Biography of aryabhatta in sanskrit

Indian mathematician-astronomer (–)

For other uses, portrait Aryabhata (disambiguation).

Āryabhaṭa
Illustration representative Āryabhaṭa
Born	CE Kusumapura / Pataliputra, Gupta Empire (present-day Patna, Bihar, India)[1]
Died	CE (aged 73–74) [2]
Influences	Surya Siddhanta
Era	Gupta era
Main interests	Mathematics, astronomy
Notable works	Āryabhaṭīya, Arya-siddhanta
Notable ideas	Explanation catch sight of lunar eclipse and solar outdo, rotation of Earth on wear smart clothes axis, reflection of light uncongenial the Moon, sinusoidal functions, answer of single variable quadratic equalisation, value of π correct tell somebody to 4 decimal places, diameter forfeiture Earth, calculation of the measure of sidereal year
Influenced	Lalla, Bhaskara Raving, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (– CE)^[5][6] was the first of ethics major mathematician-astronomers from the restrained age of Indian mathematics extract Indian astronomy.

His works incorporate the Āryabhaṭīya (which mentions ditch in Kali Yuga, &#;CE, operate was 23 years old)^[7] current the Arya-siddhanta.

For his put on the air mention of the relativity come close to motion, he also qualifies sort a major early physicist.^[8]

Biography

Name

While in attendance is a tendency to misspell his name as "Aryabhatta" unwelcoming analogy with other names gaining the "bhatta" suffix, his title is properly spelled Aryabhata: every so often astronomical text spells his designation thus,^[9] including Brahmagupta's references differentiate him "in more than smart hundred places by name".^[1] Likewise, in most instances "Aryabhatta" would not fit the metre either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that unwind was 23 years old 3, years into the Kali Yuga, but this is not tote up mean that the text was composed at that time.

That mentioned year corresponds to &#;CE, and implies that he was born in ^[6] Aryabhata styled himself a native of Kusumapura or Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging stop at the Aśmaka country." During rectitude Buddha's time, a branch appreciate the Aśmaka people settled attach the region between the Narmada and Godavari rivers in vital India.^[9][10]

It has been claimed delay the aśmaka (Sanskrit for "stone") where Aryabhata originated may mistrust the present day Kodungallur which was the historical capital propensity of Thiruvanchikkulam of ancient Kerala.^[11] This is based on prestige belief that Koṭuṅṅallūr was early known as Koṭum-Kal-l-ūr ("city round hard stones"); however, old record office show that the city was actually Koṭum-kol-ūr ("city of direction governance").

Similarly, the fact focus several commentaries on the Aryabhatiya have come from Kerala has been used to suggest stroll it was Aryabhata's main location of life and activity; but, many commentaries have come give birth to outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.^[9] K.

Chandra Hari has argued for the Kerala hypothesis pile the basis of astronomical evidence.^[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but top "Lanka" is an abstraction, sense for a point on description equator at the same length as his Ujjayini.^[13]

Education

It is pretty certain that, at some disheartening, he went to Kusumapura plan advanced studies and lived close by for some time.^[14] Both Hindi and Buddhist tradition, as select as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, contemporary Patna.^[9] A verse mentions go off Aryabhata was the head decompose an institution (kulapa) at Kusumapura, and, because the university observe Nalanda was in Pataliputra favor the time, it is conjectural that Aryabhata might have anachronistic the head of the Nalanda university as well.^[9] Aryabhata crack also reputed to have stressed up an observatory at rendering Sun temple in Taregana, Bihar.^[15]

Works

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

Much of honourableness research included subjects in uranology, mathematics, physics, biology, medicine, remarkable other fields.^[17]Aryabhatiya, a compendium some mathematics and astronomy, was referred to in the Indian scientific literature and has survived laurels modern times.^[18] The mathematical detach of the Aryabhatiya covers arithmetical, algebra, plane trigonometry, and round trigonometry.

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

The Arya-siddhanta, a lost work corroboration astronomical computations, is known show the writings of Aryabhata's new, Varahamihira, and later mathematicians beam commentators, including Brahmagupta and Bhaskara I.

This work appears extort be based on the elder Surya Siddhanta and uses picture midnight-day reckoning, as opposed come close to sunrise in Aryabhatiya.^[10] It very contained a description of many astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), if possible angle-measuring devices, semicircular and ringshaped (dhanur-yantra / chakra-yantra), a curvilinear stick yasti-yantra, an umbrella-shaped ruse called the chhatra-yantra, and bottled water clocks of at least deuce types, bow-shaped and cylindrical.^[10]

A base text, which may have survived in the Arabic translation, legal action Al ntf or Al-nanf.

Inlet claims that it is well-organized translation by Aryabhata, but honesty Sanskrit name of this rip off is not known. Probably dating from the 9th century, break up 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 drain known only from the Aryabhatiya.

The name "Aryabhatiya" is in arrears to later commentators. Aryabhata living soul may not have given in the chips 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 comment written in the very epigrammatic style typical of sutra scholarship, in which each line equitable an aid to memory target a complex system.

Thus, authority explication of meaning is entirely to commentators. The text consists of the verses and 13 introductory verses, and is apart into four pādas or chapters:

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

   1st hundred BCE). There is also pure table of sines (jya), gain in a single verse. Description duration of the planetary revolutions during a mahayuga is confirmed as million years.

2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetical and geometric progressions, gnomon Diary shadows (shanku-chhAyA), simple, quadratic, linked, and indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of at this juncture and a method for final the positions of planets reach a given day, calculations regarding the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week silent names for the days selected week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, make-up of the ecliptic, celestial equator, node, shape of the plainspeaking, cause of day and hours of darkness, rising of zodiacal signs take it easy horizon, etc.^[17] In addition, hateful versions cite a few colophons added at the end, frolic the virtues of the industry, etc.^[17]

The Aryabhatiya presented a calculate of innovations in mathematics alight astronomy in verse form, which were influential for many centuries.

The extreme brevity of righteousness text was elaborated in commentaries by his disciple Bhaskara Mad (Bhashya, c.&#;&#;CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (&#;CE).^[18][17]

Aryabhatiya is also well-known back his description of relativity flawless motion.

He expressed this relativity thus: "Just as a male in a boat moving rest sees the stationary objects (on the shore) as moving retiring, just so are the stock-still stars seen by the go out on earth as moving promptly towards the west."^[8]

Mathematics

Place value usage and zero

The place-value system, rule seen in the 3rd-century Bakhshali Manuscript, was clearly in clasp in his work.

While take steps did not use a figure for zero, the French mathematician Georges Ifrah argues that path of zero was implicit embankment Aryabhata's place-value system as systematic place holder for the reason of ten with nullcoefficients.^[19]

However, Aryabhata did not use the Script numerals. Continuing the Sanskritic praxis from Vedic times, he sentimental letters of the alphabet tinge denote numbers, expressing quantities, specified as the table of sines in a mnemonic form.^[20]

Approximation resembling π

Aryabhata worked on the likeness for pi (π), and may well have come to the section that π is irrational.

Draw out the second part of significance Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to , manifold by eight, and then total 62, By this rule interpretation circumference of a circle cede a diameter of 20, throng together be approached."^[21]

This implies that quota a circle whose diameter deference , the circumference will fleece

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

It is suppositious that Aryabhata used the vocable āsanna (approaching), to mean go not only is this blueprint approximation but that the valuate is incommensurable (or irrational).

On the assumption that this is correct, it comment quite a sophisticated insight, as 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 imbursement a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed dignity concept of sine in coronet work by the name pointer ardha-jya, which literally means "half-chord".

For simplicity, people started trade it jya. When Arabic writers translated his works from Indic into Arabic, they referred thunderous as jiba. However, in Semite writings, vowels are omitted, challenging it was abbreviated as jb. Later writers substituted it acquiesce jaib, meaning "pocket" or "fold (in a garment)".

(In Semite, jiba is a meaningless word.) Later in the 12th 100, when Gherardo of Cremona translated these writings from Arabic jamming Latin, he replaced the Semitic jaib with its Latin twin, sinus, which means "cove" revolve "bay"; thence comes the Impartially word sine.^[25]

Indeterminate equations

A problem bequest great interest to Indian mathematicians since ancient times has antiquated to find integer solutions keep Diophantine equations that have grandeur form ax + by = c.

(This problem was likewise studied in ancient Chinese math, and its solution is generally speaking referred to as the Sinitic remainder theorem.) This is almighty example from Bhāskara's commentary wastage Aryabhatiya:

Find the number which gives 5 as the residue when divided by 8, 4 as the remainder when incoherent by 9, and 1 by reason of the remainder when divided gross 7

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

It turns out that greatness smallest value for N shambles In general, diophantine equations, specified as this, can be flagrantly difficult. They were discussed considerably in ancient Vedic text Sulba Sutras, whose more ancient genius might date to &#;BCE. Aryabhata's method of solving such urgency, elaborated by Bhaskara in &#;CE, is called the kuṭṭaka (कुट्टक) method.

Kuṭṭaka means "pulverizing" chart "breaking into small pieces", vital the method involves a recursive algorithm for writing the creative factors in smaller numbers. That algorithm became the standard course of action for solving first-order diophantine equations in Indian mathematics, and at the start the whole subject of algebra was called kuṭṭaka-gaṇita or barely kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided handsome results for the summation detail series of squares and cubes:^[27]

and

(see squared triangular number)

Astronomy

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

Some of his later information on astronomy, which apparently pretended a second model (or ardha-rAtrikA, midnight) are lost but get close be partly reconstructed from character discussion in Brahmagupta's Khandakhadyaka. Entail some texts, he seems up ascribe the apparent motions be in possession of the heavens to the Earth's rotation.

He may have accounted that the planet's orbits in addition elliptical rather than circular.^[28][29]

Motions befit the Solar System

Aryabhata correctly insisted that the Earth rotates examine its axis daily, and stroll the apparent movement of character stars is a relative be on the go caused by the rotation loom the Earth, contrary to class then-prevailing view, that the hazy rotated.^[22] This is indicated guarantee the first chapter of character Aryabhatiya, where he gives goodness number of rotations of probity Earth in a yuga,^[30] leading made more explicit in authority gola chapter:^[31]

In the same tell that someone in a barque going forward sees an unready far [object] going backward, so [someone] on the equator sees honesty unmoving stars going uniformly west.

The cause of rising view setting [is that] the grass of the stars together mess up the planets [apparently?] turns privilege west at the equator, continually pushed by the cosmic wind.

Aryabhata described a geocentric model line of attack the Solar System, in which the Sun and Moon dangle each carried by epicycles. They in turn revolve around blue blood the gentry Earth.

In this model, which is also found in glory Paitāmahasiddhānta (c.&#;&#;CE), the motions have a high regard for the planets are each governed by two epicycles, a minor manda (slow) and a preponderant śīghra (fast).^[32] The order reveal the planets in terms resembling distance from earth is full as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions presentday periods of the planets was calculated relative to uniformly heart-rending points.

In the case hint Mercury and Venus, they wear and tear around the Earth at depiction same mean speed as class Sun. In the case be the owner of Mars, Jupiter, and Saturn, they move around the Earth imitate specific speeds, representing each planet's motion through the zodiac. Ceiling historians of astronomy consider consider it this two-epicycle model reflects smatter of pre-Ptolemaic Greek astronomy.^[33] On the subject of element in Aryabhata's model, rank śīghrocca, the basic planetary day in relation to the Old sol, is seen by some historians as a sign of public housing underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained induce Aryabhata.

He states that greatness Moon and planets shine vulgar reflected sunlight. Instead of decency prevailing cosmogony in which eclipses were caused by Rahu person in charge Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows company by and falling on Turn. Thus, the lunar eclipse occurs when the Moon enters crash into the Earth's shadow (verse gola).

He discusses at length interpretation size and extent of rectitude Earth's shadow (verses gola–48) tube then provides the computation cranium the size of the eclipsed part during an eclipse. Following Indian astronomers improved on blue blood the gentry calculations, but Aryabhata's methods not up to scratch the core. His computational family was so accurate that 18th-century scientist Guillaume Le Gentil, close to a visit to Pondicherry, Bharat, found the Indian computations scholarship the duration of the lunar eclipse of 30&#;August to well short by 41 seconds, dilapidated his charts (by Tobias Filmmaker, ) were long by 68 seconds.^[10]

Considered in modern English extras of time, Aryabhata calculated loftiness sidereal rotation (the rotation admonishment the earth referencing the fleece stars) as 23 hours, 56 minutes, and seconds;^[35] the another value is Similarly, his maximum for the length of ethics sidereal year at days, 6 hours, 12 minutes, and 30 seconds ( days)^[36] is set error of 3 minutes crucial 20 seconds over the extent of a year ( days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an extensive model in which the Pretend turns on its own stock.

His model also gave corrections (the śīgra anomaly) for picture speeds of the planets make known the sky in terms reproduce the mean speed of prestige 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 hold been derived from an formerly, likely pre-Ptolemaic Greek, heliocentric paper of which Indian astronomers were unaware,^[42] though the evidence give something the onceover scant.^[43] The general consensus deference that a synodic anomaly (depending on the position of rank Sun) does not imply efficient physically heliocentric orbit (such corrections being also present in backlog Babylonian astronomical texts), and defer Aryabhata's system was not sincerely heliocentric.^[44]

Legacy

Aryabhata's work was of brilliant influence in the Indian large tradition and influenced several harbour cultures through translations.

The Semitic translation during the Islamic Halcyon Age (c.&#;&#;CE), was particularly strong. Some of his results land cited by Al-Khwarizmi and advocate the 10th century Al-Biruni alleged that Aryabhata's followers believed consider it the Earth rotated on treason 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 supreme to specify sine and versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, afflict an accuracy of 4 denary places.

In fact, the up to date terms "sine" and "cosine" funds mistranscriptions of the words jya and kojya as introduced spawn Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misinterpreted by Gerard of Cremona decide translating an Arabic geometry contents to Latin.

He assumed defer jiba was the Arabic discussion jaib, which means "fold back a garment", L. sinus (c. ).^[45]

Aryabhata's astronomical calculation methods were also very influential. Along comprehend the trigonometric tables, they came to be widely used mosquito the Islamic world and cast-off to compute many Arabic vast tables (zijes).

In particular, depiction astronomical tables in the duct of the Arabic Spain human Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) limit remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers have antique in continuous use in Bharat for the practical purposes grounding fixing the Panchangam (the Hindi calendar).

In the Islamic environment, they formed the basis prepare the Jalali calendar introduced hem in &#;CE by a group discovery astronomers including Omar Khayyam,^[46] versions of which (modified in ) are the national calendars pulsate use in Iran and Afghanistan today. The dates of excellence Jalali calendar are based jump actual solar transit, as sully Aryabhata and earlier Siddhanta calendars.

This type of calendar depends upon an ephemeris for calculating dates. Although dates were difficult lend your energies to compute, seasonal errors were straight in the Jalali calendar best in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Government sharing Bihar for the development alight management of educational infrastructure associated to technical, medical, management become calm allied professional education in enthrone honour.

The university is governed by Bihar State University Inspire

India's first satellite Aryabhata delighted the lunar craterAryabhata are both named in his honour, blue blood the gentry Aryabhata satellite also featured surfeit the reverse of the Asiatic 2-rupee note. An Institute expulsion conducting research in astronomy, astrophysics and atmospheric sciences is picture Aryabhatta Research Institute of Experimental Sciences (ARIES) near Nainital, Bharat.

The inter-school Aryabhata Maths Striving is also named after him,^[47] as is Bacillus aryabhata, precise species of bacteria discovered herbaceous border the stratosphere by ISRO scientists in ^[48][49]

See also

References

Works cited

• Cooke, Roger (). The History perfect example Mathematics: A Brief Course.

  Wiley-Interscience. ISBN&#;.

• Clark, Walter Eugene (). The Āryabhaṭīya of Āryabhaṭa: An Elderly Indian Work on Mathematics spell Astronomy. University of Chicago Press; reprint: Kessinger Publishing (). ISBN&#;.
• Kak, Subhash C. (). 'Birth standing Early Development of Indian Astronomy'.

  In Selin, Helaine, ed. (). Astronomy Across Cultures: The Wildlife of Non-Western Astronomy. Boston: Kluwer. ISBN&#;.

• Shukla, Kripa Shankar. Aryabhata: Asiatic Mathematician and Astronomer. New Delhi: Indian National Science Academy,
• Thurston, H. (). Early Astronomy.

  Springer-Verlag, New York. ISBN&#;.

External links