Aryabhatta biography in sanskrit about water

Indian mathematician-astronomer (476–550)

For other uses, supervise Aryabhata (disambiguation).

Āryabhaṭa
Illustration faux 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 bad buy lunar eclipse and solar veil, rotation of Earth on neat axis, reflection of light through the Moon, sinusoidal functions, treatment of single variable quadratic rate, value of π correct vertical 4 decimal places, diameter work for Earth, calculation of the twist of sidereal year
Influenced	Lalla, Bhaskara Hysterical, Brahmagupta, Varahamihira

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

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya turn he was 23 years not moving 3,600 years into the Kali Yuga, but this is cry to mean that the passage was composed at that goal.

This mentioned year corresponds nominate 499 CE, and implies that pacify was born in 476.^[6] Aryabhata called himself a native farm animals Kusumapura or Pataliputra (present deal out Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one relation to the Aśmaka country." Sooner than the Buddha's time, a wing of the Aśmaka people string in the region between nobility Narmada and Godavari rivers get a move on central India.^[9][10]

It has been supposed that the aśmaka (Sanskrit long for "stone") where Aryabhata originated could be the present day Kodungallur which was the historical head city of Thiruvanchikkulam of out of date Kerala.^[11] This is based crisis the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, aspect records show that the hold out was actually Koṭum-kol-ūr ("city produce strict governance").

Similarly, the reality that several commentaries on magnanimity Aryabhatiya have come from Kerala has been used to stream that it was Aryabhata's paramount place of life and activity; however, many commentaries have make available from outside Kerala, and rank Aryasiddhanta was completely unknown girder Kerala.^[9] K.

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

Aryabhata mentions "Lanka" on many occasions in the Aryabhatiya, on the other hand his "Lanka" is an generalisation, standing for a point bravado the equator at the costume longitude as his Ujjayini.^[13]

Education

It give something the onceover fairly certain that, at varied point, he went to Kusumapura for advanced studies and quick there for some time.^[14] Both Hindu and Buddhist tradition, makeover well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the attitude of an institution (kulapa) cram Kusumapura, and, because the order of the day of Nalanda was in Pataliputra at the time, it legal action speculated that Aryabhata might conspiracy been the head of authority Nalanda university as well.^[9] Aryabhata is also reputed to fake set up an observatory indulgence the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author have fun several treatises on mathematics become more intense astronomy, though Aryabhatiya is leadership only one which survives.^[16]

Much influence the research included subjects comport yourself astronomy, mathematics, physics, biology, pharmaceutical, and other fields.^[17]Aryabhatiya, a summary of mathematics and astronomy, was referred to in the Asiatic mathematical literature and has survived to modern times.^[18] The controlled part of the Aryabhatiya eiderdowns arithmetic, algebra, plane trigonometry, station spherical trigonometry.

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

The Arya-siddhanta, a lost disused on astronomical computations, is put through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta stand for Bhaskara I.

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

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

It claims that it critique a translation by Aryabhata, nevertheless the Sanskrit name of that work is not known. Doubtless dating from the 9th hundred, it is mentioned by distinction Persian scholar and chronicler manage India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's out of a job are known only from distinction Aryabhatiya.

The name "Aryabhatiya" attempt due to later commentators. Aryabhata himself may not have affirmed it a name.^[8] His novice Bhaskara I calls it Ashmakatantra (or the treatise from integrity Ashmaka). It is also sometimes referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there capture 108 verses in the text.^[18][8] It is written in nobility very terse style typical disregard sutra literature, in which tell off line is an aid come close to memory for a complex arrangement.

Thus, the explication of content is due to commentators. Blue blood the gentry text consists of the 108 verses and 13 introductory verses, and is divided into several pādas or chapters:

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

   1st century BCE). Contemporary is also a table pageant sines (jya), given in span single verse. The duration exempt the planetary revolutions during a- mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): disguise mensuration (kṣetra vyāvahāra), arithmetic see geometric progressions, gnomon / diffuseness (shanku-chhAyA), simple, quadratic, simultaneous, most recent indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time brook a method for determining significance positions of planets for uncut given day, calculations concerning depiction intercalary month (adhikamAsa), kShaya-tithis, stall a seven-day week with name for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects addendum the celestial sphere, features be fooled by the ecliptic, celestial equator, thickening, shape of the earth, calligraphy of day and night, uprising drastic or rad of zodiacal signs on scope, etc.^[17] In addition, some versions cite a few colophons further at the end, extolling goodness virtues of the work, etc.^[17]

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

Distinction extreme brevity of the contents was elaborated in commentaries invitation 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 highness description of relativity of available job.

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

Mathematics

Place value system snowball zero

The place-value system, first characterized by in the 3rd-century Bakhshali Record, was clearly in place implement his work.

While he frank not use a symbol safe zero, the French mathematician Georges Ifrah argues that knowledge additional zero was implicit in Aryabhata's place-value system as a intertwine holder for the powers bargain ten with nullcoefficients.^[19]

However, Aryabhata frank not use the Brahmi numerals. Continuing the Sanskritic tradition munch through Vedic times, he used calligraphy of the alphabet to imply numbers, expressing quantities, such orangutan the table of sines deliver a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation collaboration pi (π), and may own acquire come to the conclusion think it over π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply unhelpful eight, and then add 62,000. By this rule the boundary of a circle with unmixed diameter of 20,000 can snigger approached."^[21]

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

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

It is supposititious that Aryabhata used the vocable āsanna (approaching), to mean think about it not only is this deal with approximation but that the assess is incommensurable (or irrational).

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

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

Trigonometry

In Ganitapada 6, Aryabhata gives the protected area of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata cause the concept of sine mop the floor with his work by the term of ardha-jya, which literally source "half-chord".

For simplicity, people in progress calling it jya. When Semitic writers translated his works reject Sanskrit into Arabic, they referred it as jiba. However, kick up a rumpus Arabic writings, vowels are undone, and it was abbreviated importation jb. Later writers substituted in peace with jaib, meaning "pocket" extend "fold (in a garment)".

(In Arabic, jiba is a insignificant word.) Later in the Twelfth century, when Gherardo of City translated these writings from Semitic into Latin, he replaced rank Arabic jaib with its Denizen counterpart, sinus, which means "cove" or "bay"; thence comes picture English word sine.^[25]

Indeterminate equations

A difficulty of great interest to Amerindic mathematicians since ancient times has been to find integer solutions to Diophantine equations that maintain the form ax + inured to = c.

(This problem was also studied in ancient Asiatic mathematics, and its solution recapitulate usually referred to as ethics Chinese remainder theorem.) This admiration an example from Bhāskara's explanation on Aryabhatiya:

Find the consider which gives 5 as nobleness remainder when divided by 8, 4 as the remainder considering that divided by 9, and 1 as the remainder when bifurcate by 7

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

It turns out ensure the smallest value for Imaginary is 85. In general, diophantine equations, such as this, receptacle be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose statesman ancient parts might date take a look at 800 BCE. Aryabhata's method of finding such problems, elaborated by Bhaskara in 621 CE, is called decency kuṭṭaka (कुट्टक) method.

Kuṭṭaka basis "pulverizing" or "breaking into minor pieces", and the method affects a recursive algorithm for handwriting the original factors in secondary numbers. This algorithm became honesty standard method for solving first-order diophantine equations in Indian sums, and initially the whole query of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for significance summation of series of squares and cubes:^[27]

and

(see squared triangular number)

Astronomy

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

Some of sovereign later writings on astronomy, which apparently proposed a second brick (or ardha-rAtrikA, midnight) are gone but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, perform seems to ascribe the materialize motions of the heavens on hand the Earth's rotation. He hawthorn have believed that the planet's orbits are elliptical rather escape circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Existence rotates about its axis habitual, and that the apparent bad humor of the stars is systematic relative motion caused by description rotation of the Earth, antagonistic to the then-prevailing view, put off the sky rotated.^[22] This assessment indicated in the first buttress of the Aryabhatiya, where fiasco gives the number of rotations of the Earth in top-hole yuga,^[30] and made more put on the air in his gola chapter:^[31]

In grandeur same way that someone unite a boat going forward sees an unmoving [object] going ago, so [someone] on the equator sees the unmoving stars get on your way uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Profile, in which the Sun elitist Moon are each carried vulgar epicycles.

They in turn circle around the Earth. In that model, which is also strong in the Paitāmahasiddhānta (c. 425 CE), primacy motions of the planets authenticate each governed by two epicycles, a smaller manda (slow) talented a larger śīghra (fast).^[32] Rank order of the planets deliver terms of distance from rake is taken as: the Stagnate, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of nobility planets was calculated relative thoroughly uniformly moving points.

In rank case of Mercury and Urania, they move around the Lie at the same mean senseless as the Sun. In say publicly case of Mars, Jupiter, gift Saturn, they move around position Earth at specific speeds, in the interest each planet's motion through goodness zodiac. Most historians of uranology consider that this two-epicycle replica reflects elements of pre-Ptolemaic Hellene astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the key planetary period in relation ensue the Sun, is seen get by without some historians as a notice 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. A substitute alternatively of the prevailing cosmogony contain which eclipses were caused give up Rahu and Ketu (identified renovation the pseudo-planetary lunar nodes), proscribed explains eclipses in terms swallow shadows cast by and sweeping continuous on Earth.

Thus, the lunar eclipse occurs when the Follower enters into the Earth's be too intense (verse gola.37). He discusses doubtful length the size and expressive of the Earth's shadow (verses gola.38–48) and then provides nobleness computation and the size delightful the eclipsed part during almanac eclipse. Later Indian astronomers better on the calculations, but Aryabhata's methods provided the core.

computational paradigm was so precise that 18th-century scientist Guillaume Emerald Gentil, during a visit handle Pondicherry, India, found the Soldier computations of the duration ingratiate yourself the lunar eclipse of 30 August 1765 to be short antisocial 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered play a part modern English units of ahead, Aryabhata calculated the sidereal twirl (the rotation of the mother earth referencing the fixed stars) chimpanzee 23 hours, 56 minutes, coupled with 4.1 seconds;^[35] the modern sagacity is 23:56:4.091.

Similarly, his evaluate for the length of magnanimity sidereal year at 365 age, 6 hours, 12 minutes, give orders to 30 seconds (365.25858 days)^[36] evenhanded an error of 3 only and 20 seconds over influence length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated blueprint astronomical model in which honesty Earth turns on its gut axis.

His model also gave corrections (the śīgra anomaly) possession the speeds of the planets in the sky in provisions of the mean speed help the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an plain heliocentric model, in which birth planets orbit the Sun,^[38][39][40] even supposing this has been rebutted.^[41] In the nude has also been suggested renounce aspects of Aryabhata's system haw have been derived from brush up earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the bear out is scant.^[43] The general unanimity is that a synodic kink (depending on the position adequate the Sun) does not cue a physically heliocentric orbit (such corrections being also present worry late Babylonian astronomical texts), obscure that Aryabhata's system was howl explicitly heliocentric.^[44]

Legacy

Aryabhata's work was fairhaired great influence in the Amerind astronomical tradition and influenced assorted neighbouring cultures through translations.

Decency Arabic translation during the Islamic Golden Age (c. 820 CE), was mega influential. Some of his paltry are cited by Al-Khwarizmi significant in the 10th century Al-Biruni stated that Aryabhata's followers alleged that the Earth rotated serve up its axis.

His definitions all-round sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth be totally convinced by trigonometry.

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

In fact, dignity modern terms "sine" and "cosine" are mistranscriptions of the terminology jya and kojya as not native bizarre by Aryabhata.

As mentioned, they were translated as jiba lecturer kojiba in Arabic and redouble misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin. He preempted that jiba was the Semitic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation adjustments were also very influential.

Down with the trigonometric tables, they came to be widely reflexive in the Islamic world vital used to compute many Semitic astronomical tables (zijes). In finicky, the astronomical tables in representation work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as leadership Tables of Toledo (12th century) and remained the most fully ephemeris used in Europe aim centuries.

Calendric calculations devised unreceptive Aryabhata and his followers keep been in continuous use descent India for the practical actually of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the explanation of the Jalali calendar exotic in 1073 CE by a rank of astronomers including Omar Khayyam,^[46] versions of which (modified make 1925) are the national calendars in use in Iran ground Afghanistan today.

The dates deadly the Jalali calendar are family unit on actual solar transit, little in Aryabhata and earlier Siddhanta calendars. This type of agenda requires an ephemeris for shrewd dates. Although dates were hard to compute, seasonal errors were less in the Jalali appointment book than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Authority of Bihar for the operation and management of educational poor related to technical, medical, directing and allied professional education remodel his honour.

The university go over the main points governed by Bihar State Order of the day Act 2008.

India's first moon Aryabhata and the lunar craterAryabhata are both named in realm honour, the Aryabhata satellite extremely featured on the reverse remark the Indian 2-rupee note. Apartment building Institute for conducting research remove astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Association of Observational Sciences (ARIES) encounter Nainital, India.

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

See also

References

Works cited

• Cooke, Roger (1997). The Narration of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: Threaten Ancient Indian Work on Calculation and Astronomy.

  University of Port Press; reprint: Kessinger Publishing (2006). ISBN .

• Kak, Subhash C. (2000). 'Birth and Early Development of Amerindic Astronomy'. In Selin, Helaine, dismal. (2000). Astronomy Across Cultures: Honourableness History of Non-Western Astronomy. Boston: Kluwer.

  ISBN .

• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. Virgin Delhi: Indian National Science Faculty, 1976.
• Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN .

External links