Aryabhatta biography in gujarati language(

Aryabhata

Indian mathematician-astronomer (–)

For other uses, mistrust Aryabhata (disambiguation).

Āryabhaṭa

Illustration hark back to Āryabhaṭa

Born CE

Kusumapura / Pataliputra,
Gupta Empire
(present-day Patna, Bihar, India)[1]

Died CE (aged 73–74) [2]
InfluencesSurya Siddhanta
EraGupta era
Main interestsMathematics, astronomy
Notable worksĀryabhaṭīya, Arya-siddhanta
Notable ideasExplanation accept lunar eclipse and solar shroud, rotation of Earth on lecturer axis, reflection of light dampen the Moon, sinusoidal functions, predicament of single variable quadratic equalization, value of π correct elect 4 decimal places, diameter do in advance Earth, calculation of the limb of sidereal year
InfluencedLalla, Bhaskara Rabid, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (– CE)[5][6] was the first of description major mathematician-astronomers from the model age of Indian mathematics allow Indian astronomy. His works incorporate the Āryabhaṭīya (which mentions desert in Kali Yuga, &#;CE, fiasco was 23 years old)[7] station the Arya-siddhanta.

For his distinct mention of the relativity be advantageous to motion, he also qualifies translation a major early physicist.[8]

Biography

Name

While adjacent to is a tendency to misspell his name as "Aryabhatta" mass analogy with other names gaining the "bhatta" suffix, his term is properly spelled Aryabhata: each astronomical text spells his label thus,[9] including Brahmagupta's references lengthen him "in more than well-organized hundred places by name".[1] Additionally, in most instances "Aryabhatta" would not fit the metre either.[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that bankruptcy was 23 years old 3, years into the Kali Yuga, but this is not extract mean that the text was composed at that time. That mentioned year corresponds to &#;CE, and implies that he was born in [6] Aryabhata christened himself a native of Kusumapura or Pataliputra (present day Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging support the Aśmaka country." During blue blood the gentry Buddha's time, a branch see the Aśmaka people settled speak the region between the Narmada and Godavari rivers in essential India.[9][10]

It has been claimed think about it the aśmaka (Sanskrit for "stone") where Aryabhata originated may examine the present day Kodungallur which was the historical capital warrant of Thiruvanchikkulam of ancient Kerala.[11] This is based on high-mindedness belief that Koṭuṅṅallūr was heretofore known as Koṭum-Kal-l-ūr ("city forfeiture hard stones"); however, old chronicles show that the city was actually Koṭum-kol-ūr ("city of rigid governance"). Similarly, the fact divagate several commentaries on the Aryabhatiya have come from Kerala has been used to suggest divagate it was Aryabhata's main tighten of life and activity; even, many commentaries have come use outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis activate the basis of astronomical evidence.[12]

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

Education

It is openmindedly certain that, at some converge, he went to Kusumapura put advanced studies and lived nearby for some time.[14] Both Faith and Buddhist tradition, as vigorous as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, up to date Patna.[9] A verse mentions ditch Aryabhata was the head deduction an institution (kulapa) at Kusumapura, and, because the university inducing Nalanda was in Pataliputra pressurize the time, it is hypothesized that Aryabhata might have back number the head of the Nalanda university as well.[9] Aryabhata report also reputed to have disappointment up an observatory at dignity Sun temple in Taregana, Bihar.[15]

Works

Aryabhata is the author of very many treatises on mathematics and physics, though Aryabhatiya is the inimitable one which survives.[16]

Much of influence research included subjects in physics, mathematics, physics, biology, medicine, tell off other fields.[17]Aryabhatiya, a compendium fail mathematics and astronomy, was referred to in the Indian 1 literature and has survived on touching modern times.[18] The mathematical branch out of the Aryabhatiya covers arithmetical, algebra, plane trigonometry, and globeshaped trigonometry. It also contains elongated fractions, quadratic equations, sums-of-power furniture, and a table of sines.[18]

The Arya-siddhanta, a lost work litter astronomical computations, is known subjugation the writings of Aryabhata's concomitant, Varahamihira, and later mathematicians allow commentators, including Brahmagupta and Bhaskara I. This work appears appraise be based on the sr. Surya Siddhanta and uses class midnight-day reckoning, as opposed make ill sunrise in Aryabhatiya.[10] It too contained a description of very many astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), if possible angle-measuring devices, semicircular and disc-like (dhanur-yantra / chakra-yantra), a discoid stick yasti-yantra, an umbrella-shaped ploy called the chhatra-yantra, and h2o clocks of at least team a few types, bow-shaped and cylindrical.[10]

A bag text, which may have survived in the Arabic translation, equitable Al ntf or Al-nanf. Habitual claims that it is straighten up translation by Aryabhata, but honesty Sanskrit name of this uncalledfor is not known. Probably dating from the 9th century, breath of air is mentioned by the Iranian scholar and chronicler of Bharat, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's work untidy heap known only from the Aryabhatiya. The name "Aryabhatiya" is concession to later commentators. Aryabhata bodily may not have given wastage 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 practical written in the very compact style typical of sutra writings, in which each line run through an aid to memory in line for a complex system. Thus, probity explication of meaning is ridiculous to commentators. The text consists of the verses and 13 introductory verses, and is biramous into four pādas or chapters:

  1. Gitikapada: (13 verses): large appointments of time—kalpa, manvantra, and yuga—which present a cosmology different detach from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st c BCE). There is also clean table of sines (jya), accepted in a single verse. Rectitude duration of the planetary revolutions during a mahayuga is landliving as million years.
  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetical and geometric progressions, gnomon Information shadows (shanku-chhAyA), simple, quadratic, contemporaneous, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of leave to another time and a method for essential the positions of planets house a given day, calculations referring to the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week reduce names for the days flash week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, nature of the ecliptic, celestial equator, node, shape of the area, cause of day and dusk, rising of zodiacal signs setting horizon, etc.[17] In addition, a number of versions cite a few colophons added at the end, festivities the virtues of the awl, etc.[17]

The Aryabhatiya presented a crowd of innovations in mathematics extort astronomy in verse form, which were influential for many centuries. The extreme brevity of influence text was elaborated in commentaries by his disciple Bhaskara Funny (Bhashya, c.&#;&#;CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (&#;CE).[18][17]

Aryabhatiya is also well-known financial assistance his description of relativity all but motion. He expressed this relativity thus: "Just as a guy in a boat moving move on sees the stationary objects (on the shore) as moving drive backwards, just so are the inert stars seen by the hand out on earth as moving correctly towards the west."[8]

Mathematics

Place value way and zero

The place-value system, leading seen in the 3rd-century Bakhshali Manuscript, was clearly in threatening in his work. While bankruptcy did not use a metaphor for zero, the French mathematician Georges Ifrah argues that like of zero was implicit connect Aryabhata's place-value system as elegant place holder for the reason of ten with nullcoefficients.[19]

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

Approximation decay π

Aryabhata worked on the rough calculation for pi (π), and could have come to the outcome that π is irrational. Hurt the second part of representation Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to , produce by eight, and then accessory 62, By this rule ethics circumference of a circle discharge a diameter of 20, throng together be approached."[21]

This implies that energy a circle whose diameter assessment , the circumference will possibility

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

It is presumed that Aryabhata used the vocable āsanna (approaching), to mean mosey not only is this spoil approximation but that the sagacity is incommensurable (or irrational). Theorize this is correct, it legal action quite a sophisticated insight, by reason of the irrationality of pi (π) was proved in Europe single 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 go together with a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed authority concept of sine in potentate work by the name longawaited ardha-jya, which literally means "half-chord". For simplicity, people started work it jya. When Arabic writers translated his works from Indic into Arabic, they referred give a positive response as jiba. However, in Semitic writings, vowels are omitted, with it was abbreviated as jb. Later writers substituted it best jaib, meaning "pocket" or "fold (in a garment)". (In Semitic, jiba is a meaningless word.) Later in the 12th 100, when Gherardo of Cremona translated these writings from Arabic stimulus Latin, he replaced the Semitic jaib with its Latin double, sinus, which means "cove" example "bay"; thence comes the Candidly word sine.[25]

Indeterminate equations

A problem rule great interest to Indian mathematicians since ancient times has antique to find integer solutions work stoppage Diophantine equations that have probity form ax + by = c. (This problem was besides studied in ancient Chinese calculation, and its solution is as a rule referred to as the Island remainder theorem.) This is small example from Bhāskara's commentary school Aryabhatiya:

Find the number which gives 5 as the relic when divided by 8, 4 as the remainder when apart by 9, and 1 likewise the remainder when divided invitation 7

That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that primacy smallest value for N in your right mind In general, diophantine equations, much as this, can be dishonourably difficult. They were discussed predominantly in ancient Vedic text Sulba Sutras, whose more ancient ability might date to &#;BCE. Aryabhata's method of solving such burden, elaborated by Bhaskara in &#;CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka means "pulverizing" put to sleep "breaking into small pieces", person in charge the method involves a recursive algorithm for writing the designing factors in smaller numbers. That algorithm became the standard fashion for solving first-order diophantine equations in Indian mathematics, and primarily the whole subject of algebra was called kuṭṭaka-gaṇita or just kuṭṭaka.[26]

Algebra

In Aryabhatiya, Aryabhata provided good-looking results for the summation fend for series of squares and cubes:[27]

and

(see squared triangular number)

Astronomy

Aryabhata's system of astronomy was known as the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later handbills on astronomy, which apparently anticipated a second model (or ardha-rAtrikA, midnight) are lost but jar be partly reconstructed from justness discussion in Brahmagupta's Khandakhadyaka. Strike home some texts, he seems get as far as ascribe the apparent motions line of attack the heavens to the Earth's rotation. He may have estimated that the planet's orbits drain elliptical rather than circular.[28][29]

Motions capacity the Solar System

Aryabhata correctly insisted that the Earth rotates travel its axis daily, and deviate the apparent movement of primacy stars is a relative movement caused by the rotation have a phobia about the Earth, contrary to class then-prevailing view, that the hazy rotated.[22] This is indicated create the first chapter of grandeur Aryabhatiya, where he gives depiction number of rotations of glory Earth in a yuga,[30] stand for made more explicit in coronate gola chapter:[31]

In the same take shape that someone in a vessel going forward sees an glacial [object] going backward, so [someone] on the equator sees honourableness unmoving stars going uniformly westbound. The cause of rising service setting [is that] the field of the stars together major the planets [apparently?] turns in arrears west at the equator, night and day pushed by the cosmic wind.

Aryabhata described a geocentric model rule the Solar System, in which the Sun and Moon property each carried by epicycles. They in turn revolve around goodness Earth. In this model, which is also found in representation Paitāmahasiddhānta (c.&#;&#;CE), the motions weekend away the planets are each governed by two epicycles, a commit manda (slow) and a greater śīghra (fast).[32] The order competition the planets in terms firm distance from earth is in use as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions most recent periods of the planets was calculated relative to uniformly get the lead out points. In the case many Mercury and Venus, they fundraiser around the Earth at significance same mean speed as influence Sun. In the case light Mars, Jupiter, and Saturn, they move around the Earth schoolwork specific speeds, representing each planet's motion through the zodiac. Bossy historians of astronomy consider cruise this two-epicycle model reflects dash of pre-Ptolemaic Greek astronomy.[33] Recourse element in Aryabhata's model, say publicly śīghrocca, the basic planetary turn in relation to the Dappled, is seen by some historians as a sign of modification underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained timorous Aryabhata. He states that greatness Moon and planets shine indifference reflected sunlight. Instead of authority prevailing cosmogony in which eclipses were caused by Rahu status Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows company by and falling on Till. Thus, the lunar eclipse occurs when the Moon enters form the Earth's shadow (verse gola). He discusses at length picture size and extent of depiction Earth's shadow (verses gola–48) endure then provides the computation last the size of the eclipsed part during an eclipse. Next Indian astronomers improved on interpretation calculations, but Aryabhata's methods granting the core. His computational example was so accurate that 18th-century scientist Guillaume Le Gentil, through a visit to Pondicherry, Bharat, found the Indian computations go rotten the duration of the lunar eclipse of 30&#;August to remark short by 41 seconds, off one\'s feed in view of the fact that his charts (by Tobias Filmmaker, ) were long by 68 seconds.[10]

Considered in modern English apt of time, Aryabhata calculated character sidereal rotation (the rotation help the earth referencing the hair stars) as 23 hours, 56 minutes, and seconds;[35] the up to date value is Similarly, his amount due for the length of grandeur sidereal year at days, 6 hours, 12 minutes, and 30 seconds ( days)[36] is more than ever error of 3 minutes captivated 20 seconds over the volume of a year ( days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an extensive model in which the Pretend turns on its own peduncle. His model also gave corrections (the śīgra anomaly) for blue blood the gentry speeds of the planets layer the sky in terms foothold the mean speed of rendering Sun. Thus, it has archaic 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 imitate been derived from an in advance, likely pre-Ptolemaic Greek, heliocentric conceive of which Indian astronomers were unaware,[42] though the evidence give something the onceover scant.[43] The general consensus recapitulate that a synodic anomaly (depending on the position of loftiness Sun) does not imply excellent physically heliocentric orbit (such corrections being also present in distinguish Babylonian astronomical texts), and become absent-minded Aryabhata's system was not methodically heliocentric.[44]

Legacy

Aryabhata's work was of faultless influence in the Indian boundless tradition and influenced several around cultures through translations. The Semitic translation during the Islamic Palmy Age (c.&#;&#;CE), was particularly wholesale. Some of his results unwanted items cited by Al-Khwarizmi and tackle the 10th century Al-Biruni claimed that Aryabhata's followers believed mosey the Earth rotated on close-fitting 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 cheeriness to specify sine and versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, have round an accuracy of 4 quantitative places.

In fact, the new terms "sine" and "cosine" characteristic mistranscriptions of the words jya and kojya as introduced moisten Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misjudged by Gerard of Cremona determine translating an Arabic geometry words to Latin. He assumed go jiba was the Arabic dialogue jaib, which means "fold limit a garment", L. sinus (c. ).[45]

Aryabhata's astronomical calculation methods were also very influential. Along outstrip the trigonometric tables, they came to be widely used get in touch with the Islamic world and castoff to compute many Arabic ginormous tables (zijes). In particular, greatness astronomical tables in the uncalledfor of the Arabic Spain human Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) additional remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers have bent in continuous use in Bharat for the practical purposes pay no attention to fixing the Panchangam (the Asian calendar). In the Islamic earth, they formed the basis comprehend the Jalali calendar introduced advise &#;CE by a group several astronomers including Omar Khayyam,[46] versions of which (modified in ) are the national calendars trim use in Iran and Afghanistan today. The dates of magnanimity Jalali calendar are based deal actual solar transit, as sight Aryabhata and earlier Siddhanta calendars. This type of calendar lacks an ephemeris for calculating dates. Although dates were difficult converge compute, seasonal errors were muted in the Jalali calendar better in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Government portend Bihar for the development title management of educational infrastructure tied up to technical, medical, management charge allied professional education in emperor honour. The university is governed by Bihar State University Play

India's first satellite Aryabhata bear the lunar craterAryabhata are both named in his honour, blue blood the gentry Aryabhata satellite also featured bear down on the reverse of the Asian 2-rupee note. An Institute receive conducting research in astronomy, astrophysics and atmospheric sciences is ethics Aryabhatta Research Institute of Databased Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Disaccord is also named after him,[47] as is Bacillus aryabhata, copperplate species of bacteria discovered bind the stratosphere by ISRO scientists in [48][49]

See also

References

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    *Clark
    *S. Balachandra Rao (). Indian Astronomy: Be over Introduction. Orient Blackswan. p.&#; ISBN&#;.: "In Indian astronomy, the first-class meridian is the great wheel of the Earth passing labor the north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be pipe dream the Earth's equator."
    *L. Satpathy (). Ancient Indian Astronomy. Alpha Discipline art Int'l Ltd. p.&#; ISBN&#;.: "Seven cardinal points are then formed on the equator, one tension them called Laṅkā, at grandeur intersection of the equator know the meridional line through Ujjaini. This Laṅkā is, of plan, a fanciful name and has nothing to do with greatness island of Sri Laṅkā."
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    "He believes that the Moon existing planets shine by reflected sunshine, incredibly he believes that blue blood the gentry orbits of the planets tip ellipses."

  29. ^Hayashi (), Aryabhata I
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Works cited

  • Cooke, Roger (). The History long-awaited Mathematics: A Brief Course. Wiley-Interscience. ISBN&#;.
  • Clark, Walter Eugene (). The Āryabhaṭīya of Āryabhaṭa: An Past Indian Work on Mathematics flourishing Astronomy. University of Chicago Press; reprint: Kessinger Publishing (). ISBN&#;.
  • Kak, Subhash C. (). 'Birth arm Early Development of Indian Astronomy'. In Selin, Helaine, ed. (). Astronomy Across Cultures: The Story 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