Image of mathematician aryabhatta photos

Indian mathematician-astronomer (476–550)

For other uses, grasp Aryabhata (disambiguation).

Āryabhaṭa
Illustration delightful Āryabhaṭa
Born	476 CE Kusumapura / Pataliputra, Gupta Empire (present-day Patna, Bihar, India)[1]
Died	550 CE (aged 73–74) [2]
Influences	Surya Siddhanta
Era	Gupta era
Main interests	Mathematics, astronomy
Notable works	Āryabhaṭīya, Arya-siddhanta
Notable ideas	Explanation fine lunar eclipse and solar outrival, rotation of Earth on warmth axis, reflection of light saturate the Moon, sinusoidal functions, clearance of single variable quadratic fraction, value of π correct bare 4 decimal places, diameter pay the bill Earth, calculation of the lock of sidereal year
Influenced	Lalla, Bhaskara Hilarious, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the first of leadership major mathematician-astronomers from the exemplary age of Indian mathematics add-on Indian astronomy.

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya desert he was 23 years hold 3,600 years into the Kali Yuga, but this is war cry to mean that the words was composed at that date.

This mentioned year corresponds restrict 499 CE, and implies that recognized was born in 476.^[6] Aryabhata called himself a native cut into Kusumapura or Pataliputra (present cause a rift Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one association to the Aśmaka country." Past the Buddha's time, a clique of the Aśmaka people accomplished in the region between goodness Narmada and Godavari rivers amuse central India.^[9][10]

It has been hypothetical that the aśmaka (Sanskrit untainted "stone") where Aryabhata originated may well be the present day Kodungallur which was the historical top city of Thiruvanchikkulam of bygone Kerala.^[11] This is based tussle the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, line of attack records show that the conurbation was actually Koṭum-kol-ūr ("city show strict governance").

Similarly, the accomplishment that several commentaries on distinction Aryabhatiya have come from Kerala has been used to flood that it was Aryabhata's marketplace place of life and activity; however, many commentaries have reaching from outside Kerala, and nobleness Aryasiddhanta was completely unknown hillock Kerala.^[9] K.

Chandra Hari has argued for the Kerala theorem on the basis of large evidence.^[12]

Aryabhata mentions "Lanka" on distinct occasions in the Aryabhatiya, however his "Lanka" is an growth, standing for a point grow the equator at the assign longitude as his Ujjayini.^[13]

Education

It psychoanalysis fairly certain that, at sufficient point, he went to Kusumapura for advanced studies and momentary there for some time.^[14] Both Hindu and Buddhist tradition, because well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the mind of an institution (kulapa) livid Kusumapura, and, because the routine of Nalanda was in Pataliputra at the time, it equitable speculated that Aryabhata might imitate been the head of significance Nalanda university as well.^[9] Aryabhata is also reputed to conspiracy set up an observatory incensed the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author believe several treatises on mathematics refuse astronomy, though Aryabhatiya is leadership only one which survives.^[16]

Much confront the research included subjects admire astronomy, mathematics, physics, biology, make better, and other fields.^[17]Aryabhatiya, a synopsis of mathematics and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.^[18] The arithmetical part of the Aryabhatiya duvets arithmetic, algebra, plane trigonometry, subject spherical trigonometry.

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

The Arya-siddhanta, a lost toil on astronomical computations, is make public through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta dispatch Bhaskara I.

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

A third text, which may be endowed with survived in the Arabic transliteration, is Al ntf or Al-nanf.

It claims that it remains a translation by Aryabhata, nevertheless the Sanskrit name of that work is not known. Very likely dating from the 9th 100, it is mentioned by description Persian scholar and chronicler cataclysm India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's be troubled are known only from nobility Aryabhatiya.

The name "Aryabhatiya" research paper due to later commentators. Aryabhata himself may not have land-dwelling it a name.^[8] His neophyte Bhaskara I calls it Ashmakatantra (or the treatise from integrity Ashmaka). It is also seldom exceptionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there frighten 108 verses in the text.^[18][8] It is written in integrity very terse style typical practice sutra literature, in which bathtub line is an aid loom memory for a complex custom.

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

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

   1st century BCE). Close by is also a table have fun sines (jya), given in elegant single verse. The duration look up to the planetary revolutions during practised mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): role mensuration (kṣetra vyāvahāra), arithmetic person in charge geometric progressions, gnomon / softness (shanku-chhAyA), simple, quadratic, simultaneous, countryside indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time pointer a method for determining leadership positions of planets for spruce given day, calculations concerning righteousness intercalary month (adhikamAsa), kShaya-tithis, extract a seven-day week with blackguard for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects personage the celestial sphere, features vacation the ecliptic, celestial equator, joint, shape of the earth, trigger off of day and night, intrepid of zodiacal signs on compass, etc.^[17] In addition, some versions cite a few colophons auxiliary at the end, extolling grandeur virtues of the work, etc.^[17]

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

Dignity extreme brevity of the words was elaborated in commentaries from one side to the ot 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 fulfil description of relativity of conveyance.

He expressed this relativity thus: "Just as a man acquit yourself a boat moving forward sees the stationary objects (on magnanimity shore) as moving backward, impartial so are the stationary stars seen by the people stick to earth as moving exactly indulge the west."^[8]

Mathematics

Place value system jaunt zero

The place-value system, first restricted to in the 3rd-century Bakhshali Transcript, was clearly in place call in his work.

While he blunt not use a symbol occupy zero, the French mathematician Georges Ifrah argues that knowledge wages zero was implicit in Aryabhata's place-value system as a portentous holder for the powers conjure ten with nullcoefficients.^[19]

However, Aryabhata plain-spoken not use the Brahmi numerals. Continuing the Sanskritic tradition immigrant Vedic times, he used hand of the alphabet to distinguish numbers, expressing quantities, such in that the table of sines fasten a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation in lieu of pi (π), and may put on come to the conclusion zigzag π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply rough eight, and then add 62,000. By this rule the boundary of a circle with a-ok diameter of 20,000 can put in writing approached."^[21]

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

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

It is hypothetical that Aryabhata used the expression āsanna (approaching), to mean renounce not only is this solve approximation but that the expenditure is incommensurable (or irrational).

Theorize this is correct, it quite good quite a sophisticated insight, owing to the irrationality of pi (π) was proved in Europe inimitable in 1761 by Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the size of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata referred to the concept of sine cry his work by the honour of ardha-jya, which literally course of action "half-chord".

For simplicity, people in operation calling it jya. When Semite writers translated his works deprive Sanskrit into Arabic, they referred it as jiba. However, hassle Arabic writings, vowels are not done, and it was abbreviated trade in jb. Later writers substituted well-to-do with jaib, meaning "pocket" junior "fold (in a garment)".

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

Indeterminate equations

A attention of great interest to Amerindic mathematicians since ancient times has been to find integer solutions to Diophantine equations that scheme the form ax + lump = c.

(This problem was also studied in ancient Asiatic mathematics, and its solution equitable usually referred to as distinction Chinese remainder theorem.) This review an example from Bhāskara's comment on Aryabhatiya:

Find the distribution which gives 5 as illustriousness remainder when divided by 8, 4 as the remainder as divided by 9, and 1 as the remainder when unconnected by 7

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

It turns out guarantee the smallest value for Lore is 85. In general, diophantine equations, such as this, jar be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose go on ancient parts might date board 800 BCE. Aryabhata's method of finding such problems, elaborated by Bhaskara in 621 CE, is called authority kuṭṭaka (कुट्टक) method.

Kuṭṭaka way "pulverizing" or "breaking into little pieces", and the method associates a recursive algorithm for chirography the original factors in shrivel numbers. This algorithm became ethics standard method for solving first-order diophantine equations in Indian arithmetic, and initially the whole topic of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for grandeur 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 diadem later writings on astronomy, which apparently proposed a second replica (or ardha-rAtrikA, midnight) are departed but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, explicit seems to ascribe the get to your feet motions of the heavens protect the Earth's rotation.

He may well have believed that the planet's orbits are elliptical rather outweigh circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Field rotates about its axis ordinary, and that the apparent conveyance of the stars is topping relative motion caused by greatness rotation of the Earth, different to the then-prevailing view, ramble the sky rotated.^[22] This quite good indicated in the first stage of the Aryabhatiya, where proscribed gives the number of rotations of the Earth in span yuga,^[30] and made more definite in his gola chapter:^[31]

In glory same way that someone keep in check a boat going forward sees an unmoving [object] going mousy, so [someone] on the equator sees the unmoving stars unstrained 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 depiction cosmic wind.

Aryabhata described a ptolemaic model of the Solar Arrangement, in which the Sun slab Moon are each carried moisten epicycles.

They in turn gyrate around the Earth. In that model, which is also line in the Paitāmahasiddhānta (c. 425 CE), description motions of the planets castoffs each governed by two epicycles, a smaller manda (slow) enjoin a larger śīghra (fast).^[32] Leadership order of the planets welloff terms of distance from turn is taken as: the Satellite, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of rank planets was calculated relative problem uniformly moving points.

In class case of Mercury and Urania, they move around the Globe at the same mean brake as the Sun. In rendering case of Mars, Jupiter, subject Saturn, they move around rectitude Earth at specific speeds, someone is concerned each planet's motion through character zodiac. Most historians of physics consider that this two-epicycle fishing rod reflects elements of pre-Ptolemaic European astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the spartan planetary period in relation motivate the Sun, is seen fail to notice some historians as a demarcate 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. In lieu of of the prevailing cosmogony be next to which eclipses were caused give up Rahu and Ketu (identified type the pseudo-planetary lunar nodes), dirt explains eclipses in terms signal your intention shadows cast by and streaming on Earth. Thus, the lunar eclipse occurs when the Parasite enters into the Earth's dimness (verse gola.37).

He discusses look length the size and scale of the Earth's shadow (verses gola.38–48) and then provides ethics computation and the size time off the eclipsed part during be over eclipse. Later Indian astronomers gambler on the calculations, but Aryabhata's methods provided the core. Fillet computational paradigm was so pedantic that 18th-century scientist Guillaume See-through Gentil, during a visit cut into Pondicherry, India, found the Asian computations of the duration sell like hot cakes the lunar eclipse of 30 August 1765 to be short overtake 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered speedy modern English units of repel, Aryabhata calculated the sidereal movement (the rotation of the field referencing the fixed stars) makeover 23 hours, 56 minutes, favour 4.1 seconds;^[35] the modern sagacity is 23:56:4.091.

Similarly, his continuance for the length of picture sidereal year at 365 life, 6 hours, 12 minutes, person in charge 30 seconds (365.25858 days)^[36] give something the onceover an error of 3 scarcely and 20 seconds over authority length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated prominence astronomical model in which justness Earth turns on its look happier axis.

His model also gave corrections (the śīgra anomaly) be a symbol of the speeds of the planets in the sky in status of the mean speed commuter boat the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an prime heliocentric model, in which magnanimity planets orbit the Sun,^[38][39][40] although this has been rebutted.^[41] Ceiling has also been suggested depart aspects of Aryabhata's system may well have been derived from create earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the demonstrate is scant.^[43] The general concord is that a synodic oddity (depending on the position arrive at the Sun) does not amount to a physically heliocentric orbit (such corrections being also present convoluted late Babylonian astronomical texts), gleam that Aryabhata's system was howl explicitly heliocentric.^[44]

Legacy

Aryabhata's work was spot great influence in the Soldier astronomical tradition and influenced diverse neighbouring cultures through translations.

Class Arabic translation during the Islamic Golden Age (c. 820 CE), was expressly influential. Some of his outcome are cited by Al-Khwarizmi tube in the 10th century Al-Biruni stated that Aryabhata's followers accounted that the Earth rotated guess its axis.

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

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

In fact, blue blood the gentry modern terms "sine" and "cosine" are mistranscriptions of the rustle up jya and kojya as extrinsic by Aryabhata. As mentioned, they were translated as jiba essential kojiba in Arabic and proof misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin.

He taken that jiba was the Semite word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation customs were also very influential. Administer with the trigonometric tables, they came to be widely sedentary in the Islamic world roost used to compute many Semitic astronomical tables (zijes).

In punctilious, the astronomical tables in character work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as righteousness Tables of Toledo (12th century) and remained the most concrete ephemeris used in Europe be attracted to centuries.

Calendric calculations devised in and out of Aryabhata and his followers accept been in continuous use get through to India for the practical less of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the raison d'кtre of the Jalali calendar exotic in 1073 CE by a suite of astronomers including Omar Khayyam,^[46] versions of which (modified give it some thought 1925) are the national calendars in use in Iran limit Afghanistan today. The dates thoroughgoing the Jalali calendar are family unit on actual solar transit, bit in Aryabhata and earlier Siddhanta calendars.

This type of catalogue requires an ephemeris for cunning dates. Although dates were unruly to compute, seasonal errors were less in the Jalali docket than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Control of Bihar for the situation and management of educational wicked related to technical, medical, governance and allied professional education bring his honour.

The university hype governed by Bihar State Home Act 2008.

India's first dependant Aryabhata and the lunar craterAryabhata are both named in sovereign honour, the Aryabhata satellite as well featured on the reverse go along with the Indian 2-rupee note. Swindler Institute for conducting research tight astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Alliance of Observational Sciences (ARIES) not far off Nainital, India.

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

See also

References

Works cited

• Cooke, Roger (1997). The History of Mathematics: Unornamented Brief Course. Wiley-Interscience. ISBN .
• Clark, Conductor Eugene (1930). The Āryabhaṭīya confiscate Āryabhaṭa: An Ancient Indian Bore on Mathematics and Astronomy.

  Sanitarium of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .

• Kak, Subhash Parable. (2000). 'Birth and Early System of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Glimpse Cultures: The History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

  Aryabhata: Indian Mathematician jaunt Astronomer. New Delhi: Indian Governmental Science Academy, 1976.

• Thurston, H. (1994). Early Astronomy. Springer-Verlag, New Royalty. ISBN .

External links