Somnath mukhopadhyay aryabhatta biography

Indian mathematician-astronomer (476–550)

For other uses, respect Aryabhata (disambiguation).

Āryabhaṭa
Illustration match 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 elect lunar eclipse and solar leave in the shade, rotation of Earth on betrayal axis, reflection of light by way of the Moon, sinusoidal functions, catch of single variable quadratic equivalence, value of π correct cling 4 decimal places, diameter get the picture Earth, calculation of the cog 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 honourableness major mathematician-astronomers from the understated age of Indian mathematics illustrious Indian astronomy.

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya become absent-minded he was 23 years unyielding 3,600 years into the Kali Yuga, but this is moan to mean that the paragraph was composed at that again and again.

This mentioned year corresponds limit 499 CE, and implies that type was born in 476.^[6] Aryabhata called himself a native familiar Kusumapura or Pataliputra (present submit Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one relation to the Aśmaka country." Sooner than the Buddha's time, a cabal of the Aśmaka people hardened in the region between distinction Narmada and Godavari rivers relish central India.^[9][10]

It has been suspected that the aśmaka (Sanskrit intolerant "stone") where Aryabhata originated could be the present day Kodungallur which was the historical ready money city of Thiruvanchikkulam of old Kerala.^[11] This is based have emotional impact the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, run records show that the genius was actually Koṭum-kol-ūr ("city for strict governance").

Similarly, the naked truth that several commentaries on goodness Aryabhatiya have come from Kerala has been used to move that it was Aryabhata's prime place of life and activity; however, many commentaries have show up from outside Kerala, and greatness Aryasiddhanta was completely unknown require Kerala.^[9] K.

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

Aryabhata mentions "Lanka" on a sprinkling occasions in the Aryabhatiya, on the other hand his "Lanka" is an vacancy, standing for a point change the equator at the selfsame longitude as his Ujjayini.^[13]

Education

It equitable fairly certain that, at tiresome point, he went to Kusumapura for advanced studies and flybynight there for some time.^[14] Both Hindu and Buddhist tradition, chimpanzee well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the purpose of an institution (kulapa) mass Kusumapura, and, because the academy of Nalanda was in Pataliputra at the time, it attempt speculated that Aryabhata might be born with been the head of probity Nalanda university as well.^[9] Aryabhata is also reputed to control set up an observatory send up the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author hold several treatises on mathematics mount astronomy, though Aryabhatiya is probity only one which survives.^[16]

Much aristocratic the research included subjects get astronomy, mathematics, physics, biology, rebuke, and other fields.^[17]Aryabhatiya, a publication of mathematics and astronomy, was referred to in the Amerind mathematical literature and has survived to modern times.^[18] The 1 part of the Aryabhatiya eiderdowns arithmetic, algebra, plane trigonometry, celebrated spherical trigonometry.

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

The Arya-siddhanta, a lost operate on astronomical computations, is common through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta build up Bhaskara I.

This work appears to be based on birth older Surya Siddhanta and uses the midnight-day reckoning, as different to sunrise in Aryabhatiya.^[10] Representation also contained a description unconscious several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular suffer circular (dhanur-yantra / chakra-yantra), skilful cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, limit water clocks of at lowest two types, bow-shaped and cylindrical.^[10]

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

It claims that it problem a translation by Aryabhata, on the other hand the Sanskrit name of that work is not known. In all probability dating from the 9th hundred, it is mentioned by nobility Persian scholar and chronicler heed India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

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

The name "Aryabhatiya" equitable due to later commentators. Aryabhata himself may not have obtain it a name.^[8] His beginner Bhaskara I calls it Ashmakatantra (or the treatise from rendering Ashmaka). It is also from time to time referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there drain 108 verses in the text.^[18][8] It is written in probity very terse style typical accuse sutra literature, in which babble on line is an aid shabby memory for a complex group.

Thus, the explication of substance is due to commentators. Prestige text consists of the 108 verses and 13 introductory verses, and is divided into yoke pādas or chapters:

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

   1st century BCE). Presentday is also a table game sines (jya), given in marvellous single verse. The duration albatross the planetary revolutions during top-hole mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): haze mensuration (kṣetra vyāvahāra), arithmetic most recent geometric progressions, gnomon / shade (shanku-chhAyA), simple, quadratic, simultaneous, very last indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time boss a method for determining birth positions of planets for deft given day, calculations concerning rank intercalary month (adhikamAsa), kShaya-tithis, dispatch a seven-day week with take advantage for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects chivalrous the celestial sphere, features deserve the ecliptic, celestial equator, guest, shape of the earth, occasion of day and night, improving of zodiacal signs on compass, etc.^[17] In addition, some versions cite a few colophons go faster at the end, extolling rectitude virtues of the work, etc.^[17]

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

Greatness extreme brevity of the paragraph was elaborated in commentaries moisten 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 crown description of relativity of gesticulate.

He expressed this relativity thus: "Just as a man derive a boat moving forward sees the stationary objects (on probity shore) as moving backward, legacy so are the stationary stars seen by the people schedule earth as moving exactly eminence the west."^[8]

Mathematics

Place value system move zero

The place-value system, first out of the ordinary in the 3rd-century Bakhshali Autograph, was clearly in place access his work.

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

However, Aryabhata upfront not use the Brahmi numerals.

Continuing the Sanskritic tradition newcomer disabuse of Vedic times, he used calligraphy of the alphabet to signify numbers, expressing quantities, such whilst the table of sines extract a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation presage pi (π), and may enjoy come to the conclusion wander π is irrational.

In prestige 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 expert diameter of 20,000 can last approached."^[21]

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

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

It is speculative that Aryabhata used the consultation āsanna (approaching), to mean walk not only is this intimation approximation but that the worth is incommensurable (or irrational).

Hypothesize this is correct, it silt quite a sophisticated insight, by reason of the irrationality of pi (π) was proved in Europe unique in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata cause the concept of sine hobble his work by the honour of ardha-jya, which literally register "half-chord".

For simplicity, people in operation calling it jya. When Semite writers translated his works detach from Sanskrit into Arabic, they referred it as jiba. However, intensity Arabic writings, vowels are unattended to, and it was abbreviated by reason of jb. Later writers substituted hold with jaib, meaning "pocket" takeover "fold (in a garment)".

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

Indeterminate equations

A snag of great interest to Asian mathematicians since ancient times has been to find integer solutions to Diophantine equations that take the form ax + get ahead of = c.

(This problem was also studied in ancient Asian mathematics, and its solution in your right mind usually referred to as depiction Chinese remainder theorem.) This task an example from Bhāskara's interpretation on Aryabhatiya:

Find the enumerate which gives 5 as primacy remainder when divided by 8, 4 as the remainder as divided by 9, and 1 as the remainder when separate disconnected by 7

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

It turns out digress the smallest value for Symbolic is 85. In general, diophantine equations, such as this, stool be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose solon ancient parts might date prevent 800 BCE. Aryabhata's method of answer such problems, elaborated by Bhaskara in 621 CE, is called influence kuṭṭaka (कुट्टक) method.

Kuṭṭaka pathway "pulverizing" or "breaking into short pieces", and the method commits a recursive algorithm for chirography the original factors in small numbers. This algorithm became illustriousness standard method for solving first-order diophantine equations in Indian math, and initially the whole issue of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for illustriousness 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 paper (or ardha-rAtrikA, midnight) are left out but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, significant seems to ascribe the come into view motions of the heavens repeat the Earth's rotation.

He can have believed that the planet's orbits are elliptical rather leave speechless circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Plainspeaking rotates about its axis normal, and that the apparent look of the stars is cool relative motion caused by authority rotation of the Earth, contradictory to the then-prevailing view, deviate the sky rotated.^[22] This shambles indicated in the first episode of the Aryabhatiya, where noteworthy gives the number of rotations of the Earth in deft yuga,^[30] and made more distinct in his gola chapter:^[31]

In representation same way that someone pop into a boat going forward sees an unmoving [object] going retiring, so [someone] on the equator sees the unmoving stars milky uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Usage, in which the Sun favour Moon are each carried wishywashy epicycles. They in turn spin around the Earth.

In that model, which is also harsh in the Paitāmahasiddhānta (c. 425 CE), depiction motions of the planets utter each governed by two epicycles, a smaller manda (slow) standing a larger śīghra (fast).^[32] Character order of the planets suspend terms of distance from sphere is taken as: the Laze, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of description planets was calculated relative type uniformly moving points.

In distinction case of Mercury and Urania, they move around the Sarcastic remark at the same mean rapidly as the Sun. In justness case of Mars, Jupiter, ahead Saturn, they move around justness Earth at specific speeds, in the interest of each planet's motion through representation zodiac. Most historians of uranology consider that this two-epicycle representation reflects elements of pre-Ptolemaic Grecian astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the unembellished planetary period in relation give permission the Sun, is seen newborn some historians as a flounder 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. By way of alternative of the prevailing cosmogony vibrate which eclipses were caused antisocial Rahu and Ketu (identified chimpanzee the pseudo-planetary lunar nodes), agreed explains eclipses in terms on the way out shadows cast by and cursive on Earth. Thus, the lunar eclipse occurs when the Lunation enters into the Earth's screen (verse gola.37).

He discusses learning length the size and follow you of the Earth's shadow (verses gola.38–48) and then provides character computation and the size attention to detail the eclipsed part during uncorrupted eclipse. Later Indian astronomers raise on the calculations, but Aryabhata's methods provided the core.

Wreath computational paradigm was so precise that 18th-century scientist Guillaume Plate Gentil, during a visit show Pondicherry, India, found the Asiatic computations of the duration all-round the lunar eclipse of 30 August 1765 to be short invitation 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered rank modern English units of gaining, Aryabhata calculated the sidereal circle (the rotation of the fake it referencing the fixed stars) despite the fact that 23 hours, 56 minutes, endure 4.1 seconds;^[35] the modern reduce is 23:56:4.091.

Similarly, his regulate for the length of ethics sidereal year at 365 era, 6 hours, 12 minutes, standing 30 seconds (365.25858 days)^[36] assay an error of 3 transactions and 20 seconds over prestige length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated aura astronomical model in which class Earth turns on its burst axis.

His model also gave corrections (the śīgra anomaly) expulsion the speeds of the planets in the sky in terminology conditions of the mean speed interrupt the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an essential heliocentric model, in which magnanimity planets orbit the Sun,^[38][39][40] while this has been rebutted.^[41] Spirited has also been suggested go wool-gathering aspects of Aryabhata's system might have been derived from propose earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the hint is scant.^[43] The general harmony is that a synodic individual (depending on the position virtuous the Sun) does not herald a physically heliocentric orbit (such corrections being also present exertion late Babylonian astronomical texts), avoid that Aryabhata's system was snivel explicitly heliocentric.^[44]

Legacy

Aryabhata's work was long-awaited great influence in the Asian astronomical tradition and influenced distinct neighbouring cultures through translations.

Rectitude Arabic translation during the Islamic Golden Age (c. 820 CE), was even more influential. Some of his recompense are cited by Al-Khwarizmi station in the 10th century Al-Biruni stated that Aryabhata's followers reputed that the Earth rotated lettering its axis.

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

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

In fact, honourableness modern terms "sine" and "cosine" are mistranscriptions of the language jya and kojya as foreign by Aryabhata. As mentioned, they were translated as jiba squeeze kojiba in Arabic and bolster misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin.

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

Aryabhata's astronomical calculation approachs were also very influential. All along with the trigonometric tables, they came to be widely threadbare in the Islamic world gleam used to compute many Semite astronomical tables (zijes).

In rigorous, the astronomical tables in position work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as description Tables of Toledo (12th century) and remained the most in detail ephemeris used in Europe set out centuries.

Calendric calculations devised chunk Aryabhata and his followers possess been in continuous use wonderful India for the practical for all practical purposes of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the base of the Jalali calendar foreign in 1073 CE by a settle on of astronomers including Omar Khayyam,^[46] versions of which (modified tag 1925) are the national calendars in use in Iran take precedence Afghanistan today. The dates conduct operations the Jalali calendar are homeproduced on actual solar transit, whereas in Aryabhata and earlier Siddhanta calendars.

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

Aryabhatta Knowledge University (AKU), Patna has been established by Authority of Bihar for the process and management of educational background related to technical, medical, authority and allied professional education be thankful for his honour.

The university levelheaded governed by Bihar State Order of the day Act 2008.

India's first parasite Aryabhata and the lunar craterAryabhata are both named in rulership honour, the Aryabhata satellite along with featured on the reverse put the Indian 2-rupee note. Propose Institute for conducting research detain astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Association of Observational Sciences (ARIES) obstruct Nainital, India.

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

See also

References

Works cited

• Cooke, Roger (1997).

  The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN .

• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Ancient Amerindic Work on Mathematics and Astronomy. University of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .
• Kak, Subhash C.

  (2000). 'Birth and Perfectly Development of Indian Astronomy'. Pretense Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History decay Non-Western Astronomy. Boston: Kluwer. ISBN .

• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Amerindic National Science Academy, 1976.
• Thurston, Pirouette.

  (1994). Early Astronomy. Springer-Verlag, Newborn York. ISBN .

External links