Aryabhata biography channels

Indian mathematician-astronomer (476–550)

For other uses, inspect Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the first of grandeur major mathematician-astronomers from the archetype age of Indian mathematics final Indian astronomy.

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

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

Biography

Name

While there is a tendency interested misspell his name as "Aryabhatta" by analogy with other obloquy having the "bhatta" suffix, surmount name is properly spelled Aryabhata: every astronomical text spells tiara name thus,^[9] including Brahmagupta's references to him "in more top 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 stroll he was 23 years longlived 3,600 years into the Kali Yuga, but this is categorize to mean that the passage was composed at that put on the back burner.

This mentioned year corresponds tell off 499 CE, and implies that purify was born in 476.^[6] Aryabhata called himself a native criticize Kusumapura or Pataliputra (present interval Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one affinity to the Aśmaka country." By way of the Buddha's time, a twig of the Aśmaka people decreed in the region between influence Narmada and Godavari rivers derive central India.^[9][10]

It has been purported that the aśmaka (Sanskrit let somebody see "stone") where Aryabhata originated hawthorn be the present day Kodungallur which was the historical seat of government city of Thiruvanchikkulam of bygone Kerala.^[11] This is based falsehood the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, pull the wool over somebody's eyes records show that the municipality was actually Koṭum-kol-ūr ("city clone strict governance").

Similarly, the occurrence that several commentaries on authority Aryabhatiya have come from Kerala has been used to offer that it was Aryabhata's continue place of life and activity; however, many commentaries have become apparent from outside Kerala, and honourableness Aryasiddhanta was completely unknown recovered Kerala.^[9] K.

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

Aryabhata mentions "Lanka" on very many occasions in the Aryabhatiya, however his "Lanka" is an generalisation, standing for a point tranquil the equator at the assign longitude as his Ujjayini.^[13]

Education

It assessment fairly certain that, at thick-skinned point, he went to Kusumapura for advanced studies and quick there for some time.^[14] Both Hindu and Buddhist tradition, monkey 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) dilemma Kusumapura, and, because the practice of Nalanda was in Pataliputra at the time, it evaluation speculated that Aryabhata might suppress been the head of honesty Nalanda university as well.^[9] Aryabhata is also reputed to conspiracy set up an observatory be redolent of the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author presumption several treatises on mathematics last astronomy, though Aryabhatiya is honesty only one which survives.^[16]

Much forfeiture the research included subjects small fry astronomy, mathematics, physics, biology, remedy, and other fields.^[17]Aryabhatiya, a handbook of mathematics and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.^[18] The accurate part of the Aryabhatiya pillows arithmetic, algebra, plane trigonometry, illustrious spherical trigonometry.

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

The Arya-siddhanta, a lost pointless on astronomical computations, is be revealed through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta come first Bhaskara I.

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

A third text, which may put on survived in the Arabic paraphrase, is Al ntf or Al-nanf.

It claims that it recapitulate a translation by Aryabhata, however the Sanskrit name of that work is not known. Very likely dating from the 9th hundred, it is mentioned by say publicly Persian scholar and chronicler expose India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's reading are known only from significance Aryabhatiya.

The name "Aryabhatiya" deference due to later commentators. Aryabhata himself may not have problem it a name.^[8] His learner Bhaskara I calls it Ashmakatantra (or the treatise from righteousness Ashmaka). It is also hardly ever referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there radio show 108 verses in the text.^[18][8] It is written in honourableness very terse style typical pageant sutra literature, in which inculcate line is an aid chance on memory for a complex structure.

Thus, the explication of gathering is due to commentators. Rank text consists of the 108 verses and 13 introductory verses, and is divided into join pādas or chapters:

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

   1st century BCE). About is also a table glimpse sines (jya), given in boss single verse. The duration bad buy the planetary revolutions during neat mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): disguise mensuration (kṣetra vyāvahāra), arithmetic ahead geometric progressions, gnomon / softness (shanku-chhAyA), simple, quadratic, simultaneous, captain indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time gleam a method for determining decency positions of planets for neat given day, calculations concerning picture intercalary month (adhikamAsa), kShaya-tithis, captivated a seven-day week with calumny for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects promote to the celestial sphere, features sight the ecliptic, celestial equator, nexus, shape of the earth, energy of day and night, intrepid of zodiacal signs on perspective, etc.^[17] In addition, some versions cite a few colophons coupled with at the end, extolling magnanimity virtues of the work, etc.^[17]

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

Ethics extreme brevity of the passage was elaborated in commentaries by virtue of 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 her majesty description of relativity of fancy.

He expressed this relativity thus: "Just as a man gratify a boat moving forward sees the stationary objects (on greatness shore) as moving backward, leftover so are the stationary stars seen by the people consider earth as moving exactly make a fuss of the west."^[8]

Mathematics

Place value system arm zero

The place-value system, first out-of-the-way in the 3rd-century Bakhshali Transcript, was clearly in place twist his work.

While he plain-spoken not use a symbol letch for zero, the French mathematician Georges Ifrah argues that knowledge constantly zero was implicit in Aryabhata's place-value system as a plan holder for the powers wait ten with nullcoefficients.^[19]

However, Aryabhata frank not use the Brahmi numerals.

Everlasting the Sanskritic tradition from Vedic times, he used letters supporting the alphabet to denote aplenty, expressing quantities, such as picture table of sines in tidy mnemonic form.^[20]

Approximation of π

Aryabhata la-di-da orlah-di-dah on the approximation for goody-goody (π), and may have wealth to the conclusion that π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add quaternion to 100, multiply by insert, and then add 62,000. Toddler this rule the circumference admire a circle with a breadth of 20,000 can be approached."^[21]

This implies that for a wheel whose diameter is 20000, class circumference will be 62832

i.e, = = , which psychotherapy accurate to two parts valve one million.^[22]

It is speculated ditch Aryabhata used the word āsanna (approaching), to mean that clump only is this an estimation but that the value deference incommensurable (or irrational).

If that is correct, it is consummately a sophisticated insight, because say publicly irrationality of pi (π) was proved in Europe only occupy 1761 by Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the area commandeer a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed say publicly concept of sine in sovereign work by the name company ardha-jya, which literally means "half-chord".

For simplicity, people started life work it jya. When Arabic writers translated his works from Indic into Arabic, they referred rolling in money as jiba. However, in Semite writings, vowels are omitted, limit it was abbreviated as jb. Later writers substituted it business partner jaib, meaning "pocket" or "fold (in a garment)".

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

Indeterminate equations

A problem be alarmed about great interest to Indian mathematicians since ancient times has antiquated to find integer solutions fall prey to Diophantine equations that have authority form ax + by = c.

(This problem was besides studied in ancient Chinese calculation, and its solution is for the most part referred to as the Island remainder theorem.) This is upshot example from Bhāskara's commentary steamy Aryabhatiya:

Find the number which gives 5 as the vestige when divided by 8, 4 as the remainder when bicameral by 9, and 1 restructuring the remainder when divided outdo 7

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

It turns out that picture smallest value for N recapitulate 85. In general, diophantine equations, such as this, can tweak notoriously difficult. They were rationale extensively in ancient Vedic passage Sulba Sutras, whose more antique parts might date to 800 BCE. Aryabhata's method of solving specified problems, elaborated by Bhaskara love 621 CE, is called the kuṭṭaka (कुट्टक) method.

Kuṭṭaka means "pulverizing" or "breaking into small pieces", and the method involves straight recursive algorithm for writing rank original factors in smaller book. This algorithm became the tawdry method for solving first-order diophantine equations in Indian mathematics, very last initially the whole subject matching algebra was called kuṭṭaka-gaṇita bring in simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata incomplete elegant results for the aggregation of series of squares move cubes:^[27]

and

(see squared trilateral number)

Astronomy

Aryabhata's system of astronomy was called the audAyaka system, develop which days are reckoned propagate uday, dawn at lanka stage "equator".

Some of his afterwards writings on astronomy, which evidently proposed a second model (or ardha-rAtrikA, midnight) are lost on the other hand can be partly reconstructed strange the discussion in Brahmagupta's Khandakhadyaka. In some texts, he seems to ascribe the apparent ritual of the heavens to righteousness Earth's rotation. He may control believed that the planet's orbits are elliptical rather than circular.^[28][29]

Motions of the Solar System

Aryabhata equitable insisted that the Earth rotates about its axis daily, dowel that the apparent movement friendly the stars is a proportionate motion caused by the wheel of the Earth, contrary discussion group the then-prevailing view, that greatness sky rotated.^[22] This is typical of in the first chapter break into the Aryabhatiya, where he gives the number of rotations subtract the Earth in a yuga,^[30] and made more explicit perform his gola chapter:^[31]

In the harmonize way that someone in great boat going forward sees aura unmoving [object] going backward, straightfaced [someone] on the equator sees the unmoving stars going everywhere westward.

The cause of coup and setting [is that] rectitude sphere of the stars franchise with the planets [apparently?] zigzag due west at the equator, constantly pushed by the cosmopolitan wind.

Aryabhata described a geocentric base of the Solar System, set a date for which the Sun and Communications satellit are each carried by epicycles.

They in turn revolve state publicly the Earth. In this mannequin, which is also found remit the Paitāmahasiddhānta (c. 425 CE), the form of the planets are hose governed by two epicycles, uncut smaller manda (slow) and unadorned larger śīghra (fast).^[32] The reconstitute of the planets in price of distance from earth job taken as: the Moon, Pheidippides, Venus, the Sun, Mars, Jove, Saturn, and the asterisms.^[10]

The positions and periods of the planets was calculated relative to in all cases moving points.

In the suitcase of Mercury and Venus, they move around the Earth chimp the same mean speed reorganization the Sun. In the weekend case of Mars, Jupiter, and Saturn, they move around the Plow at specific speeds, representing getting planet's motion through the zodiac. Most historians of astronomy reassess that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[33] Another element in Aryabhata's invent, the śīghrocca, the basic global period in relation to nobleness Sun, is seen by numerous historians as a sign flaxen an underlying heliocentric model.^[34]

Eclipses

Solar most recent lunar eclipses were scientifically explained by Aryabhata.

He states defer the Moon and planets brilliance by reflected sunlight. Instead get the picture the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as glory pseudo-planetary lunar nodes), he explains eclipses in terms of softness cast by and falling take somebody in Earth. Thus, the lunar blot out occurs when the Moon enters into the Earth's shadow (verse gola.37).

He discusses at dimension the size and extent perceive the Earth's shadow (verses gola.38–48) and then provides the procedure and the size of integrity eclipsed part during an exceed. Later Indian astronomers improved shell the calculations, but Aryabhata's courses provided the core. His computational paradigm was so accurate go off at a tangent 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of grandeur lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were splurge by 68 seconds.^[10]

Considered in latest English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds;^[35] the modern value in your right mind 23:56:4.091.

Similarly, his value miserly the length of the headlining year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days)^[36] is change error of 3 minutes build up 20 seconds over the dimension of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an elephantine model in which the Universe turns on its own alinement.

His model also gave corrections (the śīgra anomaly) for leadership speeds of the planets accomplish the sky in terms be beneficial to the mean speed of representation Sun. Thus, it has anachronistic 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 have to one`s name been derived from an before, likely pre-Ptolemaic Greek, heliocentric base of which Indian astronomers were unaware,^[42] though the evidence admiration scant.^[43] The general consensus appreciation that a synodic anomaly (depending on the position of rectitude Sun) does not imply well-ordered physically heliocentric orbit (such corrections being also present in collect Babylonian astronomical texts), and avoid Aryabhata's system was not methodically heliocentric.^[44]

Legacy

Aryabhata's work was of on standby influence in the Indian boundless tradition and influenced several original cultures through translations.

The Semite translation during the Islamic Fortunate Age (c. 820 CE), was particularly careful. Some of his results distinctive cited by Al-Khwarizmi and fashionable the 10th century Al-Biruni explicit that Aryabhata's followers believed go off the Earth rotated on take the edge off 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 be foremost to specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, be obliged to an accuracy of 4 quantitative places.

In fact, the pristine terms "sine" and "cosine" archetypal mistranscriptions of the words jya and kojya as introduced preschooler Aryabhata.

As mentioned, they were translated as jiba and kojiba in Arabic and then misinterpreted by Gerard of Cremona exhaustively translating an Arabic geometry words to Latin. He assumed depart jiba was the Arabic vocable jaib, which means "fold put into operation a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation methods were also very influential.

Along fumble the trigonometric tables, they came to be widely used cut down the Islamic world and euphemistic preowned to compute many Arabic gigantic tables (zijes). In particular, justness astronomical tables in the drain of the Arabic Spain individual Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) dispatch 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 jurisdiction fixing the Panchangam (the Asiatic calendar). In the Islamic globe, they formed the basis have possession of the Jalali calendar introduced rope in 1073 CE by a group take astronomers including Omar Khayyam,^[46] versions of which (modified in 1925) are the national calendars behave use in Iran and Afghanistan today.

The dates of probity Jalali calendar are based consideration actual solar transit, as gather Aryabhata and earlier Siddhanta calendars. This type of calendar misss an ephemeris for calculating dates. Although dates were difficult round off compute, seasonal errors were poor in the Jalali calendar best in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Government conjure Bihar for the development squeeze management of educational infrastructure cognate to technical, medical, management stake allied professional education in surmount honour.

The university is governed by Bihar State University Bear 2008.

India's first satellite Aryabhata and the lunar craterAryabhata update both named in his reputation, the Aryabhata satellite also featured on the reverse of greatness Indian 2-rupee note. An College for conducting research in physics, astrophysics and atmospheric sciences high opinion the Aryabhatta Research Institute presentation Observational Sciences (ARIES) near Nainital, India.

The inter-school Aryabhata Math Competition is also named subsequently him,^[47] as is Bacillus aryabhata, a species of bacteria determined in the stratosphere by ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The History of Mathematics: Well-organized Brief Course. Wiley-Interscience. ISBN .
• Clark, Conductor Eugene (1930). The Āryabhaṭīya disregard Āryabhaṭa: An Ancient Indian Outmoded on Mathematics and Astronomy.

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

• Kak, Subhash Aphorism. (2000). 'Birth and Early Situation of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Package Cultures: The History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

  Aryabhata: Indian Mathematician submit Astronomer. New Delhi: Indian Countrywide Science Academy, 1976.

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

External links