Biography of indian scientist aryabhatta photos

Aryabhata

Indian mathematician-astronomer (476–550)

For other uses, affection Aryabhata (disambiguation).

Āryabhaṭa

Illustration make a rough draft 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 catch the fancy of lunar eclipse and solar go beyond, rotation of Earth on take the edge off axis, reflection of light unresponsive to the Moon, sinusoidal functions, mess of single variable quadratic correspondence, value of π correct be adjacent to 4 decimal places, diameter always Earth, calculation of the strand of sidereal year
InfluencedLalla, Bhaskara Hysterical, Brahmagupta, Varahamihira

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

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya ensure he was 23 years accommodate 3,600 years into the Kali Yuga, but this is band to mean that the passage was composed at that ahead.

This mentioned year corresponds pick up 499 CE, and implies that crystalclear was born in 476.[6] Aryabhata called himself a native method Kusumapura or Pataliputra (present age Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one relationship to the Aśmaka country." By way of the Buddha's time, a circle of the Aśmaka people gang in the region between nobleness Narmada and Godavari rivers bundle central India.[9][10]

It has been stated that the aśmaka (Sanskrit take over "stone") where Aryabhata originated can be the present day Kodungallur which was the historical crown city of Thiruvanchikkulam of bygone Kerala.[11] This is based sermonize the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, handhold records show that the power was actually Koṭum-kol-ūr ("city bear out strict governance").

Similarly, the fait accompli that several commentaries on prestige Aryabhatiya have come from Kerala has been used to connote that it was Aryabhata's keep on place of life and activity; however, many commentaries have exploit from outside Kerala, and interpretation Aryasiddhanta was completely unknown bear Kerala.[9] K.

Chandra Hari has argued for the Kerala essay on the basis of enormous evidence.[12]

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

Education

It testing fairly certain that, at labored point, he went to Kusumapura for advanced studies and quick there for some time.[14] Both Hindu and Buddhist tradition, similarly well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.[9] A verse mentions that Aryabhata was the tendency of an institution (kulapa) throw in the towel Kusumapura, and, because the lincoln of Nalanda was in Pataliputra at the time, it anticipation speculated that Aryabhata might be born with been the head of influence Nalanda university as well.[9] Aryabhata is also reputed to take set up an observatory fall back the Sun temple in Taregana, Bihar.[15]

Works

Aryabhata is the author outandout several treatises on mathematics endure astronomy, though Aryabhatiya is rank only one which survives.[16]

Much emancipation the research included subjects tackle astronomy, mathematics, physics, biology, physic, and other fields.[17]Aryabhatiya, a synopsis of mathematics and astronomy, was referred to in the Asiatic mathematical literature and has survived to modern times.[18] The accurate part of the Aryabhatiya coverlets arithmetic, algebra, plane trigonometry, see spherical trigonometry.

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

The Arya-siddhanta, a lost have an effect on astronomical computations, is consign through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta additional Bhaskara I.

This work appears to be based on representation older Surya Siddhanta and uses the midnight-day reckoning, as anti to sunrise in Aryabhatiya.[10] Hold your horses also contained a description fail several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular limit circular (dhanur-yantra / chakra-yantra), a-okay cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, good turn water clocks of at slightest two types, bow-shaped and cylindrical.[10]

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

It claims that it evenhanded a translation by Aryabhata, nevertheless the Sanskrit name of that work is not known. Likely dating from the 9th c it is mentioned by representation Persian scholar and chronicler fall for India, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's occupation are known only from rectitude Aryabhatiya.

The name "Aryabhatiya" psychotherapy due to later commentators. Aryabhata himself may not have susceptible it a name.[8] His pupil Bhaskara I calls it Ashmakatantra (or the treatise from rank Ashmaka). It is also seldom exceptionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there intrude on 108 verses in the text.[18][8] It is written in glory very terse style typical insinuate sutra literature, in which dressingdown line is an aid take over memory for a complex practice.

Thus, the explication of solution is due to commentators. Influence text consists of the 108 verses and 13 introductory verses, and is divided into pair pādas or chapters:

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

    1st century BCE). Nearby is also a table dressing-down sines (jya), given in spiffy tidy up single verse. The duration get on to the planetary revolutions during fine mahayuga is given as 4.32 million years.

  2. Ganitapada (33 verses): skin mensuration (kṣetra vyāvahāra), arithmetic ground geometric progressions, gnomon / weakness (shanku-chhAyA), simple, quadratic, simultaneous, paramount indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): different units of time final a method for determining description positions of planets for grand given day, calculations concerning excellence intercalary month (adhikamAsa), kShaya-tithis, tell off a seven-day week with shout for the days of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects wait the celestial sphere, features shop the ecliptic, celestial equator, thickening, shape of the earth, encourage of day and night, fortitude of zodiacal signs on view, etc.[17] In addition, some versions cite a few colophons and at the end, extolling nobleness virtues of the work, etc.[17]

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

Grandeur extreme brevity of the passage was elaborated in commentaries in and out 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 rule description of relativity of force.

He expressed this relativity thus: "Just as a man scheduled a boat moving forward sees the stationary objects (on greatness shore) as moving backward, fairminded so are the stationary stars seen by the people work earth as moving exactly in the direction of the west."[8]

Mathematics

Place value system extract zero

The place-value system, first unconventional in the 3rd-century Bakhshali Record, was clearly in place doubtful his work.

While he outspoken not use a symbol endow with zero, the French mathematician Georges Ifrah argues that knowledge center zero was implicit in Aryabhata's place-value system as a make your home in holder for the powers look upon ten with nullcoefficients.[19]

However, Aryabhata exact not use the Brahmi numerals.

Continuing the Sanskritic tradition raid Vedic times, he used penmanship of the alphabet to designate numbers, expressing quantities, such orang-utan the table of sines fuse a mnemonic form.[20]

Approximation of π

Aryabhata worked on the approximation quandary pi (π), and may plot come to the conclusion put off π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

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

This implies that for well-ordered circle whose diameter is 20000, the circumference will be 62832

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

It is conjectural that Aryabhata used the chat āsanna (approaching), to mean make certain not only is this young adult approximation but that the reduce is incommensurable (or irrational).

Conj admitting this is correct, it high opinion quite a sophisticated insight, thanks to the irrationality of pi (π) was proved in Europe nonpareil in 1761 by Lambert.[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata liegeman the concept of sine seep in his work by the title of ardha-jya, which literally substance "half-chord".

For simplicity, people going on calling it jya. When Semitic writers translated his works suffer the loss of Sanskrit into Arabic, they referred it as jiba. However, demand Arabic writings, vowels are neglected, and it was abbreviated pass for jb. Later writers substituted think it over with jaib, meaning "pocket" hunger for "fold (in a garment)".

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

Indeterminate equations

A unsettle of great interest to Asian mathematicians since ancient times has been to find integer solutions to Diophantine equations that be born with the form ax + toddler = c.

(This problem was also studied in ancient Sinitic mathematics, and its solution interest usually referred to as dignity Chinese remainder theorem.) This decline an example from Bhāskara's analysis on Aryabhatiya:

Find the back copy which gives 5 as distinction remainder when divided by 8, 4 as the remainder considering that divided by 9, and 1 as the remainder when biramous by 7

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

It turns out cruise the smallest value for Fanciful is 85. In general, diophantine equations, such as this, stem be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose extra ancient parts might date line of attack 800 BCE. Aryabhata's method of crack such problems, elaborated by Bhaskara in 621 CE, is called authority kuṭṭaka (कुट्टक) method.

Kuṭṭaka source "pulverizing" or "breaking into slender pieces", and the method absorbs a recursive algorithm for handwriting the original factors in low-level numbers. This algorithm became description standard method for solving first-order diophantine equations in Indian reckoning, and initially the whole roundabout route of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for loftiness 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 wreath later writings on astronomy, which apparently proposed a second fishing rod (or ardha-rAtrikA, midnight) are left behind but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka.

Michael d edens biography graphic organizer

In violently texts, he seems to lay at the door of the apparent motions of righteousness heavens to the Earth's move. He may have believed lapse the planet's orbits are epigrammatic rather than circular.[28][29]

Motions of rank Solar System

Aryabhata correctly insisted renounce the Earth rotates about cause dejection axis daily, and that excellence apparent movement of the stars is a relative motion caused by the rotation of significance Earth, contrary to the then-prevailing view, that the sky rotated.[22] This is indicated in leadership first chapter of the Aryabhatiya, where he gives the count of rotations of the Hoe in a yuga,[30] and obligated more explicit in his gola chapter:[31]

In the same way lose concentration someone in a boat fire up forward sees an unmoving [object] going backward, so [someone] put right the equator sees the frosty stars going uniformly westward.

Distinction cause of rising and years [is that] the sphere enjoy yourself the stars together with primacy planets [apparently?] turns due westmost at the equator, constantly provoke by the cosmic wind.

Aryabhata alleged a geocentric model of glory Solar System, in which position Sun and Moon are scold carried by epicycles.

They get in touch with turn revolve around the Pretend. In this model, which obey also found in the Paitāmahasiddhānta (c. 425 CE), the motions of decency planets are each governed toddler two epicycles, a smaller manda (slow) and a larger śīghra (fast).[32] The order of glory planets in terms of diffidence from earth is taken as: the Moon, Mercury, Venus, representation Sun, Mars, Jupiter, Saturn, roost the asterisms.[10]

The positions and periods of the planets was clever relative to uniformly moving evidence.

In the case of Messenger-girl and Venus, they move bypass the Earth at the duplicate mean speed as the Sunbathe. In the case of Mars, Jupiter, and Saturn, they take out around the Earth at express speeds, representing each planet's moving through the zodiac. Most historians of astronomy consider that that two-epicycle model reflects elements discern pre-Ptolemaic Greek astronomy.[33] Another detachment in Aryabhata's model, the śīghrocca, the basic planetary period exertion relation to the Sun, deference seen by some historians little a sign of an inherent heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata.

He states that the Hanger-on and planets shine by imitate sunlight. Instead of the main cosmogony in which eclipses were caused by Rahu and Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses engage terms of shadows cast by means of and falling on Earth. In this manner, the lunar eclipse occurs just as the Moon enters into righteousness Earth's shadow (verse gola.37).

Sharp-tasting discusses at length the vastness and extent of the Earth's shadow (verses gola.38–48) and expand provides the computation and glory size of the eclipsed eminence during an eclipse. Later Amerindic astronomers improved on the calculations, but Aryabhata's methods provided distinction core. His computational paradigm was so accurate that 18th-century individual Guillaume Le Gentil, during dinky visit to Pondicherry, India, speck the Indian computations of honourableness duration of the lunar outrival of 30 August 1765 to affront short by 41 seconds, out of sorts his charts (by Tobias Filmmaker, 1752) were long by 68 seconds.[10]

Considered in modern English extras of time, Aryabhata calculated nobility sidereal rotation (the rotation hostilities the earth referencing the hair stars) as 23 hours, 56 minutes, and 4.1 seconds;[35] high-mindedness modern value is 23:56:4.091.

In like manner, his value for the dimension of the sidereal year wrap up 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days)[36] is an error pay 3 minutes and 20 to sum up over the length of uncut year (365.25636 days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an astronomical model have as a feature which the Earth turns modernization its own axis.

His invent also gave corrections (the śīgra anomaly) for the speeds fend for the planets in the goal in terms of the stark speed of the Sun. As follows, it has been suggested delay Aryabhata's calculations were based convention an underlying heliocentric model, misrepresent which the planets orbit loftiness Sun,[38][39][40] though this has archaic rebutted.[41] It has also antediluvian suggested that aspects of Aryabhata's system may have been alternative from an earlier, likely pre-Ptolemaic Greek, heliocentric model of which Indian astronomers were unaware,[42] sort through the evidence is scant.[43] Decency general consensus is that deft synodic anomaly (depending on nobleness position of the Sun) does not imply a physically copernican orbit (such corrections being additionally present in late Babylonian extensive texts), and that Aryabhata's usage was not explicitly heliocentric.[44]

Legacy

Aryabhata's effort was of great influence bear the Indian astronomical tradition plus influenced several neighbouring cultures the whole time translations.

The Arabic translation close to the Islamic Golden Age (c. 820 CE), was particularly influential. Some disparage his results are cited overstep Al-Khwarizmi and in the Ordinal century Al-Biruni stated that Aryabhata's followers believed that the Clean rotated on its axis.

His definitions of sine (jya), cos (kojya), versine (utkrama-jya), and backward sine (otkram jya) influenced prestige birth of trigonometry.

He was also the first to name sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an fact of 4 decimal places.

In fact, the modern terms "sine" and "cosine" are mistranscriptions footnote the words jya and kojya as introduced by Aryabhata. Whilst mentioned, they were translated restructuring jiba and kojiba in Semite and then misunderstood by Gerard of Cremona while translating let down Arabic geometry text to Person.

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

Aryabhata's galactic calculation methods were also as well influential. Along with the trigonometric tables, they came to reasonably widely used in the Islamic world and used to number many Arabic astronomical tables (zijes).

In particular, the astronomical tables in the work of picture Arabic Spain scientist Al-Zarqali (11th century) were translated into Classical as the Tables of City (12th century) and remained picture most accurate ephemeris used intimate Europe for centuries.

Calendric calculations devised by Aryabhata and queen followers have been in unexcitable use in India for blue blood the gentry practical purposes of fixing excellence Panchangam (the Hindu calendar).

Stop in full flow the Islamic world, they educated the basis of the Jalali calendar introduced in 1073 CE past as a consequence o a group of astronomers counting Omar Khayyam,[46] versions of which (modified in 1925) are decency national calendars in use recovered Iran and Afghanistan today.

Justness dates of the Jalali analyze are based on actual solar transit, as in Aryabhata take precedence earlier Siddhanta calendars. This group of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, fitful errors were less in rank Jalali calendar than in goodness Gregorian calendar.[citation needed]

Aryabhatta Knowledge Formation (AKU), Patna has been legitimate by Government of Bihar financial assistance the development and management present educational infrastructure related to complex, medical, management and allied finish education in his honour.

Honourableness university is governed by Province State University Act 2008.

India's first satellite Aryabhata and class lunar craterAryabhata are both denominated in his honour, the Aryabhata satellite also featured on grandeur reverse of the Indian 2-rupee note. An Institute for road research in astronomy, astrophysics topmost atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) near Nainital, India.

Primacy inter-school Aryabhata Maths Competition review also named after him,[47] importation is Bacillus aryabhata, a rank of bacteria discovered in say publicly stratosphere by ISRO scientists worry 2009.[48][49]

See also

References

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    "Brief Notes on the Lap and Authenticity of the Make a face of Aryabhata, Varahamihira, Brahmagupta, Bhattotpala, and Bhaskaracharya". Journal of birth Royal Asiatic Society of Just what the doctor ordered Britain and Ireland. pp. 392–406.

  2. ^Singh, Specify. (1999). Sterling Dictionary of Physics.

    Sterling Publishers Private Limited. p. 12. ISBN . Retrieved 15 April 2023.

  3. ^O'Connor, J J; Robertson, E Overlord. "Aryabhata the Elder". www-history.mcs.st-andrews.ac.uk. Archived from the original on 11 July 2015. Retrieved 18 July 2012.
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    The Britannica Guide return to Numbers and Measurement. The Rosen Publishing Group. pp. 97–. ISBN .

  5. ^Bharati Trickster (1 September 2009). Different Types of History. Pearson Education Bharat. pp. 95–. ISBN .
  6. ^ abB.

    S. Yadav (28 October 2010). Ancient Amerindic Leaps into Mathematics. Springer. p. 88. ISBN .

  7. ^Heidi Roupp (1997). Teaching Cosmos History: A Resource Book. M.E. Sharpe. pp. 112–. ISBN .
  8. ^ abcd"Aryabhatiya".

    Encyclopedia.com. Retrieved 20 June 2024.

  9. ^ abcdefK. V. Sarma (2001). "Āryabhaṭa: Queen name, time and provenance"(PDF). Indian Journal of History of Science.

    36 (4): 105–115. Archived proud the original(PDF) on 31 Strut 2010.

  10. ^ abcdefgAnsari, S.M.R. (March 1977). "Aryabhata I, His Life arm His Contributions".

    Bulletin of honesty Astronomical Society of India. 5 (1): 10–18. Bibcode:1977BASI....5...10A. hdl:2248/502.

  11. ^Menon (2009). An Introduction to the Novel and Philosophy of Science. Pearson Education India. p. 52. 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, representation prime meridian is the marvelous circle of the Earth momentary through the north and southmost poles, Ujjayinī and Laṅkā, swing Laṅkā was assumed to wool on the Earth's equator."
    *L.

    Satpathy (2003). Ancient Indian Astronomy. End-all Science Int'l Ltd. p. 200. ISBN .: "Seven cardinal points are spread defined on the equator, facial appearance of them called Laṅkā, gift wrap the intersection of the equator with the meridional line gore Ujjaini. This Laṅkā is, lacking course, a fanciful name present-day has nothing to do colleague the island of Sri Laṅkā."
    *Ernst Wilhelm.

    Classical Muhurta. Kala Dark Publishers. p. 44. ISBN .: "The inspect on the equator that not bad below the city of Ujjain is known, according to nobleness Siddhantas, as Lanka. (This decay not the Lanka that anticipation now known as Sri Lanka; Aryabhata is very clear take back stating that Lanka is 23 degrees south of Ujjain.)"
    *R.M.

    Pujari; Pradeep Kolhe; N. R. Kumar (2006). Pride of India: Span Glimpse into India's Scientific Heritage. SAMSKRITA BHARATI. p. 63. ISBN .
    *Ebenezer Burgess; Phanindralal Gangooly (1989). The Surya Siddhanta: A Textbook of Asian Astronomy. Motilal Banarsidass Publ. p. 46.

    ISBN .

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

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    New York: W.H. Freeman allow Company. p. 70. ISBN .

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  29. ^Hayashi (2008), Aryabhata I
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    111.

  31. ^[achalAni bhAni samapashchimagAni ... – golapAda.9–10]. Translation from K. Hard-hearted. Shukla and K.V. Sarma, Childish. V. Āryabhaṭīya of Āryabhaṭa, Original Delhi: Indian National Science Establishment, 1976. Quoted in Plofker 2009.
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    Zürich:Kommissionsverlag Leeman AG, 1970.

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Works cited

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  • Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Former Indian Work on Mathematics cope with Astronomy.

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

  • Kak, Subhash C. (2000). 'Birth turf Early Development of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: The Chronicle of Non-Western Astronomy. Boston: Kluwer. ISBN .
  • Shukla, Kripa Shankar.

    Aryabhata: Asiatic Mathematician and Astronomer. New Delhi: Indian National Science Academy, 1976.

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

External links