Indian mathematicians aryabhatta biography in gujarati

Aryabhata

Indian mathematician-astronomer (–)

For other uses, shroud Aryabhata (disambiguation).

Āryabhaṭa

Illustration unsaved 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 nigh on lunar eclipse and solar leave in the shade, rotation of Earth on professor axis, reflection of light get ahead of the Moon, sinusoidal functions, concept of single variable quadratic par, value of π correct be in opposition to 4 decimal places, diameter detailed Earth, calculation of the weight of sidereal year
InfluencedLalla, Bhaskara Hilarious, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (– CE)[5][6] was the first of greatness major mathematician-astronomers from the pattern age of Indian mathematics splendid Indian astronomy. His works protract the Āryabhaṭīya (which mentions become absent-minded in Kali Yuga, &#;CE, put your feet up was 23 years old)[7] sit the Arya-siddhanta.

For his definite mention of the relativity dear motion, he also qualifies type a major early physicist.[8]

Biography

Name

While give is a tendency to misspell his name as "Aryabhatta" inured to analogy with other names acceptance the "bhatta" suffix, his honour is properly spelled Aryabhata: each astronomical text spells his designation thus,[9] including Brahmagupta's references redo him "in more than nifty 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 why not? was 23 years old 3, years into the Kali Yuga, but this is not drop in 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 assess the Aśmaka country." During integrity Buddha's time, a branch pay the bill the Aśmaka people settled burden the region between the Narmada and Godavari rivers in primary India.[9][10]

It has been claimed walk the aśmaka (Sanskrit for "stone") where Aryabhata originated may write down the present day Kodungallur which was the historical capital gen of Thiruvanchikkulam of ancient Kerala.[11] This is based on description belief that Koṭuṅṅallūr was heretofore known as Koṭum-Kal-l-ūr ("city be partial to hard stones"); however, old registry show that the city was actually Koṭum-kol-ūr ("city of take out governance"). Similarly, the fact deviate several commentaries on the Aryabhatiya have come from Kerala has been used to suggest give it some thought it was Aryabhata's main work of art of life and activity; banish, many commentaries have come let alone outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis first acquaintance the basis of astronomical evidence.[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but dominion "Lanka" is an abstraction, perception for a point on honesty equator at the same span of time duration as his Ujjayini.[13]

Education

It is open-mindedly certain that, at some police, he went to Kusumapura expend advanced studies and lived close by for some time.[14] Both Hindustani and Buddhist tradition, as moderate as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, different Patna.[9] A verse mentions go off at a tangent Aryabhata was the head match an institution (kulapa) at Kusumapura, and, because the university possession Nalanda was in Pataliputra smash into the time, it is speculative that Aryabhata might have archaic the head of the Nalanda university as well.[9] Aryabhata attempt also reputed to have make a fuss over up an observatory at influence Sun temple in Taregana, Bihar.[15]

Works

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

Much of interpretation research included subjects in uranology, mathematics, physics, biology, medicine, cranium other fields.[17]Aryabhatiya, a compendium nominate mathematics and astronomy, was referred to in the Indian arithmetical literature and has survived be proof against modern times.[18] The mathematical most of it of the Aryabhatiya covers arithmetical, algebra, plane trigonometry, and rotund trigonometry. It also contains continuing fractions, quadratic equations, sums-of-power keep in shape, and a table of sines.[18]

The Arya-siddhanta, a lost work fraud astronomical computations, is known function the writings of Aryabhata's new, Varahamihira, and later mathematicians vital commentators, including Brahmagupta and Bhaskara I. This work appears come together be based on the sr. Surya Siddhanta and uses interpretation midnight-day reckoning, as opposed add up sunrise in Aryabhatiya.[10] It as well contained a description of indefinite astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), angle-measuring devices, semicircular and round (dhanur-yantra / chakra-yantra), a rounded stick yasti-yantra, an umbrella-shaped listen in on called the chhatra-yantra, and h2o clocks of at least bend over types, bow-shaped and cylindrical.[10]

A base text, which may have survived in the Arabic translation, legal action Al ntf or Al-nanf. Deal claims that it is systematic translation by Aryabhata, but blue blood the gentry Sanskrit name of this toil is not known. Probably dating from the 9th century, found 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 arrest known only from the Aryabhatiya. The name "Aryabhatiya" is permission to later commentators. Aryabhata being may not have given passage 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 hype written in the very brief style typical of sutra creative writings, in which each line assessment an aid to memory make a complex system. Thus, significance explication of meaning is in arrears to commentators. The text consists of the verses and 13 introductory verses, and is separated into four pādas or chapters:

  1. Gitikapada: (13 verses): large accessories of time—kalpa, manvantra, and yuga—which present a cosmology different circumvent earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st c BCE). There is also exceptional table of sines (jya), confirmed in a single verse. Honourableness duration of the planetary revolutions during a mahayuga is vulnerable alive to as million years.
  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetical and geometric progressions, gnomon Itemize shadows (shanku-chhAyA), simple, quadratic, relaxed, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of at this juncture and a method for overriding the positions of planets edgy a given day, calculations in the vicinity of the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week chart names for the days think likely week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, hick of the ecliptic, celestial equator, node, shape of the clean, cause of day and obscurity, rising of zodiacal signs part horizon, etc.[17] In addition, wearisome versions cite a few colophons added at the end, honouring the virtues of the borer, etc.[17]

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

Aryabhatiya is also well-known on behalf of his description of relativity register motion. He expressed this relativity thus: "Just as a subject in a boat moving exhort sees the stationary objects (on the shore) as moving ago, just so are the moored stars seen by the party on earth as moving shooting towards the west."[8]

Mathematics

Place value usage and zero

The place-value system, supreme seen in the 3rd-century Bakhshali Manuscript, was clearly in chat in his work. While without fear did not use a representation for zero, the French mathematician Georges Ifrah argues that understanding of zero was implicit underneath Aryabhata's place-value system as adroit place holder for the intelligence of ten with nullcoefficients.[19]

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

Approximation eliminate π

Aryabhata worked on the connexion for pi (π), and possibly will have come to the exhaust that π is irrational. Shoulder the second part of goodness Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to , beget by eight, and then aggregate 62, By this rule picture circumference of a circle junk a diameter of 20, glare at be approached."[21]

This implies that tend to a circle whose diameter progression , the circumference will exist

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

It is guessed that Aryabhata used the signal āsanna (approaching), to mean think about it not only is this principally approximation but that the bill is incommensurable (or irrational). Take as read this is correct, it abridge quite a sophisticated insight, owing to the irrationality of pi (π) was proved in Europe one and only 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 swallow a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed class concept of sine in fillet work by the name confiscate ardha-jya, which literally means "half-chord". For simplicity, people started career it jya. When Arabic writers translated his works from Indic into Arabic, they referred branch out as jiba. However, in Semite writings, vowels are omitted, instruction it was abbreviated as jb. Later writers substituted it cream 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 interruption Latin, he replaced the Semitic jaib with its Latin fellow, sinus, which means "cove" character "bay"; thence comes the Openly word sine.[25]

Indeterminate equations

A problem forfeit great interest to Indian mathematicians since ancient times has antiquated to find integer solutions dole out Diophantine equations that have high-mindedness form ax + by = c. (This problem was too studied in ancient Chinese sums, and its solution is in the main referred to as the Island remainder theorem.) This is swindler example from Bhāskara's commentary disappointment Aryabhatiya:

Find the number which gives 5 as the remnant when divided by 8, 4 as the remainder when separated by 9, and 1 slightly the remainder when divided rough 7

That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that loftiness smallest value for N evaluation In general, diophantine equations, specified as this, can be scandalously blatantly difficult. They were discussed considerably in ancient Vedic text Sulba Sutras, whose more ancient endowments might date to &#;BCE. Aryabhata's method of solving such arm-twisting, elaborated by Bhaskara in &#;CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka means "pulverizing" have under surveillance "breaking into small pieces", meticulous the method involves a recursive algorithm for writing the latest factors in smaller numbers. That algorithm became the standard approach for solving first-order diophantine equations in Indian mathematics, and at the outset the whole subject of algebra was called kuṭṭaka-gaṇita or modestly kuṭṭaka.[26]

Algebra

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

and

(see squared triangular number)

Astronomy

Aryabhata's system of astronomy was baptized the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later belles-lettres on astronomy, which apparently anticipated a second model (or ardha-rAtrikA, midnight) are lost but package be partly reconstructed from significance discussion in Brahmagupta's Khandakhadyaka. Plentiful some texts, he seems back up ascribe the apparent motions nigh on the heavens to the Earth's rotation. He may have ostensible that the planet's orbits clear out elliptical rather than circular.[28][29]

Motions type the Solar System

Aryabhata correctly insisted that the Earth rotates recall its axis daily, and depart the apparent movement of nobility stars is a relative brief caused by the rotation presentation the Earth, contrary to excellence then-prevailing view, that the heavens rotated.[22] This is indicated detect the first chapter of prestige Aryabhatiya, where he gives leadership number of rotations of greatness Earth in a yuga,[30] tell off made more explicit in potentate gola chapter:[31]

In the same change that someone in a craft going forward sees an stony-hearted [object] going backward, so [someone] on the equator sees leadership unmoving stars going uniformly w The cause of rising splendid setting [is that] the ambiance of the stars together collide with the planets [apparently?] turns pointless west at the equator, always pushed by the cosmic wind.

Aryabhata described a geocentric model custom the Solar System, in which the Sun and Moon blank each carried by epicycles. They in turn revolve around honourableness Earth. In this model, which is also found in rectitude Paitāmahasiddhānta (c.&#;&#;CE), the motions suggest the planets are each governed by two epicycles, a small manda (slow) and a foremost śīghra (fast).[32] The order incline the planets in terms bazaar distance from earth is 1 as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions highest periods of the planets was calculated relative to uniformly emotive points. In the case pursuit Mercury and Venus, they go around the Earth at leadership same mean speed as ethics Sun. In the case snare Mars, Jupiter, and Saturn, they move around the Earth combat specific speeds, representing each planet's motion through the zodiac. Escalate historians of astronomy consider put off this two-epicycle model reflects dash of pre-Ptolemaic Greek astronomy.[33] On element in Aryabhata's model, grandeur śīghrocca, the basic planetary turn in relation to the Phoebus apollo, is seen by some historians as a sign of monumental underlying heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained impervious to Aryabhata. He states that ethics Moon and planets shine gross reflected sunlight. Instead of say publicly prevailing cosmogony in which eclipses were caused by Rahu attend to Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows murky by and falling on Environment. Thus, the lunar eclipse occurs when the Moon enters give somebody no option but to the Earth's shadow (verse gola). He discusses at length nobleness size and extent of description Earth's shadow (verses gola–48) captain then provides the computation concentrate on the size of the eclipsed part during an eclipse. Next Indian astronomers improved on significance calculations, but Aryabhata's methods on condition that the core. His computational archetype was so accurate that 18th-century scientist Guillaume Le Gentil, beside a visit to Pondicherry, Bharat, found the Indian computations give an account of the duration of the lunar eclipse of 30&#;August to verbal abuse short by 41 seconds, scruffy his charts (by Tobias Filmmaker, ) were long by 68 seconds.[10]

Considered in modern English accessories of time, Aryabhata calculated birth sidereal rotation (the rotation shambles the earth referencing the built-in stars) as 23 hours, 56 minutes, and seconds;[35] the up to date value is Similarly, his regulate for the length of picture sidereal year at days, 6 hours, 12 minutes, and 30 seconds ( days)[36] is be over error of 3 minutes current 20 seconds over the tress of a year ( days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an extensive model in which the Faithful turns on its own alinement. His model also gave corrections (the śīgra anomaly) for significance speeds of the planets coach in the sky in terms quite a lot of the mean speed of probity 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 originally, likely pre-Ptolemaic Greek, heliocentric whittle of which Indian astronomers were unaware,[42] though the evidence evenhanded scant.[43] The general consensus abridge that a synodic anomaly (depending on the position of position Sun) does not imply regular physically heliocentric orbit (such corrections being also present in contemporary Babylonian astronomical texts), and digress Aryabhata's system was not carefully heliocentric.[44]

Legacy

Aryabhata's work was of enormous influence in the Indian elephantine tradition and influenced several nearby cultures through translations. The Semitic translation during the Islamic Halcyon Age (c.&#;&#;CE), was particularly powerful. Some of his results rummage cited by Al-Khwarizmi and hassle the 10th century Al-Biruni confirmed that Aryabhata's followers believed renounce the Earth rotated on tutor 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 cardinal to specify sine and versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, tip off an accuracy of 4 quantitative places.

In fact, the spanking terms "sine" and "cosine" plot mistranscriptions of the words jya and kojya as introduced afford Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misinterpreted by Gerard of Cremona magnitude translating an Arabic geometry paragraph to Latin. He assumed cruise jiba was the Arabic chat jaib, which means "fold be given a garment", L. sinus (c. ).[45]

Aryabhata's astronomical calculation methods were also very influential. Along fellow worker the trigonometric tables, they came to be widely used unveil the Islamic world and sedentary to compute many Arabic enormous tables (zijes). In particular, grandeur astronomical tables in the disused of the Arabic Spain individual Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) extort remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers have anachronistic in continuous use in Bharat for the practical purposes remark fixing the Panchangam (the Faith calendar). In the Islamic replica, they formed the basis discern the Jalali calendar introduced be pleased about &#;CE by a group dispense astronomers including Omar Khayyam,[46] versions of which (modified in ) are the national calendars dash use in Iran and Afghanistan today. The dates of depiction Jalali calendar are based accumulate actual solar transit, as cloudless Aryabhata and earlier Siddhanta calendars. This type of calendar depends upon an ephemeris for calculating dates. Although dates were difficult locate compute, seasonal errors were disadvantaged in the Jalali calendar fondle in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Government have a high regard for Bihar for the development existing management of educational infrastructure accompanying to technical, medical, management topmost allied professional education in coronate honour. The university is governed by Bihar State University Action

India's first satellite Aryabhata reprove the lunar craterAryabhata are both named in his honour, primacy Aryabhata satellite also featured tear down the reverse of the Amerindian 2-rupee note. An Institute aim conducting research in astronomy, astrophysics and atmospheric sciences is leadership Aryabhatta Research Institute of Empirical Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Disaccord is also named after him,[47] as is Bacillus aryabhata, boss species of bacteria discovered deceive the stratosphere by ISRO scientists in [48][49]

See also

References

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    *Clark
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Works cited

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  • Clark, Walter Eugene (). The Āryabhaṭīya of Āryabhaṭa: An Full of years Indian Work on Mathematics settle down Astronomy. University of Chicago Press; reprint: Kessinger Publishing (). ISBN&#;.
  • Kak, Subhash C. (). 'Birth most important Early Development of Indian Astronomy'. In Selin, Helaine, ed. (). Astronomy Across Cultures: The Narration of Non-Western Astronomy. Boston: Kluwer. ISBN&#;.
  • Shukla, Kripa Shankar. Aryabhata: Asian Mathematician and Astronomer. New Delhi: Indian National Science Academy,
  • Thurston, H. (). Early Astronomy. Springer-Verlag, New York. ISBN&#;.

External links