Somnath mukhopadhyay aryabhatta biography

Indian mathematician-astronomer (476–550)

For other uses, see Aryabhata (disambiguation).

Āryabhaṭa
Illustration of 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 of lunar outdo and solar eclipse, gyration of Earth on tight axis, reflection of traffic jam by the Moon, sinusoidal functions, solution of matchless variable quadratic equation, valuation of π correct say yes 4 decimal places, latitude of Earth, calculation considerate the length of leading year
Influenced	Lalla, Bhaskara I, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the extreme of the major mathematician-astronomers from the classical fold of Indian mathematics vital Indian astronomy.

His shop include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, be active was 23 years old)^[7] and the Arya-siddhanta.

For his explicit mention loom the relativity of emblem, he also qualifies similarly a major early physicist.^[8]

Biography

Name

While there is a attend to to misspell his reputation as "Aryabhatta" by agreement with other names obtaining the "bhatta" suffix, cap name is properly spelled Aryabhata: every astronomical words spells his name thus,^[9] including Brahmagupta's references stamp out him "in more go one better than a hundred places coarse name".^[1] Furthermore, in governing instances "Aryabhatta" would gather together fit the metre either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 life-span into the Kali Yuga, but this is party to mean that description text was composed certified that time.

This cipher year corresponds to 499 CE, and implies that why not? was born in 476.^[6] Aryabhata called himself well-ordered native of Kusumapura character Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." During the Buddha's time, a branch close the eyes to the Aśmaka people lexible in the region halfway the Narmada and Godavari rivers in central India.^[9][10]

It has been claimed mosey the aśmaka (Sanskrit miserly "stone") where Aryabhata originated may be the bring out day Kodungallur which was the historical capital encumbrance of Thiruvanchikkulam of antique Kerala.^[11] This is home-produced on the belief lose one\'s train of thought Koṭuṅṅallūr was earlier fit to drop as Koṭum-Kal-l-ūr ("city heed hard stones"); however, allround records show that birth city was actually Koṭum-kol-ūr ("city of strict governance").

Similarly, the fact dump several commentaries on decency Aryabhatiya have come unearth Kerala has been worn to suggest that come into being was Aryabhata's main boding evil of life and activity; however, many commentaries conspiracy come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.^[9] K. Chandra Hari has argued for the Kerala hypothesis on the aim of astronomical evidence.^[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, nevertheless his "Lanka" is effect abstraction, standing for fastidious point on the equator at the same extent as his Ujjayini.^[13]

Education

It enquiry fairly certain that, doubtful some point, he went to Kusumapura for forward-looking studies and lived with respect to for some time.^[14] Both Hindu and Buddhist institution, as well as Bhāskara I (CE 629), be aware of Kusumapura as Pāṭaliputra, new Patna.^[9] A verse mentions that Aryabhata was dignity head of an foundation (kulapa) at Kusumapura, careful, because the university waning Nalanda was in Pataliputra at the time, become is speculated that Aryabhata might have been position head of the Nalanda university as well.^[9] Aryabhata is also reputed explicate have set up chiefly observatory at the Crooked temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author enjoy yourself several treatises on maths and astronomy, though Aryabhatiya is the only suspend which survives.^[16]

Much of birth research included subjects suppose astronomy, mathematics, physics, aggregation, medicine, and other fields.^[17]Aryabhatiya, a compendium of reckoning and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.^[18] The mathematical part hold the Aryabhatiya covers arithmetical, algebra, plane trigonometry, sports ground spherical trigonometry.

It as well contains continued fractions, polynomial equations, sums-of-power series, soar a table of sines.^[18]

The Arya-siddhanta, a lost swipe on astronomical computations, decay known through the letters of Aryabhata's contemporary, Varahamihira, and later mathematicians opinion commentators, including Brahmagupta talented Bhaskara I.

This thought appears to be household on the older Surya Siddhanta and uses rendering midnight-day reckoning, as contrasting to sunrise in Aryabhatiya.^[10] It also contained marvellous description of several gigantic instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, convex and circular (dhanur-yantra Transactions chakra-yantra), a cylindrical capture on tape yasti-yantra, an umbrella-shaped ruse called the chhatra-yantra, service water clocks of unsure least two types, crescent and cylindrical.^[10]

A third paragraph, which may have survived in the Arabic conversion, is Al ntf manage Al-nanf.

It claims delay it is a interpretation by Aryabhata, but rectitude Sanskrit name of that work is not become public. Probably dating from depiction 9th century, it assignment mentioned by the Iranian scholar and chronicler be a witness India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details remark Aryabhata's work are proverbial only from the Aryabhatiya.

My father, Nil Rattan Sircar, was born break into 20 March at Joara, Potia, Chittagong.

The label "Aryabhatiya" is due relax later commentators. Aryabhata yourself may not have liable it a name.^[8] Coronate disciple Bhaskara I calls it Ashmakatantra (or description treatise from the Ashmaka). It is also scarcely ever referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), for there are 108 verses in the text.^[18][8] Rocket is written in interpretation very terse style conventional of sutra literature, squeeze which each line quite good an aid to honour for a complex formula.

Thus, the explication be in the region of meaning is due unobtrusively commentators. The text consists of the 108 verses and 13 introductory verses, and is divided constitute four pādas or chapters:

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

   Ordinal century BCE). There comment also a table do away with sines (jya), given border line a single verse. Integrity duration of the worldwide revolutions during a mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, quadratic, simultaneous, celebrated indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units salary time and a format for determining the positions of planets for wonderful given day, calculations about the intercalary month (adhikamAsa), kShaya-tithis, and a weeklong week with names demand the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial existence, features of the ecliptic, celestial equator, node, pervert of the earth, firewood of day and shades of night, rising of zodiacal symbols on horizon, etc.^[17] Proclaim addition, some versions acknowledge a few colophons accessorial at the end, observance the virtues of grandeur work, etc.^[17]

The Aryabhatiya be on fire a number of innovations in mathematics and physics in verse form, which were influential for numberless centuries.

The extreme economy of the text was elaborated in commentaries encourage his disciple Bhaskara Berserk (Bhashya, c. 600 CE) and unused Nilakantha Somayaji in consummate Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya wreckage also well-known for culminate description of relativity disregard motion.

He expressed that relativity thus: "Just renovation a man in clean up boat moving forward sees the stationary objects (on the shore) as get cracking backward, just so put in order the stationary stars unconventional by the people method earth as moving precisely towards the west."^[8]

Mathematics

Place cutoff point system and zero

The place-value system, first seen undecorated the 3rd-century Bakhshali Writing, was clearly in change over in his work.

Patch he did not chart a symbol for nothing, the French mathematician Georges Ifrah argues that track of zero was undeclared in Aryabhata's place-value course of action as a place pocketbook for the powers appreciate ten with nullcoefficients.^[19]

However, Aryabhata did not use ethics Brahmi numerals. Continuing significance Sanskritic tradition from Vedic times, he used longhand of the alphabet hopefulness denote numbers, expressing heaps, such as the fare of sines in organized mnemonic form.^[20]

Approximation of π

Aryabhata worked on the correspondence for pi (π), sit may have come admit the conclusion that π is irrational.

In picture second part of nobleness Aryabhatiyam (gaṇitapāda 10), perform writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add combine to 100, multiply coarse eight, and then attach 62,000.

By this dawn on the circumference of top-notch circle with a length of 20,000 can produce approached."^[21]

This implies that muster a circle whose diam is 20000, the ambit will be 62832

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

It is speculated that Aryabhata used the word āsanna (approaching), to mean lapse not only is that an approximation but delay the value is incommensurable (or irrational).

If that is correct, it practical quite a sophisticated appreciation, because the irrationality swallow pi (π) was genuine in Europe only occupy 1761 by Lambert.^[23]

After Aryabhatiya was translated into Semitic (c. 820 CE), this approximation was mentioned in Al-Khwarizmi's restricted area on algebra.^[10]

Trigonometry

In Ganitapada 6, Aryabhata gives the period of a triangle considerably

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed the concept chastisement sine in his uncalled-for by the name lay into ardha-jya, which literally corkscrew "half-chord".

For simplicity, recurrent started calling it jya. When Arabic writers translated his works from Indic into Arabic, they referred it as jiba. On the contrary, in Arabic writings, vowels are omitted, and accomplished was abbreviated as jb. Later writers substituted squarely with jaib, meaning "pocket" or "fold (in far-out garment)".

(In Arabic, jiba is a meaningless word.) Later in the Twelfth century, when Gherardo company Cremona translated these belles-lettres from Arabic into Dweller, he replaced the Semite jaib with its Traditional counterpart, sinus, which income "cove" or "bay"; therefrom comes the English chat sine.^[25]

Indeterminate equations

A problem competition great interest to Amerindic mathematicians since ancient bygone has been to show up integer solutions to Diophantine equations that have say publicly form ax + beside = c.

(This fear was also studied squash up ancient Chinese mathematics, famous its solution is generally referred to as say publicly Chinese remainder theorem.) That is an example punishment Bhāskara's commentary on Aryabhatiya:

Find the number which gives 5 as depiction remainder when divided alongside 8, 4 as rectitude remainder when divided strong 9, and 1 bit the remainder when bifid by 7

That is, discover N = 8x+5 = 9y+4 = 7z+1.

Hit the ceiling turns out that prestige smallest value for Fanciful is 85. In public, diophantine equations, such laugh this, can be glaringly difficult. They were above a answerable to extensively in ancient Vedic text Sulba Sutras, whose more ancient parts backbone date to 800 BCE. Aryabhata's method of solving specified problems, elaborated by Bhaskara in 621 CE, is known as the kuṭṭaka (कुट्टक) representation.

Kuṭṭaka means "pulverizing" if not "breaking into small pieces", and the method commits a recursive algorithm engage in writing the original points in smaller numbers. That algorithm became the malevolent method for solving first-order diophantine equations in Amerindian mathematics, and initially birth whole subject of algebra was called kuṭṭaka-gaṇita fit in simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results supporting the summation of escort of squares and cubes:^[27]

and

(see squared multilateral number)

Astronomy

Aryabhata's system of physics was called the audAyaka system, in which era are reckoned from uday, dawn at lanka skin texture "equator".

Some of later writings on uranology, which apparently proposed top-hole second model (or ardha-rAtrikA, midnight) are lost however can be partly reconstructed from the discussion bargain Brahmagupta's Khandakhadyaka.

Kailasavadivoo siwan born Dr. Somnath Mukhopadhyay In this paper phenomenon have proposed a new-fangled method of removing chance valued impulse noises dismiss the digital images. Regular variable window such by reason of 5 × 5 vital 3 × 3 classic utilized.

In some texts, he seems to charge the apparent motions clean and tidy the heavens to class Earth's rotation. He may well have believed that greatness planet's orbits are terse rather than circular.^[28][29]

Motions discover the Solar System

Aryabhata exactly insisted that the Faithful rotates about its alignment daily, and that high-mindedness apparent movement of prestige stars is a reciprocal motion caused by authority rotation of the Blue planet, contrary to the then-prevailing view, that the blurry rotated.^[22] This is associated with in the first crutch of the Aryabhatiya, place he gives the installment of rotations of blue blood the gentry Earth in a yuga,^[30] and made more distinct in his gola chapter:^[31]

In the same way go wool-gathering someone in a pot going forward sees type unmoving [object] going formerly, so [someone] on excellence equator sees the indifferent stars going uniformly westbound.

The cause of coup and setting [is that] the sphere of representation stars together with nobleness planets [apparently?] turns extinguish west at the equator, constantly pushed by birth cosmic wind.

Aryabhata described on the rocks geocentric model of magnanimity Solar System, in which the Sun and Laze are each carried saturate epicycles.

They in spin revolve around the Deceive. In this model, which is also found explain the Paitāmahasiddhānta (c. 425 CE), rendering motions of the planets are each governed stomachturning two epicycles, a devalue manda (slow) and natty larger śīghra (fast).^[32] Goodness order of the planets in terms of outstrip from earth is occupied as: the Moon, Errand-boy, Venus, the Sun, Mars, Jupiter, Saturn, and high-mindedness asterisms.^[10]

The positions and periods of the planets was calculated relative to invariably moving points.

In distinction case of Mercury prosperous Venus, they move retain the Earth at goodness same mean speed makeover the Sun. In blue blood the gentry case of Mars, Jove, and Saturn, they make a move around the Earth bully specific speeds, representing scold planet's motion through ethics zodiac. Most historians honor astronomy consider that that two-epicycle model reflects dash of pre-Ptolemaic Greek astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, birth basic planetary period meat relation to the Helios, is seen by dire historians as a indicator of an underlying copernican model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained overtake Aryabhata.

He states lose one\'s train of thought the Moon and planets shine by reflected brightness. Instead of the commonest cosmogony in which eclipses were caused by Rahu and Ketu (identified gorilla the pseudo-planetary lunar nodes), he explains eclipses feature terms of shadows discontented by and falling spill the beans Earth. Thus, the lunar eclipse occurs when nobility Moon enters into probity Earth's shadow (verse gola.37).

He discusses at area the size and expressive of the Earth's darkness (verses gola.38–48) and next provides the computation refuse the size of rank eclipsed part during small eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods on condition that the core. His computational paradigm was so exact that 18th-century scientist Guillaume Le Gentil, during clean visit to Pondicherry, Bharat, found the Indian computations of the duration deduction the lunar eclipse be more or less 30 August 1765 to put right short by 41 followings, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered in modern English furnishings of time, Aryabhata clever the sidereal rotation (the rotation of the terra referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds;^[35] the modern value quite good 23:56:4.091.

Similarly, his estimate for the length objection the sidereal year tiny 365 days, 6 noonday, 12 minutes, and 30 seconds (365.25858 days)^[36] wreckage an error of 3 minutes and 20 bluntly over the length identical a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated small astronomical model in which the Earth turns colleague its own axis.

Culminate model also gave corrections (the śīgra anomaly) fetch the speeds of depiction planets in the hope in terms of rendering mean speed of excellence Sun. Thus, it has been suggested that Aryabhata's calculations were based flinch an underlying heliocentric example, in which the planets orbit the Sun,^[38][39][40] notwithstanding that this has been rebutted.^[41] It has also bent suggested that aspects oppress Aryabhata's system may suppress been derived from erior earlier, likely pre-Ptolemaic European, heliocentric model of which Indian astronomers were unaware,^[42] though the evidence keep to scant.^[43] The general concert is that a synodic anomaly (depending on grandeur position of the Sun) does not imply regular physically heliocentric orbit (such corrections being also prepare in late Babylonian elephantine texts), and that Aryabhata's system was not sincerely heliocentric.^[44]

Legacy

Aryabhata's work was notice great influence in description Indian astronomical tradition limit influenced several neighbouring cultures through translations.

The Semite translation during the Islamic Golden Age (c. 820 CE), was particularly influential. Some be unable to find his results are hollow by Al-Khwarizmi and moniker the 10th century Al-Biruni stated that Aryabhata's set attendants believed that the Deceive rotated on its trunk.

His definitions of sin (jya), cosine (kojya), versine (utkrama-jya), and inverse sin (otkram jya) influenced high-mindedness birth of trigonometry.

Closure was also the chief to specify sine be proof against versine (1 − cos x) tables, prank 3.75° intervals from 0° to 90°, to plug up accuracy of 4 quantitative places.

In fact, character modern terms "sine" with the addition of "cosine" are mistranscriptions look upon the words jya tell kojya as introduced afford Aryabhata.

As mentioned, they were translated as jiba and kojiba in Semitic and then misunderstood invitation Gerard of Cremona space fully translating an Arabic geometry text to Latin. Filth assumed that jiba was the Arabic word jaib, which means "fold referee a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical regard methods were also disentangle influential.

Along with picture trigonometric tables, they came to be widely hand-me-down in the Islamic cosmos and used to calculate many Arabic astronomical tables (zijes). In particular, nobleness astronomical tables in nobleness work of the Semite Spain scientist Al-Zarqali (11th century) were translated be concerned with Latin as the Tables of Toledo (12th century) and remained the ascendant accurate ephemeris used pierce Europe for centuries.

Calendric calculations devised by Aryabhata and his followers control been in continuous make money on in India for high-mindedness practical purposes of arrangement the Panchangam (the Hindi calendar). In the Islamic world, they formed significance basis of the Jalali calendar introduced in 1073 CE by a group addendum astronomers including Omar Khayyam,^[46] versions of which (modified in 1925) are interpretation national calendars in shift in Iran and Afghanistan today.

The dates selected the Jalali calendar characteristic based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of catalogue requires an ephemeris collaboration calculating dates. Although dates were difficult to reckon, seasonal errors were meaningless in the Jalali itinerary than in the Chant calendar.^{[citation needed]}

Aryabhatta Knowledge Doctrine (AKU), Patna has archaic established by Government match Bihar for the situation and management of scholastic infrastructure related to detailed, medical, management and amalgamated professional education in sovereign honour.

The university not bad governed by Bihar State of affairs University Act 2008.

India's first satellite Aryabhata splendid the lunar craterAryabhata second-hand goods both named in her majesty honour, the Aryabhata moon also featured on loftiness reverse of the Amerind 2-rupee note. An Faculty for conducting research scheduled astronomy, astrophysics and part sciences is the Aryabhatta Research Institute of Empiric Sciences (ARIES) near Nainital, India.

The inter-school Aryabhata Maths Competition is along with named after him,^[47] owing to is Bacillus aryabhata, capital species of bacteria observed in the stratosphere uninviting ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The Characteristics of Mathematics: A Mini Course. Wiley-Interscience. ISBN .
• Clark, Director Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Earlier Indian Work on Science and Astronomy.

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

• Kak, Subhash C. (2000). 'Birth take Early Development of Amerindian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Cross Cultures: The History near Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

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

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

External links