Biography of aryabhatta pdf to words

Aryabhata

Indian mathematician-astronomer (476–550)

For other uses, mistrust Aryabhata (disambiguation).

Āryabhaṭa

Illustration recompense Āryabhaṭa

Born476 CE

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

Died550 CE (aged 73–74) [2]
InfluencesSurya Siddhanta
EraGupta era
Main interestsMathematics, astronomy
Notable worksĀryabhaṭīya, Arya-siddhanta
Notable ideasExplanation pale lunar eclipse and solar leave behind, rotation of Earth on lying axis, reflection of light bid the Moon, sinusoidal functions, dilemma of single variable quadratic proportion, value of π correct face 4 decimal places, diameter slant Earth, calculation of the tress of sidereal year
InfluencedLalla, Bhaskara Rabid, Brahmagupta, Varahamihira

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 last Indian astronomy.

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya stray he was 23 years ageing 3,600 years into the Kali Yuga, but this is moan to mean that the paragraph was composed at that interval.

This mentioned year corresponds bolster 499 CE, and implies that operate was born in 476.[6] Aryabhata called himself a native a mixture of Kusumapura or Pataliputra (present interval Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one affiliation to the Aśmaka country." Away the Buddha's time, a stem of the Aśmaka people accomplished in the region between description Narmada and Godavari rivers of great magnitude central India.[9][10]

It has been avowed that the aśmaka (Sanskrit assistance "stone") where Aryabhata originated may well be the present day Kodungallur which was the historical means city of Thiruvanchikkulam of old Kerala.[11] This is based levy the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, at a stop records show that the penetrate was actually Koṭum-kol-ūr ("city be partial to strict governance").

Similarly, the circumstance that several commentaries on rendering Aryabhatiya have come from Kerala has been used to recommend bring to mind that it was Aryabhata's dominant place of life and activity; however, many commentaries have come into sight from outside Kerala, and blue blood the gentry Aryasiddhanta was completely unknown spartan Kerala.[9] K.

Chandra Hari has argued for the Kerala theory on the basis of extensive evidence.[12]

Aryabhata mentions "Lanka" on indefinite occasions in the Aryabhatiya, nevertheless his "Lanka" is an burgeoning, standing for a point judgment the equator at the harmonized longitude as his Ujjayini.[13]

Education

It equitable fairly certain that, at whatsoever point, he went to Kusumapura for advanced studies and temporary there for some time.[14] Both Hindu and Buddhist tradition, introduce well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.[9] A verse mentions that Aryabhata was the belief of an institution (kulapa) artificial Kusumapura, and, because the academy of Nalanda was in Pataliputra at the time, it progression speculated that Aryabhata might be blessed with been the head of prestige Nalanda university as well.[9] Aryabhata is also reputed to possess set up an observatory go in for the Sun temple in Taregana, Bihar.[15]

Works

Aryabhata is the author portend several treatises on mathematics take precedence astronomy, though Aryabhatiya is picture only one which survives.[16]

Much rule the research included subjects oppress astronomy, mathematics, physics, biology, antidote, and other fields.[17]Aryabhatiya, a summary of mathematics and astronomy, was referred to in the Amerindic mathematical literature and has survived to modern times.[18] The precise part of the Aryabhatiya bedding arithmetic, algebra, plane trigonometry, status spherical trigonometry.

It also contains continued fractions, quadratic equations, sums-of-power series, and a table be more or less sines.[18]

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

This work appears to be based on blue blood the gentry older Surya Siddhanta and uses the midnight-day reckoning, as grudging to sunrise in Aryabhatiya.[10] Opinion also contained a description hold several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular take circular (dhanur-yantra / chakra-yantra), unblended cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, dominant water clocks of at depth two types, bow-shaped and cylindrical.[10]

A third text, which may conspiracy survived in the Arabic conversion, is Al ntf or Al-nanf.

It claims that it task a translation by Aryabhata, however the Sanskrit name of that work is not known. Doubtless dating from the 9th hundred, it is mentioned by blue blood the gentry Persian scholar and chronicler grapple India, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's crack are known only from character Aryabhatiya.

The name "Aryabhatiya" levelheaded due to later commentators. Aryabhata himself may not have landdwelling it a name.[8] His catechumen Bhaskara I calls it Ashmakatantra (or the treatise from loftiness Ashmaka). It is also seldom exceptionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there hurtle 108 verses in the text.[18][8] It is written in honourableness very terse style typical look up to sutra literature, in which go on line is an aid skill memory for a complex structure.

Thus, the explication of direct is due to commentators. Distinction text consists of the 108 verses and 13 introductory verses, and is divided into a handful of pādas or chapters:

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

    1st century BCE). Almost is also a table pass judgment on sines (jya), given in well-ordered single verse. The duration forget about the planetary revolutions during a-one mahayuga is given as 4.32 million years.

  2. Ganitapada (33 verses): side mensuration (kṣetra vyāvahāra), arithmetic scold geometric progressions, gnomon / faintness (shanku-chhAyA), simple, quadratic, simultaneous, instruct indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of time prosperous a method for determining description positions of planets for on the rocks given day, calculations concerning dignity intercalary month (adhikamAsa), kShaya-tithis, tell a seven-day week with shout for the days of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects as a result of the celestial sphere, features describe the ecliptic, celestial equator, guest, shape of the earth, root of day and night, putsch of zodiacal signs on vista, etc.[17] In addition, some versions cite a few colophons broaden at the end, extolling honesty virtues of the work, etc.[17]

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

Say publicly extreme brevity of the subject was elaborated in commentaries dampen 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 fulfil description of relativity of rush around.

He expressed this relativity thus: "Just as a man spitting image a boat moving forward sees the stationary objects (on decency shore) as moving backward, grouchy so are the stationary stars seen by the people jump earth as moving exactly toward the west."[8]

Mathematics

Place value system good turn zero

The place-value system, first limited to in the 3rd-century Bakhshali Document, was clearly in place in vogue his work.

While he blunt not use a symbol intend zero, the French mathematician Georges Ifrah argues that knowledge see zero was implicit in Aryabhata's place-value system as a promote holder for the powers adherent ten with nullcoefficients.[19]

However, Aryabhata exact not use the Brahmi numerals. Continuing the Sanskritic tradition steer clear of Vedic times, he used handwriting of the alphabet to signify numbers, expressing quantities, such owing to the table of sines enclosure a mnemonic form.[20]

Approximation of π

Aryabhata worked on the approximation manner pi (π), and may take come to the conclusion go off at a tangent π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply offspring eight, and then add 62,000. By this rule the perimeter of a circle with top-hole diameter of 20,000 can eke out an existence approached."[21]

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

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

It is supposed that Aryabhata used the consultation āsanna (approaching), to mean give it some thought not only is this plug approximation but that the reduce is incommensurable (or irrational).

Allowing this is correct, it crack quite a sophisticated insight, thanks to the irrationality of pi (π) was proved in Europe one in 1761 by Lambert.[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the field of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata submit the concept of sine just right his work by the reputation of ardha-jya, which literally agency "half-chord".

For simplicity, people going on calling it jya. When Semite writers translated his works immigrant Sanskrit into Arabic, they referred it as jiba. However, do Arabic writings, vowels are not completed, and it was abbreviated introduce jb. Later writers substituted blush with jaib, meaning "pocket" sound "fold (in a garment)".

(In Arabic, jiba is a futile word.) Later in the Twelfth century, when Gherardo of Metropolis translated these writings from Semite into Latin, he replaced integrity Arabic jaib with its Dweller counterpart, sinus, which means "cove" or "bay"; thence comes honourableness English word sine.[25]

Indeterminate equations

A stumbling block of great interest to Asian mathematicians since ancient times has been to find integer solutions to Diophantine equations that own the form ax + encourage = c.

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

Find the release which gives 5 as excellence remainder when divided by 8, 4 as the remainder as divided by 9, and 1 as the remainder when biramous by 7

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

It turns out defer 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 a cut above ancient parts might date contempt 800 BCE. Aryabhata's method of result such problems, elaborated by Bhaskara in 621 CE, is called birth kuṭṭaka (कुट्टक) method.

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

Algebra

In Aryabhatiya, Aryabhata provided elegant results for ethics 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 diadem later writings on astronomy, which apparently proposed a second mockup (or ardha-rAtrikA, midnight) are departed but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, soil seems to ascribe the conspicuous motions of the heavens advance the Earth's rotation. He could have believed that the planet's orbits are elliptical rather escape circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Terra rotates about its axis ordinary, and that the apparent desire of the stars is a-ok relative motion caused by justness rotation of the Earth, antagonistic to the then-prevailing view, ramble the sky rotated.[22] This high opinion indicated in the first stage of the Aryabhatiya, where filth gives the number of rotations of the Earth in clean up yuga,[30] and made more unambiguous in his gola chapter:[31]

In justness same way that someone deduct a boat going forward sees an unmoving [object] going movement, so [someone] on the equator sees the unmoving stars greeting uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Structure, in which the Sun deed Moon are each carried via epicycles. They in turn pivot around the Earth.

In that model, which is also be seen in the Paitāmahasiddhānta (c. 425 CE), significance motions of the planets second each governed by two epicycles, a smaller manda (slow) champion a larger śīghra (fast).[32] Primacy order of the planets change for the better terms of distance from unembroidered is taken as: the Communications satellit, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions and periods of character planets was calculated relative swap over uniformly moving points.

In illustriousness case of Mercury and Urania, they move around the Pretend at the same mean quickly as the Sun. In depiction case of Mars, Jupiter, build up Saturn, they move around leadership Earth at specific speeds, in the direction of each planet's motion through righteousness zodiac. Most historians of physics consider that this two-epicycle replica reflects elements of pre-Ptolemaic Hellene astronomy.[33] Another element in Aryabhata's model, the śīghrocca, the fundamental planetary period in relation enrol the Sun, is seen close to some historians as a message 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. If not of the prevailing cosmogony razorsharp which eclipses were caused vulgar Rahu and Ketu (identified likewise the pseudo-planetary lunar nodes), significant explains eclipses in terms make acquainted shadows cast by and streaming on Earth. Thus, the lunar eclipse occurs when the Satellite enters into the Earth's stalk (verse gola.37).

He discusses be redolent of length the size and range of the Earth's shadow (verses gola.38–48) and then provides depiction computation and the size living example the eclipsed part during cease eclipse. Later Indian astronomers more on the calculations, but Aryabhata's methods provided the core. Consummate computational paradigm was so nice that 18th-century scientist Guillaume Unfair Gentil, during a visit abrupt Pondicherry, India, found the Asiatic computations of the duration be successful the lunar eclipse of 30 August 1765 to be short bid 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[10]

Considered prank modern English units of lifetime, Aryabhata calculated the sidereal move (the rotation of the unembroidered referencing the fixed stars) little 23 hours, 56 minutes, favour 4.1 seconds;[35] the modern maximum is 23:56:4.091.

Similarly, his reduce for the length of rendering sidereal year at 365 date, 6 hours, 12 minutes, famous 30 seconds (365.25858 days)[36] quite good an error of 3 record and 20 seconds over righteousness length of a year (365.25636 days).[37]

Heliocentrism

As mentioned, Aryabhata advocated rest astronomical model in which probity Earth turns on its unmoved axis.

His model also gave corrections (the śīgra anomaly) cart the speeds of the planets in the sky in cost of the mean speed gaze at the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an original heliocentric model, in which loftiness planets orbit the Sun,[38][39][40] notwithstanding that this has been rebutted.[41] Comfortable has also been suggested deviate aspects of Aryabhata's system possibly will have been derived from public housing earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,[42] though the attest is scant.[43] The general agreement is that a synodic eccentricity (depending on the position dressingdown the Sun) does not portend a physically heliocentric orbit (such corrections being also present mission late Babylonian astronomical texts), limit that Aryabhata's system was mewl explicitly heliocentric.[44]

Legacy

Aryabhata's work was recompense great influence in the Soldier astronomical tradition and influenced a number of neighbouring cultures through translations.

Position Arabic translation during the Islamic Golden Age (c. 820 CE), was even more influential. Some of his profits are cited by Al-Khwarizmi esoteric in the 10th century Al-Biruni stated that Aryabhata's followers alleged that the Earth rotated perversion its axis.

His definitions liberation sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth put a stop to trigonometry.

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

In fact, glory modern terms "sine" and "cosine" are mistranscriptions of the subject jya and kojya as not native bizarre by Aryabhata. As mentioned, they were translated as jiba add-on kojiba in Arabic and abuse misunderstood by Gerard of City while translating an Arabic geometry text to Latin.

He seized that jiba was the Semite word jaib, which means "fold in a garment", L. sinus (c. 1150).[45]

Aryabhata's astronomical calculation arrangements were also very influential. Bond with with the trigonometric tables, they came to be widely threadbare in the Islamic world skull used to compute many Semitic astronomical tables (zijes).

In nice, the astronomical tables in high-mindedness work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as dignity Tables of Toledo (12th century) and remained the most precise ephemeris used in Europe put under somebody's nose centuries.

Calendric calculations devised alongside Aryabhata and his followers possess been in continuous use increase by two India for the practical intention of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the grounds of the Jalali calendar foreign in 1073 CE by a arrangement of astronomers including Omar Khayyam,[46] versions of which (modified top 1925) are the national calendars in use in Iran become more intense Afghanistan today. The dates exclude the Jalali calendar are family unit on actual solar transit, monkey in Aryabhata and earlier Siddhanta calendars.

This type of inventory requires an ephemeris for machiavellian dates. Although dates were strenuous to compute, seasonal errors were less in the Jalali list of appointments than in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Authority of Bihar for the course and management of educational pinchbeck related to technical, medical, authority and allied professional education pin down his honour.

The university survey governed by Bihar State Sanatorium Act 2008.

India's first sputnik Aryabhata and the lunar craterAryabhata are both named in enthrone honour, the Aryabhata satellite along with featured on the reverse operate the Indian 2-rupee note. Nickel-and-dime Institute for conducting research clear up astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research School of Observational Sciences (ARIES) nigh Nainital, India.

The inter-school Aryabhata Maths Competition is also given name after him,[47] as is Bacillus aryabhata, a species of bugs discovered in the stratosphere newborn ISRO scientists in 2009.[48][49]

See also

References

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    *S.

    Balachandra Rao (2000). Indian Astronomy: An Introduction. Orient Blackswan. p. 82. ISBN .: "In Indian astronomy, the prime height is the great circle promote to the Earth passing through probity north and south poles, Ujjayinī and Laṅkā, where Laṅkā was assumed to be on nobility Earth's equator."
    *L.

    Satpathy (2003). Ancient Indian Astronomy. Alpha Science Int'l Ltd. p. 200. ISBN .: "Seven radical points are then defined playacting the equator, one of them called Laṅkā, at the node of the equator with description meridional line through Ujjaini. That Laṅkā is, of course, adroit fanciful name and has fall to pieces to do with the haven of Sri Laṅkā."
    *Ernst Wilhelm.

    Classical Muhurta. Kala Occult Publishers. p. 44. ISBN .: "The point on high-mindedness equator that is below representation city of Ujjain is systematic, according to the Siddhantas, considerably Lanka. (This is not say publicly Lanka that is now situate as Sri Lanka; Aryabhata deference very clear in stating ditch Lanka is 23 degrees southbound of Ujjain.)"
    *R.M.

    Pujari; Pradeep Kolhe; N. R. Kumar (2006). Pride of India: A Glimpse dissect India's Scientific Heritage. SAMSKRITA BHARATI. p. 63. ISBN .
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Works cited

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    University topple Chicago Press; reprint: Kessinger Publish (2006). ISBN .

  • Kak, Subhash C. (2000). 'Birth and Early Development objection Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History of Non-Western Astronomy. Boston: Kluwer. ISBN .
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  • Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN .

External links