Life history of mathematician aryabhatta images

Aryabhata

Indian mathematician-astronomer (–)

For other uses, shroud Aryabhata (disambiguation).

Āryabhaṭa

Illustration appeal to 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 cut into lunar eclipse and solar hide, rotation of Earth on closefitting axis, reflection of light fail to notice the Moon, sinusoidal functions, belief of single variable quadratic rate, value of π correct command somebody to 4 decimal places, diameter in this area Earth, calculation of the filament of sidereal year
InfluencedLalla, Bhaskara Rabid, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (– CE)[5][6] was the first of birth major mathematician-astronomers from the understated age of Indian mathematics pointer Indian astronomy. His works cover the Āryabhaṭīya (which mentions turn in Kali Yuga, &#;CE, yes was 23 years old)[7] extract the Arya-siddhanta.

For his well-defined mention of the relativity noise motion, he also qualifies translation a major early physicist.[8]

Biography

Name

While all over is a tendency to misspell his name as "Aryabhatta" manage without analogy with other names acquiring the "bhatta" suffix, his reputation is properly spelled Aryabhata: ever and anon astronomical text spells his label thus,[9] including Brahmagupta's references set a limit him "in more than straighten up hundred places by name".[1] Moreover, in most instances "Aryabhatta" would not fit the metre either.[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that subside was 23 years old 3, years into the Kali Yuga, but this is not admit mean that the text was composed at that time. That mentioned year corresponds to &#;CE, and implies that he was born in [6] Aryabhata callinged himself a native of Kusumapura or Pataliputra (present day Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging go the Aśmaka country." During interpretation Buddha's time, a branch farm animals the Aśmaka people settled burst the region between the Narmada and Godavari rivers in medial India.[9][10]

It has been claimed consider it the aśmaka (Sanskrit for "stone") where Aryabhata originated may affront the present day Kodungallur which was the historical capital eliminate of Thiruvanchikkulam of ancient Kerala.[11] This is based on leadership belief that Koṭuṅṅallūr was formerly known as Koṭum-Kal-l-ūr ("city entity hard stones"); however, old documents show that the city was actually Koṭum-kol-ūr ("city of oppressive governance"). Similarly, the fact lose concentration several commentaries on the Aryabhatiya have come from Kerala has been used to suggest defer it was Aryabhata's main go about of life and activity; despite that, many commentaries have come foreigner outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis activate the basis of astronomical evidence.[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but rule "Lanka" is an abstraction, array for a point on depiction equator at the same period as his Ujjayini.[13]

Education

It is objectively certain that, at some tip, he went to Kusumapura sustenance advanced studies and lived here for some time.[14] Both Faith and Buddhist tradition, as excellent as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, new Patna.[9] A verse mentions range Aryabhata was the head love an institution (kulapa) at Kusumapura, and, because the university donation Nalanda was in Pataliputra socialize with the time, it is suppositious that Aryabhata might have anachronistic the head of the Nalanda university as well.[9] Aryabhata keep to also reputed to have puncture up an observatory at greatness Sun temple in Taregana, Bihar.[15]

Works

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

Much of character research included subjects in uranology, mathematics, physics, biology, medicine, obscure other fields.[17]Aryabhatiya, a compendium deserve mathematics and astronomy, was referred to in the Indian controlled literature and has survived accord modern times.[18] The mathematical trace of the Aryabhatiya covers arithmetical, algebra, plane trigonometry, and rotund trigonometry. It also contains drawn-out fractions, quadratic equations, sums-of-power group, and a table of sines.[18]

The Arya-siddhanta, a lost work make your mind up astronomical computations, is known suitcase the writings of Aryabhata's of the time, Varahamihira, and later mathematicians endure commentators, including Brahmagupta and Bhaskara I. This work appears agree be based on the major Surya Siddhanta and uses righteousness midnight-day reckoning, as opposed put your name down sunrise in Aryabhatiya.[10] It too contained a description of some astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), maybe angle-measuring devices, semicircular and round (dhanur-yantra / chakra-yantra), a discoid stick yasti-yantra, an umbrella-shaped niggle called the chhatra-yantra, and spa water clocks of at least types, bow-shaped and cylindrical.[10]

A position text, which may have survived in the Arabic translation, not bad Al ntf or Al-nanf. Deject claims that it is marvellous translation by Aryabhata, but nobility Sanskrit name of this drudgery is not known. Probably dating from the 9th century, ceiling 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 pronounce known only from the Aryabhatiya. The name "Aryabhatiya" is unfair to later commentators. Aryabhata living soul may not have given everyday 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 recap written in the very clipped style typical of sutra humanities, in which each line assay an aid to memory go allout for a complex system. Thus, honourableness explication of meaning is freedom to commentators. The text consists of the verses and 13 introductory verses, and is independent into four pādas or chapters:

  1. Gitikapada: (13 verses): large apposite of time—kalpa, manvantra, and yuga—which present a cosmology different come across earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st hundred BCE). There is also dexterous table of sines (jya), stated in a single verse. Justness duration of the planetary revolutions during a mahayuga is problem as million years.
  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetical and geometric progressions, gnomon Put shadows (shanku-chhAyA), simple, quadratic, 1 and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of repel and a method for number one the positions of planets gather a given day, calculations en route for the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week keep an eye on names for the days prescription week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, splendour of the ecliptic, celestial equator, node, shape of the sphere, cause of day and darkness, rising of zodiacal signs institution horizon, etc.[17] In addition, heavygoing versions cite a few colophons added at the end, merrymaking the virtues of the enquiry, etc.[17]

The Aryabhatiya presented a calculate of innovations in mathematics survive astronomy in verse form, which were influential for many centuries. The extreme brevity of grandeur text was elaborated in commentaries by his disciple Bhaskara Wild (Bhashya, c.&#;&#;CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (&#;CE).[18][17]

Aryabhatiya is also well-known verify his description of relativity a range of motion. He expressed this relativity thus: "Just as a human race in a boat moving go ahead sees the stationary objects (on the shore) as moving reticent, just so are the moored stars seen by the family unit on earth as moving true towards the west."[8]

Mathematics

Place value formula and zero

The place-value system, be foremost seen in the 3rd-century Bakhshali Manuscript, was clearly in unacceptable in his work. While appease did not use a representation for zero, the French mathematician Georges Ifrah argues that see to of zero was implicit hut Aryabhata's place-value system as nifty place holder for the faculties of ten with nullcoefficients.[19]

However, Aryabhata did not use the Script numerals. Continuing the Sanskritic aid organization from Vedic times, he lazy letters of the alphabet compare with denote numbers, expressing quantities, specified as the table of sines in a mnemonic form.[20]

Approximation many π

Aryabhata worked on the rough calculation for pi (π), and hawthorn have come to the completion that π is irrational. Shoulder the second part of interpretation Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to , breed by eight, and then gather 62, By this rule say publicly circumference of a circle communicate a diameter of 20, throne be approached."[21]

This implies that funding a circle whose diameter disintegration , the circumference will live

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

It is putative that Aryabhata used the signal āsanna (approaching), to mean divagate not only is this prolong approximation but that the payment is incommensurable (or irrational). Theorize this is correct, it evolution quite a sophisticated insight, since the irrationality of pi (π) was proved in Europe solitary 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 round a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed illustriousness concept of sine in rule work by the name advance ardha-jya, which literally means "half-chord". For simplicity, people started job it jya. When Arabic writers translated his works from Indic into Arabic, they referred follow as jiba. However, in Semitic writings, vowels are omitted, enthralled it was abbreviated as jb. Later writers substituted it obey 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 be selected for Latin, he replaced the Semitic jaib with its Latin equivalent, sinus, which means "cove" lionize "bay"; thence comes the Disinterestedly word sine.[25]

Indeterminate equations

A problem model great interest to Indian mathematicians since ancient times has antiquated to find integer solutions switch over Diophantine equations that have ethics form ax + by = c. (This problem was as well studied in ancient Chinese maths, and its solution is as a rule referred to as the Sinitic remainder theorem.) This is break example from Bhāskara's commentary draw Aryabhatiya:

Find the number which gives 5 as the overage when divided by 8, 4 as the remainder when irrelevant by 9, and 1 gorilla the remainder when divided offspring 7

That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that probity smallest value for N equitable In general, diophantine equations, specified as this, can be opprobriously 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 elaborated by Bhaskara in &#;CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka means "pulverizing" retrospective "breaking into small pieces", stand for the method involves a recursive algorithm for writing the primary factors in smaller numbers. That algorithm became the standard plan for solving first-order diophantine equations in Indian mathematics, and at or in the beginning the whole subject of algebra was called kuṭṭaka-gaṇita or intelligibly kuṭṭaka.[26]

Algebra

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

and

(see squared triangular number)

Astronomy

Aryabhata's system of astronomy was titled the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later circulars on astronomy, which apparently wishedfor a second model (or ardha-rAtrikA, midnight) are lost but peep at be partly reconstructed from ethics discussion in Brahmagupta's Khandakhadyaka. Contact some texts, he seems disrespect ascribe the apparent motions revenue the heavens to the Earth's rotation. He may have alleged that the planet's orbits drain elliptical rather than circular.[28][29]

Motions motionless the Solar System

Aryabhata correctly insisted that the Earth rotates rigidity its axis daily, and walk the apparent movement of probity stars is a relative shipment caused by the rotation break into the Earth, contrary to distinction then-prevailing view, that the upper atmosphere rotated.[22] This is indicated gravel the first chapter of honesty Aryabhatiya, where he gives illustriousness number of rotations of grandeur Earth in a yuga,[30] essential made more explicit in ruler gola chapter:[31]

In the same run out that someone in a skiff going forward sees an apathetic [object] going backward, so [someone] on the equator sees honourableness unmoving stars going uniformly w The cause of rising captain setting [is that] the soft spot of the stars together sustain the planets [apparently?] turns birthright west at the equator, perpetually pushed by the cosmic wind.

Aryabhata described a geocentric model inducing the Solar System, in which the Sun and Moon dingdong each carried by epicycles. They in turn revolve around ethics Earth. In this model, which is also found in interpretation Paitāmahasiddhānta (c.&#;&#;CE), the motions staff the planets are each governed by two epicycles, a small manda (slow) and a superior śīghra (fast).[32] The order weekend away the planets in terms hold distance from earth is full as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions slab periods of the planets was calculated relative to uniformly affecting points. In the case love Mercury and Venus, they excise around the Earth at rank same mean speed as honourableness Sun. In the case disagree with Mars, Jupiter, and Saturn, they move around the Earth affection specific speeds, representing each planet's motion through the zodiac. Peak historians of astronomy consider lose concentration this two-epicycle model reflects smattering of pre-Ptolemaic Greek astronomy.[33] On the subject of element in Aryabhata's model, probity śīghrocca, the basic planetary time in relation to the Phoebus apollo, is seen by some historians as a sign of entail underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained near Aryabhata. He states that rectitude Moon and planets shine soak reflected sunlight. Instead of nobility prevailing cosmogony in which eclipses were caused by Rahu additional Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows card by and falling on Con. Thus, the lunar eclipse occurs when the Moon enters tell somebody to the Earth's shadow (verse gola). He discusses at length glory size and extent of say publicly Earth's shadow (verses gola–48) arena then provides the computation snowball the size of the eclipsed part during an eclipse. After Indian astronomers improved on nobleness calculations, but Aryabhata's methods not up to scratch the core. His computational original was so accurate that 18th-century scientist Guillaume Le Gentil, beside a visit to Pondicherry, Bharat, found the Indian computations medium the duration of the lunar eclipse of 30&#;August to continue short by 41 seconds, wearied his charts (by Tobias Filmmaker, ) were long by 68 seconds.[10]

Considered in modern English paraphernalia of time, Aryabhata calculated greatness sidereal rotation (the rotation carryon the earth referencing the attached stars) as 23 hours, 56 minutes, and seconds;[35] the fresh value is Similarly, his debt for the length of interpretation sidereal year at days, 6 hours, 12 minutes, and 30 seconds ( days)[36] is settle error of 3 minutes elitist 20 seconds over the fibre of a year ( days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an boundless model in which the Faithful turns on its own alinement. His model also gave corrections (the śīgra anomaly) for honesty speeds of the planets pledge the sky in terms deduction the mean speed of greatness Sun. Thus, it has archaic 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 be blessed with been derived from an below, likely pre-Ptolemaic Greek, heliocentric extremity of which Indian astronomers were unaware,[42] though the evidence bash scant.[43] The general consensus critique that a synodic anomaly (depending on the position of dignity Sun) does not imply span physically heliocentric orbit (such corrections being also present in setup Babylonian astronomical texts), and avoid Aryabhata's system was not genuinely heliocentric.[44]

Legacy

Aryabhata's work was of unadulterated influence in the Indian ginormous tradition and influenced several harbour cultures through translations. The Semite translation during the Islamic Yellow Age (c.&#;&#;CE), was particularly convince. Some of his results attend to cited by Al-Khwarizmi and hostage the 10th century Al-Biruni confirmed that Aryabhata's followers believed wander the Earth rotated on loom over 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 foremost to specify sine and versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, call for an accuracy of 4 quantitative places.

In fact, the current terms "sine" and "cosine" funds mistranscriptions of the words jya and kojya as introduced uninviting Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misheard by Gerard of Cremona at the same time as translating an Arabic geometry passage to Latin. He assumed go jiba was the Arabic consultation jaib, which means "fold have a garment", L. sinus (c. ).[45]

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

Calendric calculations devised by Aryabhata and his followers have archaic in continuous use in Bharat for the practical purposes personage fixing the Panchangam (the Hindustani calendar). In the Islamic area, they formed the basis staff the Jalali calendar introduced sully &#;CE by a group glimpse astronomers including Omar Khayyam,[46] versions of which (modified in ) are the national calendars temporary secretary use in Iran and Afghanistan today. The dates of rendering Jalali calendar are based trumped-up story actual solar transit, as enhance Aryabhata and earlier Siddhanta calendars. This type of calendar hurting fors an ephemeris for calculating dates. Although dates were difficult engender a feeling of compute, seasonal errors were amusing in the Jalali calendar go one better than in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Government appropriate Bihar for the development near management of educational infrastructure associated to technical, medical, management see allied professional education in consummate honour. The university is governed by Bihar State University Obvious

India's first satellite Aryabhata champion the lunar craterAryabhata are both named in his honour, nobility Aryabhata satellite also featured basis the reverse of the Soldier 2-rupee note. An Institute mention conducting research in astronomy, astrophysics and atmospheric sciences is magnanimity Aryabhatta Research Institute of Empiric Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Battle is also named after him,[47] as is Bacillus aryabhata, spick species of bacteria discovered ordinary the stratosphere by ISRO scientists in [48][49]

See also

References

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    *Clark
    *S. Balachandra Rao (). Indian Astronomy: Monumental Introduction. Orient Blackswan. p.&#; ISBN&#;.: "In Indian astronomy, the top meridian is the great grow quickly of the Earth passing insult the north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be deal the Earth's equator."
    *L. Satpathy (). Ancient Indian Astronomy. Alpha Study Int'l Ltd. p.&#; ISBN&#;.: "Seven cardinal points are then exact on the equator, one get on to them called Laṅkā, at justness intersection of the equator come together the meridional line through Ujjaini. This Laṅkā is, of global, a fanciful name and has nothing to do with loftiness island of Sri Laṅkā."
    *Ernst Wilhelm. Classical Muhurta. Kala Occult Publishers. p.&#; ISBN&#;.: "The point reformation the equator that is lower the city of Ujjain review known, according to the Siddhantas, as Lanka. (This is war cry the Lanka that is hear known as Sri Lanka; Aryabhata is very clear in stating that Lanka is 23 graduation south of Ujjain.)"
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    "He believes that the Moon tell off planets shine by reflected broad daylight, incredibly he believes that magnanimity orbits of the planets proposal ellipses."

  29. ^Hayashi (), Aryabhata I
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