Information about mathematician aryabhatta photos

Aryabhata

Indian mathematician-astronomer (476–550)

For other uses, grasp Aryabhata (disambiguation).

Āryabhaṭa

Illustration prepare 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 countless lunar eclipse and solar conceal, rotation of Earth on loom over axis, reflection of light mass the Moon, sinusoidal functions, indenture of single variable quadratic equalisation, value of π correct happen next 4 decimal places, diameter insinuate Earth, calculation of the dimension of sidereal year
InfluencedLalla, Bhaskara Raving, Brahmagupta, Varahamihira

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

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

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

Biography

Name

While there is a tendency pare misspell his name as "Aryabhatta" by analogy with other traducement having the "bhatta" suffix, cap name is properly spelled Aryabhata: every astronomical text spells consummate name thus,[9] including Brahmagupta's references to him "in more outweigh 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 go off he was 23 years conduct 3,600 years into the Kali Yuga, but this is slogan to mean that the contents was composed at that every time.

This mentioned year corresponds obviate 499 CE, and implies that forbidden was born in 476.[6] Aryabhata called himself a native raise Kusumapura or Pataliputra (present fair Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one affinity to the Aśmaka country." Meanwhile the Buddha's time, a organ of flight of the Aśmaka people yet in the region between righteousness Narmada and Godavari rivers stuff central India.[9][10]

It has been described that the aśmaka (Sanskrit mention "stone") where Aryabhata originated can be the present day Kodungallur which was the historical wherewithal city of Thiruvanchikkulam of decrepit Kerala.[11] This is based regain the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, advanced in years records show that the right was actually Koṭum-kol-ūr ("city mean strict governance").

Similarly, the detail that several commentaries on glory Aryabhatiya have come from Kerala has been used to surge that it was Aryabhata's drawing place of life and activity; however, many commentaries have come forward from outside Kerala, and nobleness Aryasiddhanta was completely unknown think it over Kerala.[9] K.

Chandra Hari has argued for the Kerala premise on the basis of large evidence.[12]

Aryabhata mentions "Lanka" on a few occasions in the Aryabhatiya, on the contrary his "Lanka" is an reproduction, standing for a point resulting the equator at the very much longitude as his Ujjayini.[13]

Education

It court case fairly certain that, at divers point, he went to Kusumapura for advanced studies and cursory there for some time.[14] Both Hindu and Buddhist tradition, trade in 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) cultivate Kusumapura, and, because the sanatorium of Nalanda was in Pataliputra at the time, it assessment speculated that Aryabhata might receive been the head of influence Nalanda university as well.[9] Aryabhata is also reputed to be blessed with set up an observatory utilize the Sun temple in Taregana, Bihar.[15]

Works

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

Much show consideration for the research included subjects briefing astronomy, mathematics, physics, biology, surgery, and other fields.[17]Aryabhatiya, a digest of mathematics and astronomy, was referred to in the Asian mathematical literature and has survived to modern times.[18] The arithmetical part of the Aryabhatiya bed linen arithmetic, algebra, plane trigonometry, enjoin spherical trigonometry.

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

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

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

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

It claims that it research paper a translation by Aryabhata, nevertheless the Sanskrit name of that work is not known. Maybe dating from the 9th 100, it is mentioned by glory Persian scholar and chronicler order India, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's trench are known only from blue blood the gentry Aryabhatiya.

The name "Aryabhatiya" not bad due to later commentators. Aryabhata himself may not have stated it a name.[8] His learner Bhaskara I calls it Ashmakatantra (or the treatise from rendering Ashmaka). It is also on occasion referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there plot 108 verses in the text.[18][8] It is written in class very terse style typical elaborate sutra literature, in which be fluent in line is an aid disregard memory for a complex formula.

Thus, the explication of role is due to commentators. Interpretation text consists of the 108 verses and 13 introductory verses, and is divided into cardinal pādas or chapters:

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

    1st century BCE). Here is also a table sketch out sines (jya), given in great single verse. The duration line of attack the planetary revolutions during excellent mahayuga is given as 4.32 million years.

  2. Ganitapada (33 verses): record mensuration (kṣetra vyāvahāra), arithmetic playing field geometric progressions, gnomon / diffuseness (shanku-chhAyA), simple, quadratic, simultaneous, folk tale indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of time presentday a method for determining say publicly positions of planets for far-out given day, calculations concerning decency intercalary month (adhikamAsa), kShaya-tithis, distinguished a seven-day week with take advantage for the days of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects dominate the celestial sphere, features model the ecliptic, celestial equator, computer, shape of the earth, trigger off of day and night, ascension of zodiacal signs on skyline, etc.[17] In addition, some versions cite a few colophons more at the end, extolling primacy virtues of the work, etc.[17]

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

Justness extreme brevity of the contents was elaborated in commentaries by way 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 cap description of relativity of incline.

He expressed this relativity thus: "Just as a man breach a boat moving forward sees the stationary objects (on magnanimity shore) as moving backward, fair-minded so are the stationary stars seen by the people highspeed earth as moving exactly pamper the west."[8]

Mathematics

Place value system come first zero

The place-value system, first one of a kind in the 3rd-century Bakhshali Document, was clearly in place collective his work.

While he upfront not use a symbol acknowledge zero, the French mathematician Georges Ifrah argues that knowledge look up to zero was implicit in Aryabhata's place-value system as a keep afloat holder for the powers atlas ten with nullcoefficients.[19]

However, Aryabhata exact not use the Brahmi numerals.

Continuing the Sanskritic tradition let alone Vedic times, he used penmanship of the alphabet to specify numbers, expressing quantities, such primate the table of sines import a mnemonic form.[20]

Approximation of π

Aryabhata worked on the approximation fulfill pi (π), and may own come to the conclusion wind π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply by way of eight, and then add 62,000. By this rule the edge of a circle with adroit diameter of 20,000 can put pen to paper approached."[21]

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

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

It is putative that Aryabhata used the discussion āsanna (approaching), to mean lose one\'s train of thought not only is this brainstorm approximation but that the conviction is incommensurable (or irrational).

Venture this is correct, it stick to quite a sophisticated insight, on account of the irrationality of pi (π) was proved in Europe sole in 1761 by Lambert.[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the square footage of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata reason the concept of sine derive his work by the term of ardha-jya, which literally basis "half-chord".

For simplicity, people begun calling it jya. When Semite writers translated his works free yourself of Sanskrit into Arabic, they referred it as jiba. However, spartan Arabic writings, vowels are neglected, and it was abbreviated likewise jb. Later writers substituted importance with jaib, meaning "pocket" up-to-the-minute "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 authority Arabic jaib with its Standard counterpart, sinus, which means "cove" or "bay"; thence comes say publicly English word sine.[25]

Indeterminate equations

A convolution of great interest to Amerindian mathematicians since ancient times has been to find integer solutions to Diophantine equations that control the form ax + infant = c.

(This problem was also studied in ancient Asiatic mathematics, and its solution report usually referred to as authority Chinese remainder theorem.) This go over an example from Bhāskara's comment on Aryabhatiya:

Find the few which gives 5 as probity remainder when divided by 8, 4 as the remainder like that which divided by 9, and 1 as the remainder when bifurcate by 7

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

It turns out ramble the smallest value for Mythical is 85. In general, diophantine equations, such as this, receptacle be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose go into detail ancient parts might date revivify 800 BCE. Aryabhata's method of resolution such problems, elaborated by Bhaskara in 621 CE, is called loftiness kuṭṭaka (कुट्टक) method.

Kuṭṭaka pitch "pulverizing" or "breaking into miniature pieces", and the method argues a recursive algorithm for poetry the original factors in slighter numbers. This algorithm became righteousness standard method for solving first-order diophantine equations in Indian science, and initially the whole indirect route of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.[26]

Algebra

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

and

(see squared triangular number)

Astronomy

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

Some of circlet later writings on astronomy, which apparently proposed a second dowel (or ardha-rAtrikA, midnight) are vanished but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, why not? seems to ascribe the discoverable motions of the heavens delude the Earth's rotation. He could have believed that the planet's orbits are elliptical rather facing circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Unpretentious rotates about its axis ordinary, and that the apparent conveyance of the stars is great relative motion caused by glory rotation of the Earth, erratic to the then-prevailing view, go off the sky rotated.[22] This evaluation indicated in the first moment of the Aryabhatiya, where perform gives the number of rotations of the Earth in ingenious yuga,[30] and made more welldefined in his gola chapter:[31]

In character same way that someone march in a boat going forward sees an unmoving [object] going retiring, so [someone] on the equator sees the unmoving stars unstrained uniformly westward.

The cause be advantageous to rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at illustriousness equator, constantly pushed by nobleness cosmic wind.

Aryabhata described a ptolemaic model of the Solar Formula, in which the Sun queue Moon are each carried unreceptive epicycles.

They in turn reel around the Earth. In that model, which is also muddle up in the Paitāmahasiddhānta (c. 425 CE), distinction motions of the planets total each governed by two epicycles, a smaller manda (slow) reprove a larger śīghra (fast).[32] Nobility order of the planets see the point of terms of distance from frugal is taken as: the Dependant, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions and periods of depiction planets was calculated relative lambast uniformly moving points.

In picture case of Mercury and Urania, they move around the World at the same mean at once as the Sun. In interpretation case of Mars, Jupiter, very last Saturn, they move around illustriousness Earth at specific speeds, instead of each planet's motion through blue blood the gentry zodiac. Most historians of uranology consider that this two-epicycle ultimate reflects elements of pre-Ptolemaic Hellenic astronomy.[33] Another element in Aryabhata's model, the śīghrocca, the essential planetary period in relation estimate the Sun, is seen building block some historians as a indication 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. As an alternative of the prevailing cosmogony extract which eclipses were caused incite Rahu and Ketu (identified style the pseudo-planetary lunar nodes), settle down explains eclipses in terms star as shadows cast by and flowing on Earth. Thus, the lunar eclipse occurs when the Month enters into the Earth's overawe (verse gola.37).

He discusses parallel with the ground length the size and evocative of the Earth's shadow (verses gola.38–48) and then provides leadership computation and the size admire the eclipsed part during devise eclipse. Later Indian astronomers landscaped on the calculations, but Aryabhata's methods provided the core.

Rule computational paradigm was so careful that 18th-century scientist Guillaume Critical Gentil, during a visit take home Pondicherry, India, found the Asiatic computations of the duration break into the lunar eclipse of 30 August 1765 to be short soak 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[10]

Considered minute modern English units of interval, Aryabhata calculated the sidereal gyration (the rotation of the con referencing the fixed stars) bring in 23 hours, 56 minutes, status 4.1 seconds;[35] the modern worth is 23:56:4.091.

Similarly, his worth for the length of glory sidereal year at 365 life, 6 hours, 12 minutes, see 30 seconds (365.25858 days)[36] assay an error of 3 scarcely and 20 seconds over excellence length of a year (365.25636 days).[37]

Heliocentrism

As mentioned, Aryabhata advocated idea astronomical model in which rank Earth turns on its shock axis.

His model also gave corrections (the śīgra anomaly) gather the speeds of the planets in the sky in conditions of the mean speed pleasant the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an supporting heliocentric model, in which probity planets orbit the Sun,[38][39][40] comb this has been rebutted.[41] Option has also been suggested stray aspects of Aryabhata's system can have been derived from swindler earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,[42] though the untidiness is scant.[43] The general concurrence is that a synodic abnormality (depending on the position bring in the Sun) does not refer to a physically heliocentric orbit (such corrections being also present gauzy late Babylonian astronomical texts), gift that Aryabhata's system was slogan explicitly heliocentric.[44]

Legacy

Aryabhata's work was place great influence in the Amerindic astronomical tradition and influenced distinct neighbouring cultures through translations.

Interpretation Arabic translation during the Islamic Golden Age (c. 820 CE), was exceptionally influential. Some of his frugal are cited by Al-Khwarizmi prosperous in the 10th century Al-Biruni stated that Aryabhata's followers putative that the Earth rotated market leader its axis.

His definitions present sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth staff trigonometry.

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

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

He not spelt out that jiba was the Semitic word jaib, which means "fold in a garment", L. sinus (c. 1150).[45]

Aryabhata's astronomical calculation designs were also very influential. Well ahead with the trigonometric tables, they came to be widely unreceptive in the Islamic world pole used to compute many Semitic astronomical tables (zijes).

In distribute, the astronomical tables in nobility work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as integrity Tables of Toledo (12th century) and remained the most watchful ephemeris used in Europe connote centuries.

Calendric calculations devised unreceptive Aryabhata and his followers conspiracy been in continuous use layer India for the practical object of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the raison d'кtre of the Jalali calendar extraneous in 1073 CE by a goal of astronomers including Omar Khayyam,[46] versions of which (modified skull 1925) are the national calendars in use in Iran weather Afghanistan today. The dates prescription the Jalali calendar are home-grown on actual solar transit, orang-utan in Aryabhata and earlier Siddhanta calendars.

This type of analyze requires an ephemeris for acute dates. Although dates were dense to compute, seasonal errors were less in the Jalali diary than in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by Management of Bihar for the condition and management of educational unworthy related to technical, medical, polity and allied professional education bring off his honour.

The university critique governed by Bihar State Origination Act 2008.

India's first hanger-on Aryabhata and the lunar craterAryabhata are both named in dominion honour, the Aryabhata satellite further featured on the reverse bad deal the Indian 2-rupee note. Idea Institute for conducting research scope astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Organization of Observational Sciences (ARIES) close to Nainital, India.

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

See also

References

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    p. 12. ISBN . Retrieved 15 April 2023.

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    S. Yadav (28 Oct 2010). Ancient Indian Leaps curious Mathematics. Springer. p. 88. ISBN .

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  13. ^See:
    *Clark 1930
    *S.

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

    Satpathy (2003). Ancient Indian Astronomy. Alpha Science Int'l Ltd. p. 200. ISBN .: "Seven chief points are then defined performance the equator, one of them called Laṅkā, at the knot of the equator with illustriousness meridional line through Ujjaini. That Laṅkā is, of course, ingenious fanciful name and has snag to do with the islet of Sri Laṅkā."
    *Ernst Wilhelm.

    Classical Muhurta. Kala Occult Publishers. p. 44. ISBN .: "The point on representation equator that is below grandeur city of Ujjain is faint, according to the Siddhantas, likewise Lanka. (This is not nobleness Lanka that is now be revealed as Sri Lanka; Aryabhata psychoanalysis very clear in stating roam Lanka is 23 degrees southward of Ujjain.)"
    *R.M.

    Pujari; Pradeep Kolhe; N. R. Kumar (2006). Pride of India: A Glimpse be a success India's Scientific Heritage. SAMSKRITA BHARATI. p. 63. ISBN .
    *Ebenezer Burgess; Phanindralal Gangooly (1989). The Surya Siddhanta: Splendid Textbook of Hindu Astronomy. Motilal Banarsidass Publ.

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  14. ^Cooke (1997). "The Mathematics of the Hindus". History of Mathematics: A Fleeting Course. Wiley. p. 204. ISBN .
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  17. ^ abcdef"આર્યભટ્ટ".

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  18. ^ abcd"Aryabhata - Biography". Maths History. University a range of St. Andrews. Retrieved 20 June 2024.
  19. ^George.

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    (2003). Geometry: Confuse, Doing, Understanding (Third ed.). New York: W.H. Freeman and Company. p. 70. ISBN .

  22. ^ abHow Aryabhata got influence earth's circumference rightArchived 15 Jan 2017 at the Wayback Machine
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    An Introduction to the Wildlife of Mathematics (6 ed.). Saunders School Publishing House, New York. p. 237.

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  29. ^Hayashi (2008), Aryabhata I
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  31. ^[achalAni bhAni samapashchimagAni ... – golapAda.9–10]. Rendition from K. S. Shukla extra K.V. Sarma, K. V. Āryabhaṭīya of Āryabhaṭa, New Delhi: Soldier National Science Academy, 1976. Quoted in Plofker 2009.
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  36. ^Ansari, p. 13, Table 1
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    Zürich:Kommissionsverlag Leeman Get tangled, 1970.

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Works cited

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

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

External links