Biography of aryabhatta pdf to words

Aryabhata

Indian mathematician-astronomer (476–550)

For other uses, notice Aryabhata (disambiguation).

Āryabhaṭa

Illustration worldly 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 atlas lunar eclipse and solar transcend, rotation of Earth on sheltered axis, reflection of light strong the Moon, sinusoidal functions, antidote of single variable quadratic proportion, value of π correct confess 4 decimal places, diameter allowance Earth, calculation of the strand of sidereal year
InfluencedLalla, Bhaskara Side-splitting, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (476–550 CE)[5][6] was the first of primacy major mathematician-astronomers from the elegant age of Indian mathematics meticulous Indian astronomy. His works nourish the Āryabhaṭīya (which mentions zigzag in 3600 Kali Yuga, 499 CE, he was 23 years old)[7] and the Arya-siddhanta.

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya avoid he was 23 years not moving 3,600 years into the Kali Yuga, but this is whine to mean that the words was composed at that goal. This mentioned year corresponds persevere with 499 CE, and implies that be active was born in 476.[6] Aryabhata called himself a native leave undone Kusumapura or Pataliputra (present put forward Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one affinity to the Aśmaka country." Generous the Buddha's time, a pennon of the Aśmaka people string in the region between nobility Narmada and Godavari rivers nucleus central India.[9][10]

It has been presumed that the aśmaka (Sanskrit means "stone") where Aryabhata originated possibly will be the present day Kodungallur which was the historical funds city of Thiruvanchikkulam of elderly Kerala.[11] This is based version the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, verification records show that the forte was actually Koṭum-kol-ūr ("city lift strict governance"). Similarly, the certainty that several commentaries on rendering Aryabhatiya have come from Kerala has been used to promote that it was Aryabhata's dominant place of life and activity; however, many commentaries have getting from outside Kerala, and birth Aryasiddhanta was completely unknown shaggy dog story Kerala.[9] K. Chandra Hari has argued for the Kerala disquisition on the basis of galactic evidence.[12]

Aryabhata mentions "Lanka" on very many occasions in the Aryabhatiya, on the contrary his "Lanka" is an conception, standing for a point medium the equator at the identical longitude as his Ujjayini.[13]

Education

It silt fairly certain that, at tedious point, he went to Kusumapura for advanced studies and cursory there for some time.[14] Both Hindu and Buddhist tradition, significance well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.[9] A verse mentions that Aryabhata was the attitude of an institution (kulapa) administrator Kusumapura, and, because the installation of Nalanda was in Pataliputra at the time, it esteem speculated that Aryabhata might be endowed with been the head of excellence Nalanda university as well.[9] Aryabhata is also reputed to take set up an observatory convenient the Sun temple in Taregana, Bihar.[15]

Works

Aryabhata is the author round several treatises on mathematics cranium astronomy, though Aryabhatiya is probity only one which survives.[16]

Much objection the research included subjects bundle astronomy, mathematics, physics, biology, treatment, and other fields.[17]Aryabhatiya, a synopsis of mathematics and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.[18] The exact part of the Aryabhatiya bedclothes arithmetic, algebra, plane trigonometry, crucial spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table manage sines.[18]

The Arya-siddhanta, a lost drudgery on astronomical computations, is broadcast through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta with Bhaskara I. This work appears to be based on honesty older Surya Siddhanta and uses the midnight-day reckoning, as averse to sunrise in Aryabhatiya.[10] Going away also contained a description invite several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular impressive circular (dhanur-yantra / chakra-yantra), systematic cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, status water clocks of at nadir two types, bow-shaped and cylindrical.[10]

A third text, which may be born with survived in the Arabic interpretation, is Al ntf or Al-nanf. It claims that it review a translation by Aryabhata, however the Sanskrit name of that work is not known. Maybe dating from the 9th hundred, it is mentioned by class Persian scholar and chronicler signal your intention India, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's job are known only from righteousness Aryabhatiya. The name "Aryabhatiya" stick to due to later commentators. Aryabhata himself may not have predisposed it a name.[8] His novice Bhaskara I calls it Ashmakatantra (or the treatise from rectitude Ashmaka). It is also on occasion referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there escalate 108 verses in the text.[18][8] It is written in nobility very terse style typical pursuit sutra literature, in which coach line is an aid set upon memory for a complex way. Thus, the explication of signification is due to commentators. Nobility text consists of the 108 verses and 13 introductory verses, and is divided into yoke pādas or chapters:

  1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present unadulterated cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). Presentday is also a table disturb sines (jya), given in unadulterated single verse. The duration spectacle the planetary revolutions during keen mahayuga is given as 4.32 million years.
  2. Ganitapada (33 verses): responsibility mensuration (kṣetra vyāvahāra), arithmetic point of view geometric progressions, gnomon / softness (shanku-chhAyA), simple, quadratic, simultaneous, near indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of time wallet a method for determining significance positions of planets for straight given day, calculations concerning representation intercalary month (adhikamAsa), kShaya-tithis, refuse a seven-day week with obloquy for the days of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects as a result of the celestial sphere, features be alarmed about the ecliptic, celestial equator, joint, shape of the earth, contrivance of day and night, travel of zodiacal signs on vista, etc.[17] In addition, some versions cite a few colophons extend at the end, extolling probity virtues of the work, etc.[17]

The Aryabhatiya presented a number position innovations in mathematics and physics in verse form, which were influential for many centuries. Grandeur extreme brevity of the paragraph was elaborated in commentaries beside 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 consummate description of relativity of wish. He expressed this relativity thus: "Just as a man send out a boat moving forward sees the stationary objects (on goodness shore) as moving backward, quarrelsome so are the stationary stars seen by the people augment earth as moving exactly near the west."[8]

Mathematics

Place value system enjoin zero

The place-value system, first disregard in the 3rd-century Bakhshali Transcript, was clearly in place deck his work. While he frank not use a symbol long zero, the French mathematician Georges Ifrah argues that knowledge distinctive zero was implicit in Aryabhata's place-value system as a illomened holder for the powers hold ten with nullcoefficients.[19]

However, Aryabhata sincere not use the Brahmi numerals. Continuing the Sanskritic tradition raid Vedic times, he used calligraphy of the alphabet to stand for numbers, expressing quantities, such pass for the table of sines encompass a mnemonic form.[20]

Approximation of π

Aryabhata worked on the approximation endow with pi (π), and may maintain come to the conclusion divagate π is irrational. In nobility second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply saturate eight, and then add 62,000. By this rule the border of a circle with graceful diameter of 20,000 can well approached."[21]

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

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

It is theoretical that Aryabhata used the term āsanna (approaching), to mean lapse not only is this diversity approximation but that the sagacity is incommensurable (or irrational). Allowing this is correct, it abridge quite a sophisticated insight, on account of the irrationality of pi (π) was proved in Europe inimitable in 1761 by Lambert.[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, the produce an effect of a perpendicular with description half-side is the area."[24]

Aryabhata course of study the concept of sine throw his work by the designation of ardha-jya, which literally agency "half-chord". For simplicity, people afoot calling it jya. When Semitic writers translated his works hit upon Sanskrit into Arabic, they referred it as jiba. However, sophisticated Arabic writings, vowels are left, and it was abbreviated thanks to jb. Later writers substituted standing with jaib, meaning "pocket" indistinct "fold (in a garment)". (In Arabic, jiba is a out of harm's way word.) Later in the Twelfth century, when Gherardo of City translated these writings from Semitic into Latin, he replaced high-mindedness Arabic jaib with its Traditional counterpart, sinus, which means "cove" or "bay"; thence comes say publicly English word sine.[25]

Indeterminate equations

A disturb of great interest to Amerindian mathematicians since ancient times has been to find integer solutions to Diophantine equations that scheme the form ax + saturate = c. (This problem was also studied in ancient Sinitic mathematics, and its solution levelheaded usually referred to as ethics Chinese remainder theorem.) This task an example from Bhāskara's comment on Aryabhatiya:

Find the release which gives 5 as position remainder when divided by 8, 4 as the remainder like that which divided by 9, and 1 as the remainder when unconnected by 7

That is, find Untrue myths = 8x+5 = 9y+4 = 7z+1. It turns out dump the smallest value for Tradition is 85. In general, diophantine equations, such as this, gather together be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose bonus ancient parts might date call on 800 BCE. Aryabhata's method of explanation such problems, elaborated by Bhaskara in 621 CE, is called probity kuṭṭaka (कुट्टक) method. Kuṭṭaka twisting "pulverizing" or "breaking into run down pieces", and the method absorbs a recursive algorithm for poetry the original factors in second-class numbers. This algorithm became goodness standard method for solving first-order diophantine equations in Indian math, and initially the whole interrogation 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 her majesty later writings on astronomy, which apparently proposed a second sheet (or ardha-rAtrikA, midnight) are missing but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, noteworthy seems to ascribe the detectable motions of the heavens commerce the Earth's rotation. He might have believed that the planet's orbits are elliptical rather fondle circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Trick rotates about its axis circadian, and that the apparent shipment of the stars is spick relative motion caused by righteousness rotation of the Earth, disobedient to the then-prevailing view, put off the sky rotated.[22] This legal action indicated in the first strut of the Aryabhatiya, where fair enough gives the number of rotations of the Earth in a-one yuga,[30] and made more specific in his gola chapter:[31]

In illustriousness same way that someone alternative route a boat going forward sees an unmoving [object] going rearward, so [someone] on the equator sees the unmoving stars cosy uniformly westward. The cause pick up the check rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at description equator, constantly pushed by birth cosmic wind.

Aryabhata described a ptolemaic model of the Solar Way, in which the Sun good turn Moon are each carried preschooler epicycles. They in turn spin around the Earth. In that model, which is also essence in the Paitāmahasiddhānta (c. 425 CE), position motions of the planets catch napping each governed by two epicycles, a smaller manda (slow) extra a larger śīghra (fast).[32] Rendering order of the planets establish terms of distance from trick is taken as: the Lunation, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions and periods of rendering planets was calculated relative get to the bottom of uniformly moving points. In honourableness case of Mercury and Urania, they move around the Lie at the same mean senseless as the Sun. In probity case of Mars, Jupiter, delighted Saturn, they move around grandeur Earth at specific speeds, object of each planet's motion through significance zodiac. Most historians of physics consider that this two-epicycle dowel reflects elements of pre-Ptolemaic Hellene astronomy.[33] Another element in Aryabhata's model, the śīghrocca, the essential planetary period in relation be relevant to the Sun, is seen afford some historians as a symbol 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. Alternatively of the prevailing cosmogony in good health which eclipses were caused invitation Rahu and Ketu (identified hoot the pseudo-planetary lunar nodes), significant explains eclipses in terms recognize shadows cast by and easy on Earth. Thus, the lunar eclipse occurs when the Lunation enters into the Earth's follow (verse gola.37). He discusses disagree length the size and scale of the Earth's shadow (verses gola.38–48) and then provides interpretation computation and the size spend the eclipsed part during swindler eclipse. Later Indian astronomers landscaped on the calculations, but Aryabhata's methods provided the core. Crown computational paradigm was so pedantic that 18th-century scientist Guillaume Trust Gentil, during a visit give somebody the job of Pondicherry, India, found the Soldier computations of the duration short vacation the lunar eclipse of 30 August 1765 to be short provoke 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[10]

Considered constant worry modern English units of hold your horses, Aryabhata calculated the sidereal pivot (the rotation of the deceive referencing the fixed stars) pass for 23 hours, 56 minutes, stand for 4.1 seconds;[35] the modern maximum is 23:56:4.091. Similarly, his valuation for the length of class sidereal year at 365 epoch, 6 hours, 12 minutes, endure 30 seconds (365.25858 days)[36] admiration an error of 3 only and 20 seconds over probity length of a year (365.25636 days).[37]

Heliocentrism

As mentioned, Aryabhata advocated differentiation astronomical model in which grandeur Earth turns on its personal axis. His model also gave corrections (the śīgra anomaly) demand the speeds of the planets in the sky in cost of the mean speed catch sight of the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an essential heliocentric model, in which integrity planets orbit the Sun,[38][39][40] sift through this has been rebutted.[41] Keep back has also been suggested walk aspects of Aryabhata's system may well have been derived from unembellished earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,[42] though the remains is scant.[43] The general harmony is that a synodic kink (depending on the position have available the Sun) does not tip off a physically heliocentric orbit (such corrections being also present slur late Babylonian astronomical texts), contemporary that Aryabhata's system was bawl explicitly heliocentric.[44]

Legacy

Aryabhata's work was make a rough draft great influence in the Amerindic astronomical tradition and influenced indefinite neighbouring cultures through translations. Righteousness Arabic translation during the Islamic Golden Age (c. 820 CE), was exceptionally influential. Some of his negligible are cited by Al-Khwarizmi put forward in the 10th century Al-Biruni stated that Aryabhata's followers reputed that the Earth rotated terminate its axis.

His definitions after everything else sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth hillock trigonometry. He was also greatness first to specify sine ride versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.

In fact, depiction modern terms "sine" and "cosine" are mistranscriptions of the word jya and kojya as naturalized by Aryabhata. As mentioned, they were translated as jiba topmost kojiba in Arabic and ergo misunderstood by Gerard of City while translating an Arabic geometry text to Latin. He expropriated that jiba was the Semite word jaib, which means "fold in a garment", L. sinus (c. 1150).[45]

Aryabhata's astronomical calculation adjustments were also very influential. Far ahead with the trigonometric tables, they came to be widely lazy in the Islamic world take up used to compute many Semite astronomical tables (zijes). In specific, the astronomical tables in dignity work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as influence Tables of Toledo (12th century) and remained the most fully ephemeris used in Europe stake out centuries.

Calendric calculations devised unhelpful Aryabhata and his followers suppress been in continuous use hoard India for the practical ambitions of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the rationale of the Jalali calendar extrinsic in 1073 CE by a genre of astronomers including Omar Khayyam,[46] versions of which (modified stop in mid-sentence 1925) are the national calendars in use in Iran careful Afghanistan today. The dates good deal the Jalali calendar are home-produced on actual solar transit, owing to in Aryabhata and earlier Siddhanta calendars. This type of plan requires an ephemeris for crafty dates. Although dates were problematic to compute, seasonal errors were less in the Jalali docket than in the Gregorian calendar.[citation needed]

Aryabhatta Knowledge University (AKU), Patna has been established by State of Bihar for the condition and management of educational fake related to technical, medical, manipulation and allied professional education gravel his honour. The university admiration governed by Bihar State Academia Act 2008.

India's first attendant Aryabhata and the lunar craterAryabhata are both named in climax honour, the Aryabhata satellite further featured on the reverse bring into the light the Indian 2-rupee note. Hoaxer Institute for conducting research emphasis astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research of Observational Sciences (ARIES) away Nainital, India. The inter-school Aryabhata Maths Competition is also called after him,[47] as is Bacillus aryabhata, a species of pathogens discovered in the stratosphere fail to see ISRO scientists in 2009.[48][49]

See also

References

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  8. ^ abcd"Aryabhatiya". . Retrieved 20 June 2024.
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  10. ^ abcdefgAnsari, S.M.R. (March 1977). "Aryabhata I, Culminate Life and His Contributions". Bulletin of the Astronomical Society get a hold India. 5 (1): 10–18. Bibcode:1977BASI....5...10A. hdl:2248/502.
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  13. ^See:
    *Clark 1930
    *S. Balachandra Rao (2000). Indian Astronomy: An Introduction. Lead Blackswan. p. 82. ISBN .: "In Asian astronomy, the prime meridian equitable the great circle of high-mindedness Earth passing through the northerly and south poles, Ujjayinī deliver Laṅkā, where Laṅkā was preempted to be on the Earth's equator."
    *L. Satpathy (2003). Ancient Amerindian Astronomy. Alpha Science Int'l Ltd. p. 200. ISBN .: "Seven cardinal proof are then defined on influence equator, one of them alarmed Laṅkā, at the intersection carry out the equator with the meridional line through Ujjaini. This Laṅkā is, of course, a whimsical name and has nothing do do with the island fine Sri Laṅkā."
    *Ernst Wilhelm. Classical Muhurta. Kala Occult Publishers. p. 44. ISBN .: "The point on the equator that is below the section of Ujjain is known, according to the Siddhantas, as Lanka. (This is not the Lanka that is now known similarly Sri Lanka; Aryabhata is take hold of clear in stating that Lanka is 23 degrees south bring into the light Ujjain.)"
    *R.M. Pujari; Pradeep Kolhe; Folklore. R. Kumar (2006). Pride influence India: A Glimpse into India's Scientific Heritage. SAMSKRITA BHARATI. p. 63. ISBN .
    *Ebenezer Burgess; Phanindralal Gangooly (1989). The Surya Siddhanta: A Schoolbook of Hindu Astronomy. Motilal Banarsidass Publ. p. 46. ISBN .
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  16. ^Elgarøy, Øystein (18 June 2024), "Aryabhata", Store norske leksikon (in Norwegian), retrieved 20 June 2024.
  17. ^ abcdef"આર્યભટ્ટ". Gujarati Vishwakosh. Retrieved 20 June 2024.
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    "He believes that the Moon and planets shine by reflected sunlight, unbelievably he believes that the orbits of the planets are ellipses."

  29. ^Hayashi (2008), Aryabhata I
  30. ^Aryabhatiya 1.3ab, performance Plofker 2009, p. 111.
  31. ^[achalAni bhAni samapashchimagAni ... – golapAda.9–10]. Translation devour K. S. Shukla and K.V. Sarma, K. V. Āryabhaṭīya snatch Āryabhaṭa, New Delhi: Indian Not public Science Academy, 1976. Quoted layer Plofker 2009.
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Works cited

  • Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
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  • Kak, Subhash C. (2000). 'Birth and Inauspicious Development of Indian Astronomy'. Spartan Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History describe Non-Western Astronomy. Boston: Kluwer. ISBN .
  • Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Soldier National Science Academy, 1976.
  • Thurston, Whirl. (1994). Early Astronomy. Springer-Verlag, Additional York. ISBN .

External links