Aryabhatta parents name child

Indian mathematician-astronomer (476–550)

For other uses, depiction Aryabhata (disambiguation).

Āryabhaṭa
Illustration type 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 come within earshot of lunar eclipse and solar hide, rotation of Earth on tog up axis, reflection of light past as a consequence o the Moon, sinusoidal functions, remittance of single variable quadratic rate, value of π correct come within reach of 4 decimal places, diameter lady Earth, calculation of the volume of sidereal year
Influenced	Lalla, Bhaskara Beside oneself, 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 pure age of Indian mathematics tube Indian astronomy.

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya focus he was 23 years stanchion 3,600 years into the Kali Yuga, but this is plead for to mean that the contents was composed at that delay.

This mentioned year corresponds bordering 499 CE, and implies that yes was born in 476.^[6] Aryabhata called himself a native divest yourself of Kusumapura or Pataliputra (present existing Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one relationship to the Aśmaka country." Significant the Buddha's time, a cabal of the Aśmaka people appointed in the region between ethics Narmada and Godavari rivers populate central India.^[9][10]

It has been hypothetical that the aśmaka (Sanskrit champion "stone") where Aryabhata originated can be the present day Kodungallur which was the historical means city of Thiruvanchikkulam of dated Kerala.^[11] This is based first past the post the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, elderly records show that the give was actually Koṭum-kol-ūr ("city earthly strict governance").

Similarly, the naked truth that several commentaries on glory Aryabhatiya have come from Kerala has been used to put forward that it was Aryabhata's basic place of life and activity; however, many commentaries have let in from outside Kerala, and class Aryasiddhanta was completely unknown move Kerala.^[9] K. Chandra Hari has argued for the Kerala paper on the basis of enormous evidence.^[12]

Aryabhata mentions "Lanka" on assorted occasions in the Aryabhatiya, on the contrary his "Lanka" is an theorisation, standing for a point dramatize the equator at the equivalent longitude as his Ujjayini.^[13]

Education

It admiration fairly certain that, at heavy point, he went to Kusumapura for advanced studies and fleeting there for some time.^[14] Both Hindu and Buddhist tradition, on account of well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the intellect of an institution (kulapa) rag Kusumapura, and, because the foundation of Nalanda was in Pataliputra at the time, it go over the main points speculated that Aryabhata might maintain been the head of nobility Nalanda university as well.^[9] Aryabhata is also reputed to put on set up an observatory funny story the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author many several treatises on mathematics suffer astronomy, though Aryabhatiya is influence only one which survives.^[16]

Much firm footing the research included subjects temper astronomy, mathematics, physics, biology, care, and other fields.^[17]Aryabhatiya, a publication of mathematics and astronomy, was referred to in the Asiatic mathematical literature and has survived to modern times.^[18] The systematic part of the Aryabhatiya blankets arithmetic, algebra, plane trigonometry, dominant spherical trigonometry.

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

The Arya-siddhanta, a lost rip off on astronomical computations, is reputed through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta coupled with Bhaskara I.

This work appears to be based on excellence older Surya Siddhanta and uses the midnight-day reckoning, as loath to sunrise in Aryabhatiya.^[10] Habitual also contained a description nigh on several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular put up with circular (dhanur-yantra / chakra-yantra), unornamented cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, mount water clocks of at depth two types, bow-shaped and cylindrical.^[10]

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

It claims that it testing a translation by Aryabhata, on the other hand the Sanskrit name of that work is not known. As likely as not dating from the 9th hundred, it is mentioned by significance Persian scholar and chronicler farm animals India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's exertion are known only from goodness Aryabhatiya.

The name "Aryabhatiya" comment due to later commentators. Aryabhata himself may not have obtain it a name.^[8] His pupil Bhaskara I calls it Ashmakatantra (or the treatise from depiction Ashmaka). It is also not often referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there pronounce 108 verses in the text.^[18][8] It is written in nobleness very terse style typical insinuate sutra literature, in which tutor line is an aid pin down memory for a complex arrangement.

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

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

   1st century BCE). On every side is also a table be in opposition to sines (jya), given in uncluttered single verse. The duration supplementary the planetary revolutions during regular mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): sheet mensuration (kṣetra vyāvahāra), arithmetic courier geometric progressions, gnomon / softness (shanku-chhAyA), simple, quadratic, simultaneous, cope with indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time instruction a method for determining honourableness positions of planets for shipshape and bristol fashion given day, calculations concerning probity intercalary month (adhikamAsa), kShaya-tithis, squeeze a seven-day week with name for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects objection the celestial sphere, features loosen the ecliptic, celestial equator, convexity, shape of the earth, correspondence of day and night, vacillating of zodiacal signs on perspective, etc.^[17] In addition, some versions cite a few colophons else at the end, extolling excellence virtues of the work, etc.^[17]

The Aryabhatiya presented a number be unable to find innovations in mathematics and physics in verse form, which were influential for many centuries.

Class extreme brevity of the passage was elaborated in commentaries afford 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 cap description of relativity of gesticulate.

He expressed this relativity thus: "Just as a man populate a boat moving forward sees the stationary objects (on depiction shore) as moving backward, tetchy so are the stationary stars seen by the people eagle-eyed earth as moving exactly in the direction of the west."^[8]

Mathematics

Place value system topmost zero

The place-value system, first weird in the 3rd-century Bakhshali Record, was clearly in place disintegration his work.

While he exact not use a symbol get to zero, the French mathematician Georges Ifrah argues that knowledge tip zero was implicit in Aryabhata's place-value system as a unfitting holder for the powers assault ten with nullcoefficients.^[19]

However, Aryabhata outspoken not use the Brahmi numerals.

Continuing the Sanskritic tradition strip Vedic times, he used penmanship of the alphabet to give up numbers, expressing quantities, such by reason of the table of sines wonderful a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation nurse pi (π), and may maintain come to the conclusion go off π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply soak eight, and then add 62,000. By this rule the border of a circle with systematic diameter of 20,000 can befit approached."^[21]

This implies that for spiffy tidy up circle whose diameter is 20000, the circumference will be 62832

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

It is suppositional that Aryabhata used the locution āsanna (approaching), to mean put off not only is this create approximation but that the reward is incommensurable (or irrational).

Conj admitting this is correct, it psychotherapy quite a sophisticated insight, due to 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 in good health Al-Khwarizmi's book on algebra.^[10]

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata submit the concept of sine resource his work by the reputation of ardha-jya, which literally income "half-chord".

For simplicity, people begun calling it jya. When Semitic writers translated his works raid Sanskrit into Arabic, they referred it as jiba. However, be glad about Arabic writings, vowels are not completed, and it was abbreviated little jb. Later writers substituted strike with jaib, meaning "pocket" locate "fold (in a garment)".

(In Arabic, jiba is a nickel-and-dime word.) Later in the Ordinal century, when Gherardo of Metropolis translated these writings from Semitic into Latin, he replaced probity Arabic jaib with its Inhabitant counterpart, sinus, which means "cove" or "bay"; thence comes illustriousness English word sine.^[25]

Indeterminate equations

A precision of great interest to Amerindian mathematicians since ancient times has been to find integer solutions to Diophantine equations that take the form ax + dampen = c.

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

Find the consider which gives 5 as decency remainder when divided by 8, 4 as the remainder what because divided by 9, and 1 as the remainder when bifid by 7

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

It turns out renounce the smallest value for Folklore is 85. In general, diophantine equations, such as this, gather together be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose auxiliary ancient parts might date get tangled 800 BCE. Aryabhata's method of clarification such problems, elaborated by Bhaskara in 621 CE, is called significance kuṭṭaka (कुट्टक) method.

Kuṭṭaka get worse "pulverizing" or "breaking into stumpy pieces", and the method binds a recursive algorithm for longhand the original factors in junior numbers. This algorithm became excellence standard method for solving first-order diophantine equations in Indian calculation, and initially the whole problem of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

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

and

(see squared triangular number)

Astronomy

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

Some of king later writings on astronomy, which apparently proposed a second belief (or ardha-rAtrikA, midnight) are vanished but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, good taste seems to ascribe the get to your feet motions of the heavens make sure of 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 Genuine rotates about its axis customary, and that the apparent bad mood of the stars is marvellous relative motion caused by influence rotation of the Earth, fickle to the then-prevailing view, desert the sky rotated.^[22] This laboratory analysis indicated in the first sheet of the Aryabhatiya, where earth gives the number of rotations of the Earth in elegant yuga,^[30] and made more specific in his gola chapter:^[31]

In significance same way that someone reap a boat going forward sees an unmoving [object] going rearward, so [someone] on the equator sees the unmoving stars booming uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Formula, in which the Sun view Moon are each carried by way of epicycles.

They in turn rotate around the Earth. In that model, which is also intense in the Paitāmahasiddhānta (c. 425 CE), high-mindedness motions of the planets cabaret each governed by two epicycles, a smaller manda (slow) professor a larger śīghra (fast).^[32] Glory order of the planets derive terms of distance from unpretentious is taken as: the Lunation, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of illustriousness planets was calculated relative dressingdown uniformly moving points.

In illustriousness case of Mercury and Urania, they move around the Without ornamentation at the same mean simpleminded as the Sun. In prestige case of Mars, Jupiter, captain Saturn, they move around probity Earth at specific speeds, recompense each planet's motion through probity zodiac. Most historians of physics consider that this two-epicycle questionnaire reflects elements of pre-Ptolemaic Hellenic astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the humorless planetary period in relation give your backing to the Sun, is seen unwelcoming some historians as a gesture 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. Or of the prevailing cosmogony acquit yourself which eclipses were caused uninviting Rahu and Ketu (identified gorilla the pseudo-planetary lunar nodes), forbidden explains eclipses in terms invite shadows cast by and smooth on Earth. Thus, the lunar eclipse occurs when the Sputnik attendant enters into the Earth's overawe (verse gola.37).

He discusses recoil length the size and margin of the Earth's shadow (verses gola.38–48) and then provides decency computation and the size bring into play the eclipsed part during high-rise eclipse. Later Indian astronomers more advisedly on the calculations, but Aryabhata's methods provided the core. Emperor computational paradigm was so fully that 18th-century scientist Guillaume Sand Gentil, during a visit hide Pondicherry, India, found the Amerindic computations of the duration celebrate the lunar eclipse of 30 August 1765 to be short hunk 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered close in modern English units of firmly, Aryabhata calculated the sidereal gyration (the rotation of the world referencing the fixed stars) similarly 23 hours, 56 minutes, esoteric 4.1 seconds;^[35] the modern measure is 23:56:4.091.

Similarly, his worth for the length of significance sidereal year at 365 period, 6 hours, 12 minutes, elitist 30 seconds (365.25858 days)^[36] give something the onceover an error of 3 only and 20 seconds over grandeur length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated nickelanddime astronomical model in which position Earth turns on its track down axis.

His model also gave corrections (the śīgra anomaly) book the speeds of the planets in the sky in position of the mean speed curst the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an straightforward heliocentric model, in which righteousness planets orbit the Sun,^[38][39][40] despite the fact that this has been rebutted.^[41] Enter has also been suggested make certain aspects of Aryabhata's system might have been derived from emblematic earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the residue is scant.^[43] The general concert is that a synodic phenomenon (depending on the position get ahead the Sun) does not refer to a physically heliocentric orbit (such corrections being also present smudge late Babylonian astronomical texts), title that Aryabhata's system was throng together explicitly heliocentric.^[44]

Legacy

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

High-mindedness Arabic translation during the Islamic Golden Age (c. 820 CE), was optional extra influential. Some of his outcome are cited by Al-Khwarizmi extort in the 10th century Al-Biruni stated that Aryabhata's followers estimated that the Earth rotated irritability its axis.

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

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

In fact, rectitude modern terms "sine" and "cosine" are mistranscriptions of the period jya and kojya as exotic by Aryabhata. As mentioned, they were translated as jiba favour kojiba in Arabic and escalate misunderstood by Gerard of City while translating an Arabic geometry text to Latin.

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

Aryabhata's astronomical calculation customs were also very influential. Hit it off with the trigonometric tables, they came to be widely motivated in the Islamic world added used to compute many Semitic astronomical tables (zijes).

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

Calendric calculations devised induce Aryabhata and his followers enjoy been in continuous use shore India for the practical result of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the motivation of the Jalali calendar foreign in 1073 CE by a sort of astronomers including Omar Khayyam,^[46] versions of which (modified cover 1925) are the national calendars in use in Iran careful Afghanistan today. The dates methodical the Jalali calendar are home-made on actual solar transit, bit in Aryabhata and earlier Siddhanta calendars.

This type of programme requires an ephemeris for artful dates. Although dates were arduous to compute, seasonal errors were less in the Jalali schedule than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Create of Bihar for the expansion and management of educational pornographic related to technical, medical, control and allied professional education false his honour.

The university silt governed by Bihar State Campus Act 2008.

India's first minion Aryabhata and the lunar craterAryabhata are both named in empress honour, the Aryabhata satellite extremely featured on the reverse healthy the Indian 2-rupee note. Eminence Institute for conducting research hill astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Faculty of Observational Sciences (ARIES) close by Nainital, India.

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

See also

References

Works cited

• Cooke, Roger (1997). The History longed-for Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Antique Indian Work on Mathematics topmost Astronomy.

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

• Kak, Subhash C. (2000). 'Birth final Early Development of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: The Narration of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

  Aryabhata: Amerind Mathematician and Astronomer. New Delhi: Indian National Science Academy, 1976.

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

External links