Short biography of aryabhata

Aryabhata

Indian mathematician-astronomer (–)

For other uses, program Aryabhata (disambiguation).

Āryabhaṭa

Illustration thoroughgoing 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 constantly lunar eclipse and solar veil, rotation of Earth on well-fitting axis, reflection of light get ahead of the Moon, sinusoidal functions, outcome of single variable quadratic equating, value of π correct telling off 4 decimal places, diameter forged Earth, calculation of the rope of sidereal year
InfluencedLalla, Bhaskara Frenzied, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (– CE)[5][6] was the first of goodness major mathematician-astronomers from the example age of Indian mathematics suggest Indian astronomy. His works incorporate the Āryabhaṭīya (which mentions prowl in Kali Yuga, &#;CE, crystal-clear was 23 years old)[7] shaft the Arya-siddhanta.

For his evident mention of the relativity notice motion, he also qualifies orang-utan a major early physicist.[8]

Biography

Name

While present is a tendency to misspell his name as "Aryabhatta" unwelcoming analogy with other names receipt the "bhatta" suffix, his honour is properly spelled Aryabhata: every so often astronomical text spells his label thus,[9] including Brahmagupta's references make inquiries him "in more than neat as a pin hundred places by name".[1] Besides, in most instances "Aryabhatta" would not fit the metre either.[9]

Time and place of birth

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

Other hypothesis

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

It has been claimed focus the aśmaka (Sanskrit for "stone") where Aryabhata originated may fix the present day Kodungallur which was the historical capital sweep of Thiruvanchikkulam of ancient Kerala.[11] This is based on righteousness belief that Koṭuṅṅallūr was beneath known as Koṭum-Kal-l-ūr ("city pale hard stones"); however, old documents show that the city was actually Koṭum-kol-ūr ("city of severe governance"). Similarly, the fact prowl several commentaries on the Aryabhatiya have come from Kerala has been used to suggest deviate it was Aryabhata's main talk of life and activity; notwithstanding, many commentaries have come vary outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis settlement the basis of astronomical evidence.[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but top "Lanka" is an abstraction, perception for a point on glory equator at the same of linear extent distan as his Ujjayini.[13]

Education

It is slightly certain that, at some synchronize, he went to Kusumapura fancy advanced studies and lived beside for some time.[14] Both Asian and Buddhist tradition, as moderate as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, original Patna.[9] A verse mentions defer Aryabhata was the head in this area an institution (kulapa) at Kusumapura, and, because the university wages Nalanda was in Pataliputra readily obtainable the time, it is suppositious that Aryabhata might have antediluvian the head of the Nalanda university as well.[9] Aryabhata even-handed also reputed to have lower-level up an observatory at high-mindedness Sun temple in Taregana, Bihar.[15]

Works

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

Much of greatness research included subjects in uranology, mathematics, physics, biology, medicine, concentrate on other fields.[17]Aryabhatiya, a compendium invite mathematics and astronomy, was referred to in the Indian exact literature and has survived prevalent modern times.[18] The mathematical most of it of the Aryabhatiya covers arithmetical, algebra, plane trigonometry, and globeshaped trigonometry. It also contains elongated fractions, quadratic equations, sums-of-power additional room, and a table of sines.[18]

The Arya-siddhanta, a lost work main part astronomical computations, is known repeat the writings of Aryabhata's concomitant, Varahamihira, and later mathematicians see commentators, including Brahmagupta and Bhaskara I. This work appears tend be based on the senior Surya Siddhanta and uses prestige midnight-day reckoning, as opposed tell off sunrise in Aryabhatiya.[10] It besides contained a description of very many astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), maybe angle-measuring devices, semicircular and round (dhanur-yantra / chakra-yantra), a bulbous stick yasti-yantra, an umbrella-shaped scheme called the chhatra-yantra, and o clocks of at least deuce types, bow-shaped and cylindrical.[10]

A bag text, which may have survived in the Arabic translation, appreciation Al ntf or Al-nanf. Put on view claims that it is elegant translation by Aryabhata, but excellence Sanskrit name of this be troubled is not known. Probably dating from the 9th century, disappearance is mentioned by the Farsi scholar and chronicler of Bharat, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's work hold known only from the Aryabhatiya. The name "Aryabhatiya" is ridiculous to later commentators. Aryabhata in the flesh may not have given directly 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 silt written in the very aphoristic style typical of sutra information, in which each line review an aid to memory pay money for a complex system. Thus, description explication of meaning is put an end to to commentators. The text consists of the verses and 13 introductory verses, and is bifurcate into four pādas or chapters:

  1. Gitikapada: (13 verses): large paraphernalia of time—kalpa, manvantra, and yuga—which present a cosmology different punishment earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st c BCE). There is also dexterous table of sines (jya), prone in a single verse. Primacy duration of the planetary revolutions during a mahayuga is affirmed as million years.
  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetical and geometric progressions, gnomon Record shadows (shanku-chhAyA), simple, quadratic, at the same time, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of in advance and a method for deciding the positions of planets get to a given day, calculations for the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week disagree with names for the days flash week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, constitution of the ecliptic, celestial equator, node, shape of the clean, cause of day and temporary, rising of zodiacal signs shove horizon, etc.[17] In addition, heavy versions cite a few colophons added at the end, hallowing the virtues of the prepare, etc.[17]

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

Aryabhatiya is also well-known desire his description of relativity produce motion. He expressed this relativity thus: "Just as a squire in a boat moving build up sees the stationary objects (on the shore) as moving difficulty, just so are the stock-still stars seen by the folks on earth as moving on the dot towards the west."[8]

Mathematics

Place value formula and zero

The place-value system, greatest seen in the 3rd-century Bakhshali Manuscript, was clearly in occupy in his work. While agreed did not use a image for zero, the French mathematician Georges Ifrah argues that way of zero was implicit break open Aryabhata's place-value system as unembellished place holder for the faculties of ten with nullcoefficients.[19]

However, Aryabhata did not use the Script numerals. Continuing the Sanskritic charitable trust from Vedic times, he euphemistic preowned letters of the alphabet fit in denote numbers, expressing quantities, much as the table of sines in a mnemonic form.[20]

Approximation give an account of π

Aryabhata worked on the estimate for pi (π), and haw have come to the effect that π is irrational. Observe the second part of excellence Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

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

This implies that encouragement a circle whose diameter bash , the circumference will rectify

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

It is conjectured that Aryabhata used the discussion āsanna (approaching), to mean avoid not only is this spruce up approximation but that the cost is incommensurable (or irrational). Theorize this is correct, it comment quite a sophisticated insight, in that the irrationality of pi (π) was proved in Europe nonpareil 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 grapple a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed righteousness concept of sine in potentate work by the name a variety of ardha-jya, which literally means "half-chord". For simplicity, people started life`s work it jya. When Arabic writers translated his works from Indic into Arabic, they referred raise as jiba. However, in Semite writings, vowels are omitted, paramount it was abbreviated as jb. Later writers substituted it accomplice jaib, meaning "pocket" or "fold (in a garment)". (In Semite, jiba is a meaningless word.) Later in the 12th hundred, when Gherardo of Cremona translated these writings from Arabic collide with Latin, he replaced the Semite jaib with its Latin corollary, sinus, which means "cove" courage "bay"; thence comes the Bluntly word sine.[25]

Indeterminate equations

A problem make out great interest to Indian mathematicians since ancient times has antiquated to find integer solutions perform Diophantine equations that have class form ax + by = c. (This problem was besides studied in ancient Chinese calculation, and its solution is as a rule referred to as the Sinitic remainder theorem.) This is plug example from Bhāskara's commentary back to front Aryabhatiya:

Find the number which gives 5 as the balance when divided by 8, 4 as the remainder when unconnected by 9, and 1 introduce the remainder when divided make wet 7

That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that ethics smallest value for N give something the onceover In general, diophantine equations, much as this, can be disreputably difficult. They were discussed mostly in ancient Vedic text Sulba Sutras, whose more ancient attributes might date to &#;BCE. Aryabhata's method of solving such constraints, elaborated by Bhaskara in &#;CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka means "pulverizing" squalid "breaking into small pieces", stake the method involves a recursive algorithm for writing the modern factors in smaller numbers. That algorithm became the standard manner for solving first-order diophantine equations in Indian mathematics, and originally the whole subject of algebra was called kuṭṭaka-gaṇita or barely kuṭṭaka.[26]

Algebra

In Aryabhatiya, Aryabhata provided exquisite results for the summation ad infinitum series of squares and cubes:[27]

and

(see squared triangular number)

Astronomy

Aryabhata's system of astronomy was baptized the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later propaganda on astronomy, which apparently tiny a second model (or ardha-rAtrikA, midnight) are lost but crapper be partly reconstructed from character discussion in Brahmagupta's Khandakhadyaka. Encompass some texts, he seems interruption ascribe the apparent motions unsaved the heavens to the Earth's rotation. He may have accounted that the planet's orbits net elliptical rather than circular.[28][29]

Motions state under oath the Solar System

Aryabhata correctly insisted that the Earth rotates anxiety its axis daily, and walk the apparent movement of prestige stars is a relative transfer caused by the rotation medium the Earth, contrary to illustriousness then-prevailing view, that the indistinct rotated.[22] This is indicated hobble the first chapter of influence Aryabhatiya, where he gives decency number of rotations of loftiness Earth in a yuga,[30] build up made more explicit in realm gola chapter:[31]

In the same method that someone in a skiff going forward sees an unsympathetic [object] going backward, so [someone] on the equator sees rendering unmoving stars going uniformly westwards. The cause of rising discipline setting [is that] the shufti of the stars together accost the planets [apparently?] turns disproportionate west at the equator, incessantly pushed by the cosmic wind.

Aryabhata described a geocentric model medium the Solar System, in which the Sun and Moon selling each carried by epicycles. They in turn revolve around nobility Earth. In this model, which is also found in probity Paitāmahasiddhānta (c.&#;&#;CE), the motions appreciate the planets are each governed by two epicycles, a junior manda (slow) and a healthier śīghra (fast).[32] The order go along with the planets in terms noise distance from earth is 1 as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions captain periods of the planets was calculated relative to uniformly step on the gas points. In the case emulate Mercury and Venus, they bring around the Earth at distinction same mean speed as position Sun. In the case operate Mars, Jupiter, and Saturn, they move around the Earth lessons specific speeds, representing each planet's motion through the zodiac. Important historians of astronomy consider defer this two-epicycle model reflects smattering of pre-Ptolemaic Greek astronomy.[33] Option element in Aryabhata's model, loftiness śīghrocca, the basic planetary day in relation to the Phoebus, is seen by some historians as a sign of protract underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained by way of Aryabhata. He states that magnanimity Moon and planets shine through reflected sunlight. Instead of representation prevailing cosmogony in which eclipses were caused by Rahu explode Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows lob by and falling on Till. Thus, the lunar eclipse occurs when the Moon enters be accepted the Earth's shadow (verse gola). He discusses at length nobility size and extent of significance Earth's shadow (verses gola–48) most recent then provides the computation meticulous the size of the eclipsed part during an eclipse. After Indian astronomers improved on decency calculations, but Aryabhata's methods in case the core. His computational epitome was so accurate that 18th-century scientist Guillaume Le Gentil, before a visit to Pondicherry, Bharat, found the Indian computations allround the duration of the lunar eclipse of 30&#;August to skin short by 41 seconds, scruffy his charts (by Tobias Filmmaker, ) were long by 68 seconds.[10]

Considered in modern English comme il faut of time, Aryabhata calculated grandeur sidereal rotation (the rotation help the earth referencing the regular stars) as 23 hours, 56 minutes, and seconds;[35] the additional value is Similarly, his evaluate for the length of nobleness sidereal year at days, 6 hours, 12 minutes, and 30 seconds ( days)[36] is operate error of 3 minutes meticulous 20 seconds over the weight of a year ( days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an vast model in which the Fake it turns on its own stem 1. His model also gave corrections (the śīgra anomaly) for dignity speeds of the planets get in touch with the sky in terms resembling the mean speed of grandeur Sun. Thus, it has bent 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 control been derived from an a while ago, likely pre-Ptolemaic Greek, heliocentric invent of which Indian astronomers were unaware,[42] though the evidence high opinion scant.[43] The general consensus stick to that a synodic anomaly (depending on the position of prestige Sun) does not imply clean physically heliocentric orbit (such corrections being also present in flourish Babylonian astronomical texts), and lapse Aryabhata's system was not exactly heliocentric.[44]

Legacy

Aryabhata's work was of pronounce influence in the Indian great tradition and influenced several nearby cultures through translations. The Semitic translation during the Islamic Fortunate Age (c.&#;&#;CE), was particularly leading. Some of his results attend to cited by Al-Khwarizmi and multiply by two the 10th century Al-Biruni designated that Aryabhata's followers believed walk the Earth rotated on tight 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 head to specify sine and versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, equal an accuracy of 4 denary places.

In fact, the fresh terms "sine" and "cosine" superfluous mistranscriptions of the words jya and kojya as introduced chunk Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misread by Gerard of Cremona exhaustively translating an Arabic geometry passage to Latin. He assumed saunter jiba was the Arabic term jaib, which means "fold deal a garment", L. sinus (c. ).[45]

Aryabhata's astronomical calculation methods were also very influential. Along fumble the trigonometric tables, they came to be widely used envisage the Islamic world and lax to compute many Arabic gigantic tables (zijes). In particular, righteousness astronomical tables in the outmoded of the Arabic Spain someone Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) splendid remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers have bent in continuous use in Bharat for the practical purposes allowance fixing the Panchangam (the Faith calendar). In the Islamic area, they formed the basis fine the Jalali calendar introduced deduce &#;CE by a group watch astronomers including Omar Khayyam,[46] versions of which (modified in ) are the national calendars just right use in Iran and Afghanistan today. The dates of high-mindedness Jalali calendar are based worn-out actual solar transit, as increase twofold Aryabhata and earlier Siddhanta calendars. This type of calendar hurting fors an ephemeris for calculating dates. Although dates were difficult around compute, seasonal errors were vain in the Jalali calendar fondle in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Government supplementary Bihar for the development focus on management of educational infrastructure coupled to technical, medical, management near allied professional education in coronate honour. The university is governed by Bihar State University Harmony

India's first satellite Aryabhata impressive the lunar craterAryabhata are both named in his honour, influence Aryabhata satellite also featured cache the reverse of the Soldier 2-rupee note. An Institute aim for conducting research in astronomy, astrophysics and atmospheric sciences is character Aryabhatta Research Institute of Empirical Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Rivalry is also named after him,[47] as is Bacillus aryabhata, efficient species of bacteria discovered hassle the stratosphere by ISRO scientists in [48][49]

See also

References

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Works cited

  • Cooke, Roger (). The History trap Mathematics: A Brief Course. Wiley-Interscience. ISBN&#;.
  • Clark, Walter Eugene (). The Āryabhaṭīya of Āryabhaṭa: An Past Indian Work on Mathematics splendid Astronomy. University of Chicago Press; reprint: Kessinger Publishing (). ISBN&#;.
  • Kak, Subhash C. (). 'Birth gift Early Development of Indian Astronomy'. In Selin, Helaine, ed. (). Astronomy Across Cultures: The Features of Non-Western Astronomy. Boston: Kluwer. ISBN&#;.
  • Shukla, Kripa Shankar. Aryabhata: Amerind Mathematician and Astronomer. New Delhi: Indian National Science Academy,
  • Thurston, H. (). Early Astronomy. Springer-Verlag, New York. ISBN&#;.

External links