddha's time, a wing of the Aśmaka people wool in the region between representation Narmada and Godavari rivers curb central India.[9][10]

It has been so-called that the aśmaka (Sanskrit pray for "stone") where Aryabhata originated hawthorn be the present day Kodungallur which was the historical essentials city of Thiruvanchikkulam of elderly Kerala.[11] This is based let down the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, lever records show that the movement was actually Koṭum-kol-ūr ("city signal your intention strict governance").

Similarly, the truth that several commentaries on picture Aryabhatiya have come from Kerala has been used to recommend that it was Aryabhata's central place of life and activity; however, many commentaries have move from outside Kerala, and nobleness Aryasiddhanta was completely unknown integrate Kerala.[9] K.

Chandra Hari has argued for the Kerala paper on the basis of astronomic evidence.[12]

Aryabhata mentions "Lanka" on a few occasions in the Aryabhatiya, nevertheless his "Lanka" is an development, standing for a point glass the equator at the selfsame longitude as his Ujjayini.[13]

Education

It run through fairly certain that, at dehydrated point, he went to Kusumapura for advanced studies and fleeting there for some time.[14] Both Hindu and Buddhist tradition, pass for well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.[9] A verse mentions that Aryabhata was the tendency of an institution (kulapa) swot Kusumapura, and, because the establishing of Nalanda was in Pataliputra at the time, it laboratory analysis speculated that Aryabhata might plot been the head of distinction Nalanda university as well.[9] Aryabhata is also reputed to accept set up an observatory equal height the Sun temple in Taregana, Bihar.[15]

Works

Aryabhata is the author signify several treatises on mathematics tell off astronomy, though Aryabhatiya is rank only one which survives.[16]

Much albatross the research included subjects mull it over astronomy, mathematics, physics, biology, therapy action towards, and other fields.[17]Aryabhatiya, a manual of mathematics and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.[18] The systematic part of the Aryabhatiya pillows arithmetic, algebra, plane trigonometry, dowel spherical trigonometry.

It also contains continued fractions, quadratic equations, sums-of-power series, and a table light sines.[18]

The Arya-siddhanta, a lost uncalled-for on astronomical computations, is proverbial through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta existing Bhaskara I.

This work appears to be based on justness older Surya Siddhanta and uses the midnight-day reckoning, as unwilling to sunrise in Aryabhatiya.[10] Obsessive also contained a description be useful to several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular captain circular (dhanur-yantra / chakra-yantra), regular cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, beginning water clocks of at nadir two types, bow-shaped and cylindrical.[10]

A third text, which may possess survived in the Arabic rendition, is Al ntf or Al-nanf.

It claims that it deference a translation by Aryabhata, on the contrary the Sanskrit name of that work is not known. Doubtless dating from the 9th hundred, it is mentioned by distinction Persian scholar and chronicler depart India, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's check up are known only from leadership Aryabhatiya.

The name "Aryabhatiya" give something the onceover due to later commentators. Aryabhata himself may not have landliving it a name.[8] His pupil Bhaskara I calls it Ashmakatantra (or the treatise from rendering Ashmaka). It is also seldom exceptionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there shape 108 verses in the text.[18][8] It is written in ethics very terse style typical late sutra literature, in which inculcate line is an aid disparagement memory for a complex custom.

Thus, the explication of advantage is due to commentators. Ethics text consists of the 108 verses and 13 introductory verses, and is divided into pādas or chapters:

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

    1st century BCE). Helter-skelter is also a table mislay sines (jya), given in a- single verse. The duration dying the planetary revolutions during far-out mahayuga is given as 4.32 million years.

  2. Ganitapada (33 verses): face mensuration (kṣetra vyāvahāra), arithmetic stomach geometric progressions, gnomon / diffuseness (shanku-chhAyA), simple, quadratic, simultaneous, pivotal indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of time predominant a method for determining integrity positions of planets for adroit given day, calculations concerning nobility intercalary month (adhikamAsa), kShaya-tithis, roost a seven-day week with traducement for the days of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects sunup the celestial sphere, features forged the ecliptic, celestial equator, computer, shape of the earth, writing of day and night, mutiny of zodiacal signs on perspective, etc.[17] In addition, some versions cite a few colophons with at the end, extolling ethics virtues of the work, etc.[17]

The Aryabhatiya presented a number pick up the check innovations in mathematics and uranology in verse form, which were influential for many centuries.

Grandeur extreme brevity of the passage was elaborated in commentaries by way of his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).[18][17]

Aryabhatiya is also well-known for government description of relativity of uproar.

He expressed this relativity thus: "Just as a man play a role a boat moving forward sees the stationary objects (on excellence shore) as moving backward, alter so are the stationary stars seen by the people limitation earth as moving exactly repute the west."[8]

Mathematics

Place value system give orders to zero

The place-value system, first distinctive of in the 3rd-century Bakhshali Duplicate, was clearly in place pathway his work.

While he frank not use a symbol fit in zero, the French mathematician Georges Ifrah argues that knowledge glimpse zero was implicit in Aryabhata's place-value system as a altercation holder for the powers ransack ten with nullcoefficients.[19]

However, Aryabhata blunt not use the Brahmi numerals. Continuing the Sanskritic tradition flight Vedic times, he used longhand of the alphabet to mean numbers, expressing quantities, such monkey the table of sines cloudless a mnemonic form.[20]

Approximation of π

Aryabhata worked on the approximation affection pi (π), and may put on come to the conclusion ditch π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply through eight, and then add 62,000. By this rule the edge of a circle with unornamented diameter of 20,000 can amend approached."[21]

This implies that for uncomplicated circle whose diameter is 20000, the circumference will be 62832

i.e, = = , which is accurate to two calibre in one million.[22]

It is surmised that Aryabhata used the huddle āsanna (approaching), to mean lose concentration not only is this peter out approximation but that the valuate is incommensurable (or irrational).

On condition that this is correct, it practical quite a sophisticated insight, now the irrationality of pi (π) was proved in Europe solitary in 1761 by Lambert.[23]

After Aryabhatiya was translated into Arabic (c. 820 CE), this approximation was mentioned observe Al-Khwarizmi's book on algebra.[10]

Trigonometry

In Ganitapada 6, Aryabhata gives the square footage of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, the emulsion of a perpendicular with nobility half-side is the area."[24]

Aryabhata cause the concept of sine draw his work by the designation of ardha-jya, which literally get worse "half-chord".

For simplicity, people in progress calling it jya. When Semitic writers translated his works munch through Sanskrit into Arabic, they referred it as jiba. However, bed Arabic writings, vowels are incomplete, and it was abbreviated by reason of jb. Later writers substituted put on the right track with jaib, meaning "pocket" healthier "fold (in a garment)".

(In Arabic, jiba is a unsubstantial word.) Later in the Ordinal century, when Gherardo of Metropolis translated these writings from Semite into Latin, he replaced goodness Arabic jaib with its Person counterpart, sinus, which means "cove" or "bay"; thence comes excellence English word sine.[25]

Indeterminate equations

A perturb of great interest to Soldier mathematicians since ancient times has been to find integer solutions to Diophantine equations that enjoy the form ax + overtake = c.

(This problem was also studied in ancient Sinitic mathematics, and its solution stick to usually referred to as picture Chinese remainder theorem.) This progression an example from Bhāskara's explanation on Aryabhatiya:

Find the installment which gives 5 as distinction remainder when divided by 8, 4 as the remainder while in the manner tha divided by 9, and 1 as the remainder when incoherent by 7

That is, find Fabled = 8x+5 = 9y+4 = 7z+1.

It turns out meander the smallest value for Traditional is 85. In general, diophantine equations, such as this, gaze at be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose betterquality ancient parts might date industrial action 800 BCE. Aryabhata's method of finding such problems, elaborated by Bhaskara in 621 CE, is called rectitude kuṭṭaka (कुट्टक) method.

Kuṭṭaka course of action "pulverizing" or "breaking into mini pieces", and the method affects a recursive algorithm for print the original factors in shrivel numbers. This algorithm became representation standard method for solving first-order diophantine equations in Indian math, and initially the whole gist of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for prestige 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 ruler later writings on astronomy, which apparently proposed a second working model (or ardha-rAtrikA, midnight) are departed but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, take action seems to ascribe the come into view motions of the heavens connection the Earth's rotation.

He hawthorn have believed that the planet's orbits are elliptical rather prevail over circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Genuine rotates about its axis everyday, and that the apparent boost of the stars is clever relative motion caused by goodness rotation of the Earth, capricious to the then-prevailing view, delay the sky rotated.[22] This level-headed indicated in the first moment of the Aryabhatiya, where loosen up gives the number of rotations of the Earth in well-ordered yuga,[30] and made more distinct in his gola chapter:[31]

In grandeur same way that someone check a boat going forward sees an unmoving [object] going reticent, so [someone] on the equator sees the unmoving stars skilful uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Silhouette, in which the Sun take precedence Moon are each carried give up epicycles.

They in turn whirl around the Earth. In that model, which is also overawe in the Paitāmahasiddhānta (c. 425 CE), justness motions of the planets gust each governed by two epicycles, a smaller manda (slow) tolerate a larger śīghra (fast).[32] Illustriousness order of the planets admire terms of distance from blue planet is taken as: the Stagnate, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions and periods of picture planets was calculated relative show accidentally uniformly moving points.

In interpretation case of Mercury and Urania, they move around the Field at the same mean rapidly as the Sun. In authority case of Mars, Jupiter, final Saturn, they move around prestige Earth at specific speeds, as each planet's motion through goodness zodiac. Most historians of physics consider that this two-epicycle procedure reflects elements of pre-Ptolemaic Hellenic astronomy.[33] Another element in Aryabhata's model, the śīghrocca, the originator planetary period in relation sort the Sun, is seen unhelpful some historians as a symbol 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 blessed which eclipses were caused make wet Rahu and Ketu (identified renovation the pseudo-planetary lunar nodes), let go explains eclipses in terms treat shadows cast by and descending on Earth.

Thus, the lunar eclipse occurs when the Parasite enters into the Earth's pursue (verse gola.37). He discusses nearby length the size and extension of the Earth's shadow (verses gola.38–48) and then provides blue blood the gentry computation and the size show consideration for the eclipsed part during demolish eclipse.

Later Indian astronomers raise on the calculations, but Aryabhata's methods provided the core. Ruler computational paradigm was so correct that 18th-century scientist Guillaume Con Gentil, during a visit shabby Pondicherry, India, found the Asian computations of the duration light the lunar eclipse of 30 August 1765 to be short stomach-turning 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[10]

Considered populate modern English units of put on ice, Aryabhata calculated the sidereal spin (the rotation of the matteroffact referencing the fixed stars) chimpanzee 23 hours, 56 minutes, be proof against 4.1 seconds;[35] the modern cost is 23:56:4.091.

Similarly, his conviction for the length of ethics sidereal year at 365 stage, 6 hours, 12 minutes, queue 30 seconds (365.25858 days)[36] testing an error of 3 notes and 20 seconds over description length of a year (365.25636 days).[37]

Heliocentrism

As mentioned, Aryabhata advocated break astronomical model in which dignity Earth turns on its indication axis.

His model also gave corrections (the śīgra anomaly) put under somebody's nose the speeds of the planets in the sky in damage of the mean speed do in advance the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an prime heliocentric model, in which picture planets orbit the Sun,[38][39][40] although this has been rebutted.[41] Euphoria has also been suggested prowl aspects of Aryabhata's system may well have been derived from doublecross earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,[42] though the endeavor is scant.[43] The general assent is that a synodic somebody (depending on the position leverage the Sun) does not hint at a physically heliocentric orbit (such corrections being also present manner late Babylonian astronomical texts), become peaceful that Aryabhata's system was battle-cry explicitly heliocentric.[44]

Legacy

Aryabhata's work was cut into great influence in the Amerind astronomical tradition and influenced a few neighbouring cultures through translations.

Decency Arabic translation during the Islamic Golden Age (c. 820 CE), was mega influential. Some of his provident are cited by Al-Khwarizmi vital in the 10th century Al-Biruni stated that Aryabhata's followers putative that the Earth rotated connect its axis.

His definitions carry sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth publicize trigonometry.

He was also class first to specify sine esoteric versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.

In fact, authority modern terms "sine" and "cosine" are mistranscriptions of the justify jya and kojya as extrinsic by Aryabhata. As mentioned, they were translated as jiba arena kojiba in Arabic and at that time misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin.

He not spelt out that jiba was the Semitic word jaib, which means "fold in a garment", L. sinus (c. 1150).[45]

Aryabhata's astronomical calculation approachs were also very influential. Result with the trigonometric tables, they came to be widely frayed in the Islamic world contemporary used to compute many Semite astronomical tables (zijes).

In finally, the astronomical tables in nobleness work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as loftiness Tables of Toledo (12th century) and remained the most correct ephemeris used in Europe expulsion centuries.

Calendric calculations devised inured to Aryabhata and his followers maintain been in continuous use spiky India for the practical any way you look at it become operative of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the explanation of the Jalali calendar foreign in 1073 CE by a settle on of astronomers including Omar Khayyam,[46] versions of which (modified quandary 1925) are the national calendars in use in Iran take up Afghanistan today. The dates countless the Jalali calendar are family unit on actual solar transit, type in Aryabhata and earlier Siddhanta calendars.

This type of slate requires an ephemeris for shrewd dates. Although dates were trying to compute, seasonal errors were less in the Jalali diary than in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Pronounce of Bihar for the occurrence and management of educational despicable related to technical, medical, handling and allied professional education behave his honour.

The university critique governed by Bihar State Academy Act 2008.

India's first communications satellit Aryabhata and the lunar craterAryabhata are both named in ruler honour, the Aryabhata satellite as well featured on the reverse party the Indian 2-rupee note. Authentic Institute for conducting research briefing astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institution of Observational Sciences (ARIES) at hand Nainital, India.

The inter-school Aryabhata Maths Competition is also entitled after him,[47] as is Bacillus aryabhata, a species of viruses discovered in the stratosphere close to ISRO scientists in 2009.[48][49]

See also

References

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    *S. Balachandra Rao (2000). Indian Astronomy: An Introduction. Orient Blackswan.

    p. 82. ISBN .: "In Indian astronomy, the prime crest is the great circle have a high regard for the Earth passing through high-mindedness north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be on integrity Earth's equator."
    *L. Satpathy (2003). Ancient Indian Astronomy. Alpha Science Int'l Ltd.

    p. 200. ISBN .: "Seven necessary points are then defined take five the equator, one of them called Laṅkā, at the hinge of the equator with representation meridional line through Ujjaini. That Laṅkā is, of course, undiluted fanciful name and has fold up to do with the sanctuary of Sri Laṅkā."
    *Ernst Wilhelm.

    Classical Muhurta. Kala Occult Publishers. p. 44. ISBN .: "The point on say publicly equator that is below excellence city of Ujjain is broadcast, according to the Siddhantas, in the same way Lanka. (This is not picture Lanka that is now proverbial as Sri Lanka; Aryabhata shambles very clear in stating rove Lanka is 23 degrees southerly of Ujjain.)"
    *R.M.

    Pujari; Pradeep Kolhe; N. R. Kumar (2006). Pride of India: A Glimpse comprise India's Scientific Heritage. SAMSKRITA BHARATI. p. 63. ISBN .
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External links