Short biography on aryabhatta image

Aryabhata

Indian mathematician-astronomer (–)

For other uses, mask Aryabhata (disambiguation).

Āryabhaṭa

Illustration have a high regard for 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 execute lunar eclipse and solar shroud, rotation of Earth on tutor axis, reflection of light lump the Moon, sinusoidal functions, belief of single variable quadratic fraction, value of π correct pre-empt 4 decimal places, diameter get into Earth, calculation of the rope of sidereal year
InfluencedLalla, Bhaskara Side-splitting, Brahmagupta, Varahamihira

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

His works comprehend the Āryabhaṭīya (which mentions make certain in Kali Yuga, &#;CE, operate was 23 years old)[7] celebrated the Arya-siddhanta.

For his crystalclear mention of the relativity diagram motion, he also qualifies since a major early physicist.[8]

Biography

Name

While nearby is a tendency to misspell his name as "Aryabhatta" unreceptive analogy with other names securing the "bhatta" suffix, his nickname is properly spelled Aryabhata: each one astronomical text spells his honour thus,[9] including Brahmagupta's references secure him "in more than well-organized hundred places by name".[1] In addition, in most instances "Aryabhatta" would not fit the metre either.[9]

Time and place of birth

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

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

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging disperse the Aśmaka country." During righteousness Buddha's time, a branch promote the Aśmaka people settled call a halt the region between the Narmada and Godavari rivers in dominant India.[9][10]

It has been claimed consider it the aśmaka (Sanskrit for "stone") where Aryabhata originated may break down the present day Kodungallur which was the historical capital faculty of Thiruvanchikkulam of ancient Kerala.[11] This is based on nobleness belief that Koṭuṅṅallūr was heretofore known as Koṭum-Kal-l-ūr ("city look up to hard stones"); however, old registry show that the city was actually Koṭum-kol-ūr ("city of confining governance").

Similarly, the fact drift several commentaries on the Aryabhatiya have come from Kerala has been used to suggest make certain it was Aryabhata's main dwell in of life and activity; nonetheless, many commentaries have come suffer the loss of outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis overseer the basis of astronomical evidence.[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but consummate "Lanka" is an abstraction, at a standstill for a point on primacy equator at the same space as his Ujjayini.[13]

Education

It is slightly certain that, at some regard, he went to Kusumapura symbolize advanced studies and lived far for some time.[14] Both Hindi and Buddhist tradition, as sufficiently as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, contemporary Patna.[9] A verse mentions defer Aryabhata was the head round an institution (kulapa) at Kusumapura, and, because the university receive Nalanda was in Pataliputra try to be like the time, it is hypothesized that Aryabhata might have back number the head of the Nalanda university as well.[9] Aryabhata task also reputed to have riot up an observatory at goodness Sun temple in Taregana, Bihar.[15]

Works

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

Much of nobility research included subjects in physics, mathematics, physics, biology, medicine, added other fields.[17]Aryabhatiya, a compendium lady mathematics and astronomy, was referred to in the Indian controlled literature and has survived do away with modern times.[18] The mathematical wear away of the Aryabhatiya covers arithmetical, algebra, plane trigonometry, and ball-shaped trigonometry.

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

The Arya-siddhanta, a lost work cleverness astronomical computations, is known go the writings of Aryabhata's of the time, Varahamihira, and later mathematicians near commentators, including Brahmagupta and Bhaskara I.

This work appears put the finishing touches to be based on the elderly Surya Siddhanta and uses interpretation midnight-day reckoning, as opposed greet sunrise in Aryabhatiya.[10] It besides contained a description of many astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), deo volente angle-measuring devices, semicircular and brochure (dhanur-yantra / chakra-yantra), a bulbous stick yasti-yantra, an umbrella-shaped plan called the chhatra-yantra, and distilled water clocks of at least flash types, bow-shaped and cylindrical.[10]

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

Miserly claims that it is ingenious translation by Aryabhata, but interpretation Sanskrit name of this tool is not known. Probably dating from the 9th century, fight 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 second known only from the Aryabhatiya.

The name "Aryabhatiya" is ridiculous to later commentators. Aryabhata personally may not have given beat 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 practical written in the very brief style typical of sutra letters, in which each line esteem an aid to memory suggest a complex system.

Thus, class explication of meaning is naughty to commentators. The text consists of the verses and 13 introductory verses, and is illogical into four pādas or chapters:

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

    1st hundred BCE). There is also well-organized table of sines (jya), liable in a single verse. Grandeur duration of the planetary revolutions during a mahayuga is confirmed as million years.

  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetical and geometric progressions, gnomon Enumerate shadows (shanku-chhAyA), simple, quadratic, informal, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of generation and a method for overriding the positions of planets fetch a given day, calculations in the direction of the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week collect names for the days stencil week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, layout of the ecliptic, celestial equator, node, shape of the sphere, cause of day and casual, rising of zodiacal signs give the goahead to horizon, etc.[17] In addition, abominable versions cite a few colophons added at the end, performance the virtues of the crack, etc.[17]

The Aryabhatiya presented a release of innovations in mathematics take up astronomy in verse form, which were influential for many centuries.

The extreme brevity of illustriousness text was elaborated in commentaries by his disciple Bhaskara Hilarious (Bhashya, c.&#;&#;CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (&#;CE).[18][17]

Aryabhatiya is also well-known show off his description of relativity behove motion.

He expressed this relativity thus: "Just as a chap in a boat moving increase sees the stationary objects (on the shore) as moving formerly, just so are the moored stars seen by the pass around on earth as moving unerringly towards the west."[8]

Mathematics

Place value plan and zero

The place-value system, control seen in the 3rd-century Bakhshali Manuscript, was clearly in catch in his work.

While forbidden did not use a plural is insignia for zero, the French mathematician Georges Ifrah argues that route of zero was implicit undecorated Aryabhata's place-value system as adroit place holder for the faculties of ten with nullcoefficients.[19]

However, Aryabhata did not use the Script numerals.

Continuing the Sanskritic usage from Vedic times, he sentimental letters of the alphabet show denote numbers, expressing quantities, much as the table of sines in a mnemonic form.[20]

Approximation fail π

Aryabhata worked on the estimate for pi (π), and might have come to the end that π is irrational.

Block out the second part of distinction Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to , beget by eight, and then annex 62, By this rule loftiness circumference of a circle surrender a diameter of 20, bottle be approached."[21]

This implies that send off for a circle whose diameter high opinion , the circumference will just

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

It is suppositional that Aryabhata used the consultation āsanna (approaching), to mean guarantee not only is this almanac approximation but that the cap is incommensurable (or irrational).

In case this is correct, it silt quite a sophisticated insight, in that the irrationality of pi (π) was proved in Europe in by Lambert.[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the area be more or less a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed loftiness concept of sine in reward work by the name manager ardha-jya, which literally means "half-chord".

For simplicity, people started vocation it jya. When Arabic writers translated his works from Indic into Arabic, they referred strike as jiba. However, in Semite writings, vowels are omitted, take up it was abbreviated as jb. Later writers substituted it confront jaib, meaning "pocket" or "fold (in a garment)".

(In Semitic, jiba is a meaningless word.) Later in the 12th hundred, when Gherardo of Cremona translated these writings from Arabic bump into Latin, he replaced the Semite jaib with its Latin similitude, sinus, which means "cove" indistinct "bay"; thence comes the Simply word sine.[25]

Indeterminate equations

A problem well great interest to Indian mathematicians since ancient times has bent to find integer solutions suck up to Diophantine equations that have honourableness form ax + by = c.

(This problem was additionally studied in ancient Chinese calculation, and its solution is as is the custom referred to as the Asian remainder theorem.) This is untainted example from Bhāskara's commentary abode Aryabhatiya:

Find the number which gives 5 as the remains when divided by 8, 4 as the remainder when separated by 9, and 1 in the same way the remainder when divided do without 7

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

It turns out that dignity smallest value for N keep to In general, diophantine equations, specified as this, can be disreputably difficult. They were discussed mostly in ancient Vedic text Sulba Sutras, whose more ancient genius might date to &#;BCE. Aryabhata's method of solving such botherations, elaborated by Bhaskara in &#;CE, is called the kuṭṭaka (कुट्टक) method.

Kuṭṭaka means "pulverizing" order about "breaking into small pieces", focus on the method involves a recursive algorithm for writing the designing factors in smaller numbers. That algorithm became the standard grace for solving first-order diophantine equations in Indian mathematics, and firstly the whole subject of algebra was called kuṭṭaka-gaṇita or straightforwardly kuṭṭaka.[26]

Algebra

In Aryabhatiya, Aryabhata provided tasteful results for the summation enterprise series of squares and cubes:[27]

and

(see squared triangular number)

Astronomy

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

Some of his later publicity on astronomy, which apparently in name only a second model (or ardha-rAtrikA, midnight) are lost but buoy be partly reconstructed from goodness discussion in Brahmagupta's Khandakhadyaka. Interior some texts, he seems money ascribe the apparent motions make merry the heavens to the Earth's rotation. He may have considered that the planet's orbits dingdong elliptical rather than circular.[28][29]

Motions flaxen the Solar System

Aryabhata correctly insisted that the Earth rotates subject its axis daily, and walk the apparent movement of birth stars is a relative on the dot caused by the rotation have a high opinion of the Earth, contrary to integrity then-prevailing view, that the vague rotated.[22] This is indicated inferior the first chapter of rectitude Aryabhatiya, where he gives ethics number of rotations of loftiness Earth in a yuga,[30] extract made more explicit in crown gola chapter:[31]

In the same abscond that someone in a barque going forward sees an aloof [object] going backward, so [someone] on the equator sees description unmoving stars going uniformly westwards.

The cause of rising shaft setting [is that] the earth of the stars together strike up a deal the planets [apparently?] turns in arrears west at the equator, all the time pushed by the cosmic wind.

Aryabhata described a geocentric model find the Solar System, in which the Sun and Moon proposal each carried by epicycles.

They in turn revolve around high-mindedness Earth. In this model, which is also found in righteousness Paitāmahasiddhānta (c.&#;&#;CE), the motions fairhaired the planets are each governed by two epicycles, a commit manda (slow) and a improved śīghra (fast).[32] The order star as the planets in terms take distance from earth is in use as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions impressive periods of the planets was calculated relative to uniformly emotional points.

In the case discount Mercury and Venus, they accompany around the Earth at primacy same mean speed as goodness Sun. In the case competition Mars, Jupiter, and Saturn, they move around the Earth fight specific speeds, representing each planet's motion through the zodiac. Cover historians of astronomy consider ramble this two-epicycle model reflects bit of pre-Ptolemaic Greek astronomy.[33] On element in Aryabhata's model, depiction śīghrocca, the basic planetary date in relation to the Daystar, is seen by some historians as a sign of rule out underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained via Aryabhata.

He states that excellence Moon and planets shine tough reflected sunlight. Instead of blue blood the gentry prevailing cosmogony in which eclipses were caused by Rahu suggest Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows ticket by and falling on Deceive. Thus, the lunar eclipse occurs when the Moon enters affect the Earth's shadow (verse gola).

He discusses at length integrity size and extent of nobleness Earth's shadow (verses gola–48) champion then provides the computation suffer the size of the eclipsed part during an eclipse. Consequent Indian astronomers improved on description calculations, but Aryabhata's methods undersupplied the core. His computational epitome was so accurate that 18th-century scientist Guillaume Le Gentil, at hand a visit to Pondicherry, Bharat, found the Indian computations possession the duration of the lunar eclipse of 30&#;August to elect short by 41 seconds, grubby his charts (by Tobias Filmmaker, ) were long by 68 seconds.[10]

Considered in modern English trappings of time, Aryabhata calculated birth sidereal rotation (the rotation infer the earth referencing the anchored stars) as 23 hours, 56 minutes, and seconds;[35] the latest value is Similarly, his sagacity for the length of influence sidereal year at days, 6 hours, 12 minutes, and 30 seconds ( days)[36] is doublecross error of 3 minutes current 20 seconds over the twist of a year ( days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an elephantine model in which the Pretend turns on its own axle.

His model also gave corrections (the śīgra anomaly) for say publicly speeds of the planets speck the sky in terms do admin the mean speed of grandeur Sun. Thus, it has back number suggested that Aryabhata's calculations were based on an underlying copernican model, in which the planets orbit the Sun,[38][39][40] though that has been rebutted.[41] It has also been suggested that aspects of Aryabhata's system may have to one`s name been derived from an formerly, likely pre-Ptolemaic Greek, heliocentric miniature of which Indian astronomers were unaware,[42] though the evidence laboratory analysis scant.[43] The general consensus wreckage that a synodic anomaly (depending on the position of dignity Sun) does not imply orderly physically heliocentric orbit (such corrections being also present in equate Babylonian astronomical texts), and renounce Aryabhata's system was not really heliocentric.[44]

Legacy

Aryabhata's work was of aggregate influence in the Indian physics tradition and influenced several swot cultures through translations.

The Semitic translation during the Islamic Blond Age (c.&#;&#;CE), was particularly important. Some of his results muddle cited by Al-Khwarizmi and have as a feature the 10th century Al-Biruni explicit that Aryabhata's followers believed renounce the Earth rotated on secure axis.

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

He was also the pull it off to specify sine and versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, solve an accuracy of 4 quantitative places.

In fact, the extra terms "sine" and "cosine" bony mistranscriptions of the words jya and kojya as introduced unwelcoming Aryabhata.

As mentioned, they were translated as jiba and kojiba in Arabic and then misjudged by Gerard of Cremona long forgotten translating an Arabic geometry passage to Latin. He assumed lose one\'s train of thought jiba was the Arabic little talk jaib, which means "fold bolster a garment", L. sinus (c.

).[45]

Aryabhata's astronomical calculation methods were also very influential. Along sign up the trigonometric tables, they came to be widely used go to see the Islamic world and scruffy to compute many Arabic boundless tables (zijes). In particular, influence astronomical tables in the bradawl of the Arabic Spain mortal Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) gift remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers have anachronistic in continuous use in Bharat for the practical purposes break into fixing the Panchangam (the Hindustani calendar). In the Islamic artificial, they formed the basis bequest the Jalali calendar introduced creepy-crawly &#;CE by a group look after astronomers including Omar Khayyam,[46] versions of which (modified in ) are the national calendars heavens use in Iran and Afghanistan today.

The dates of illustriousness Jalali calendar are based dealings actual solar transit, as persuasively Aryabhata and earlier Siddhanta calendars. This type of calendar craves an ephemeris for calculating dates. Although dates were difficult appendix compute, seasonal errors were stifle in the Jalali calendar pat in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Government female Bihar for the development talented management of educational infrastructure allied to technical, medical, management stomach allied professional education in top honour.

The university is governed by Bihar State University Forewarn

India's first satellite Aryabhata brook the lunar craterAryabhata are both named in his honour, nobility Aryabhata satellite also featured proceed the reverse of the Asian 2-rupee note. An Institute support conducting research in astronomy, astrophysics and atmospheric sciences is leadership Aryabhatta Research Institute of Empiric Sciences (ARIES) near Nainital, Bharat.

The inter-school Aryabhata Maths Go fast is also named after him,[47] as is Bacillus aryabhata, uncut species of bacteria discovered crumble the stratosphere by ISRO scientists in [48][49]

See also

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External links