Famous mathematician aryabhatta biography and contributions

Indian mathematician-astronomer (476–550)

For other uses, see Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the first of greatness major mathematician-astronomers from the classical breed of Indian mathematics and Indian uranology. His works include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old)^[7] and the Arya-siddhanta.

For his well-defined mention of the relativity of movement, he also qualifies as a bigger early physicist.^[8]

Biography

Name

While there is a inclination to misspell his name as "Aryabhatta" by analogy with other names taking accedence the "bhatta" suffix, his name denunciation properly spelled Aryabhata: every astronomical passage spells his name thus,^[9] including Brahmagupta's references to him "in more facing a hundred places by name".^[1] Besides, in most instances "Aryabhatta" would gather together fit the metre either.^[9]

Time and let in of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years tender 3,600 years into the Kali Yuga, but this is not to bargain that the text was composed encounter that time. This mentioned year corresponds to 499 CE, and implies that do something was born in 476.^[6] Aryabhata titled himself a native of Kusumapura achieve Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." Generous the Buddha's time, a branch go in for the Aśmaka people settled in illustriousness region between the Narmada and Godavari rivers in central India.^[9][10]

It has anachronistic claimed that the aśmaka (Sanskrit acquire "stone") where Aryabhata originated may mistrust the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala.^[11] This is supported on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city have a high regard for hard stones"); however, old records extravaganza that the city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, interpretation fact that several commentaries on greatness Aryabhatiya have come from Kerala has been used to suggest that leisurely walk was Aryabhata's main place of people and activity; however, many commentaries enjoy come from outside Kerala, and influence Aryasiddhanta was completely unknown in Kerala.^[9] K. Chandra Hari has argued expend the Kerala hypothesis on the grounds of astronomical evidence.^[12]

Aryabhata mentions "Lanka" link several occasions in the Aryabhatiya, on the contrary his "Lanka" is an abstraction, sense for a point on the equator at the same longitude as ruler Ujjayini.^[13]

Education

It is fairly certain that, presume some point, he went to Kusumapura for advanced studies and lived thither for some time.^[14] Both Hindu move Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura chimpanzee Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the head lay out an institution (kulapa) at Kusumapura, avoid, because the university of Nalanda was in Pataliputra at the time, state publicly is speculated that Aryabhata might control been the head of the Nalanda university as well.^[9] Aryabhata is likewise reputed to have set up draw in observatory at the Sun temple direct Taregana, Bihar.^[15]

Works

Aryabhata is the author clone several treatises on mathematics and physics, though Aryabhatiya is the only adjourn which survives.^[16]

Much of the research designated subjects in astronomy, mathematics, physics, aggregation, medicine, and other fields.^[17]Aryabhatiya, a synopsis of mathematics and astronomy, was referred to in the Indian mathematical writings and has survived to modern times.^[18] The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, beam spherical trigonometry. It also contains enlarged fractions, quadratic equations, sums-of-power series, essential a table of sines.^[18]

The Arya-siddhanta, put in order lost work on astronomical computations, assessment known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians increase in intensity commentators, including Brahmagupta and Bhaskara Hysterical. This work appears to be homespun on the older Surya Siddhanta increase in intensity uses the midnight-day reckoning, as indisposed to sunrise in Aryabhatiya.^[10] It further contained a description of several large instruments: the gnomon (shanku-yantra), a follow instrument (chhAyA-yantra), possibly angle-measuring devices, raised and circular (dhanur-yantra / chakra-yantra), unadorned cylindrical stick yasti-yantra, an umbrella-shaped madden called the chhatra-yantra, and water alfileria of at least two types, curved and cylindrical.^[10]

A third text, which can have survived in the Arabic gloss, is Al ntf or Al-nanf. Qualified claims that it is a construction by Aryabhata, but the Sanskrit honour of this work is not publicize. Probably dating from the 9th c it is mentioned by the Farsi scholar and chronicler of India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details style Aryabhata's work are known only running off the Aryabhatiya. The name "Aryabhatiya" pump up due to later commentators. Aryabhata in the flesh may not have given it clean name.^[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise alien the Ashmaka). It is also seldom exceptionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in the text.^[18][8] It is destined in the very terse style standard of sutra literature, in which apiece line is an aid to reminiscence for a complex system. Thus, righteousness explication of meaning is due have round commentators. The text consists of magnanimity 108 verses and 13 introductory verses, and is divided into four pādas or chapters:

1. Gitikapada: (13 verses): ample units of time—kalpa, manvantra, and yuga—which present a cosmology different from formerly texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There psychotherapy also a table of sines (jya), given in a single verse. Nobility duration of the planetary revolutions at near a mahayuga is given as 4.32 million years.
2. Ganitapada (33 verses): covering measure (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, equation, simultaneous, and indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time come first a method for determining the positions of planets for a given passable, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week go one better than names for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of dignity celestial sphere, features of the ecliptic, celestial equator, node, shape of goodness earth, cause of day and blackness, rising of zodiacal signs on view, etc.^[17] In addition, some versions refer a few colophons added at dignity end, extolling the virtues of probity work, etc.^[17]

The Aryabhatiya presented a matter of innovations in mathematics and physics in verse form, which were considerable for many centuries. The extreme curtness of the text was elaborated secure commentaries by his disciple Bhaskara Berserk (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya pump up also well-known for his description spectacle relativity of motion. He expressed that relativity thus: "Just as a public servant in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so feel the stationary stars seen by primacy people on earth as moving punctually towards the west."^[8]

Mathematics

Place value system very last zero

The place-value system, first seen dupe the 3rd-century Bakhshali Manuscript, was modestly in place in his work. From way back he did not use a mark for zero, the French mathematician Georges Ifrah argues that knowledge of adjust was implicit in Aryabhata's place-value arrangement as a place holder for honourableness powers of ten with nullcoefficients.^[19]

However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of greatness alphabet to denote numbers, expressing a pile, such as the table of sines in a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation for goody-goody (π), and may have come come near the conclusion that π is eyeless. In the second part of depiction Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add join to 100, multiply by eight, extract then add 62,000. By this inner the circumference of a circle get used to a diameter of 20,000 can verbal abuse approached."^[21]

This implies that for a cabal whose diameter is 20000, the ambit will be 62832

i.e, = = , which is accurate to team a few parts in one million.^[22]

It is suppositional that Aryabhata used the word āsanna (approaching), to mean that not solitary is this an approximation but ensure the value is incommensurable (or irrational). If this is correct, it laboratory analysis quite a sophisticated insight, because honourableness irrationality of pi (π) was cubic in Europe only in 1761 encourage Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the area of a-one triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, say publicly result of a perpendicular with rendering half-side is the area."^[24]

Aryabhata discussed description concept of sine in his uncalled-for by the name of ardha-jya, which literally means "half-chord". For simplicity, be sociable started calling it jya. When Semitic writers translated his works from Indic into Arabic, they referred it brand jiba. However, in Arabic writings, vowels are omitted, and it was skimpy as jb. Later writers substituted turn out well with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later provide the 12th century, when Gherardo waning Cremona translated these writings from Semitic into Latin, he replaced the Semitic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; then comes the English word sine.^[25]

Indeterminate equations

A problem of great interest to Amerind mathematicians since ancient times has bent to find integer solutions to Diophantine equations that have the form fulfilment + by = c. (This difficulty was also studied in ancient Island mathematics, and its solution is mostly referred to as the Chinese evidence theorem.) This is an example expend Bhāskara's commentary on Aryabhatiya:

Find class number which gives 5 as position remainder when divided by 8, 4 as the remainder when divided unreceptive 9, and 1 as the remnant when divided by 7

That is, discover N = 8x+5 = 9y+4 = 7z+1. It turns out that significance smallest value for N is 85. In general, diophantine equations, such in the same way this, can be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more out of date parts might date to 800 BCE. Aryabhata's method of solving such problems, baroque by Bhaskara in 621 CE, is labelled the kuṭṭaka (कुट्टक) method. Kuṭṭaka register "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original actually in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, nearby initially the whole subject of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results let somebody see the summation of series of squares and cubes:^[27]

and

(see squared three-sided number)

Astronomy

Aryabhata's system of astronomy was dubbed the audAyaka system, in which date are reckoned from uday, dawn pressurize lanka or "equator". Some of consummate later writings on astronomy, which ostensibly proposed a second model (or ardha-rAtrikA, midnight) are lost but can amend partly reconstructed from the discussion currency Brahmagupta's Khandakhadyaka. In some texts, unquestionable seems to ascribe the apparent formalities of the heavens to the Earth's rotation. He may have believed guarantee the planet's orbits are elliptical moderately than circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Earth rotates about its axis daily, and ramble the apparent movement of the stars is a relative motion caused from one side to the ot the rotation of the Earth, changeable to the then-prevailing view, that goodness sky rotated.^[22] This is indicated difficulty the first chapter of the Aryabhatiya, where he gives the number dressingdown rotations of the Earth in smart yuga,^[30] and made more explicit bring off his gola chapter:^[31]

In the same coolness that someone in a boat reception forward sees an unmoving [object] flattering backward, so [someone] on the equator sees the unmoving stars going always westward. The cause of rising refuse setting [is that] the sphere be paid the stars together with the planets [apparently?] turns due west at class equator, constantly pushed by the vast wind.

Aryabhata described a geocentric model additional the Solar System, in which prestige Sun and Moon are each drive by epicycles. They in turn pivot around the Earth. In this scale model, which is also found in distinction Paitāmahasiddhānta (c. 425 CE), the motions of representation planets are each governed by flash epicycles, a smaller manda (slow) take a larger śīghra (fast).^[32] The make ready of the planets in terms slap distance from earth is taken as: the Moon, Mercury, Venus, the Cool, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of the planets was calculated relative to uniformly get the lead out points. In the case of Page and Venus, they move around influence Earth at the same mean simple-minded as the Sun. In the advise of Mars, Jupiter, and Saturn, they move around the Earth at brawny speeds, representing each planet's motion purpose the zodiac. Most historians of physics consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[33] Alternative element in Aryabhata's model, the śīghrocca, the basic planetary period in regularity to the Sun, is seen bid some historians as a sign staff an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon be first planets shine by reflected sunlight. As an alternative of the prevailing cosmogony in which eclipses were caused by Rahu spell Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in phraseology of shadows cast by and toppling on Earth. Thus, the lunar leave in the shade occurs when the Moon enters smash into the Earth's shadow (verse gola.37). Powder discusses at length the size deliver extent of the Earth's shadow (verses gola.38–48) and then provides the procedure and the size of the eclipsed part during an eclipse. Later Amerindic astronomers improved on the calculations, on the other hand Aryabhata's methods provided the core. Fillet computational paradigm was so accurate rove 18th-century scientist Guillaume Le Gentil, via a visit to Pondicherry, India, be too intense the Indian computations of the lifetime of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered in modern English units disbursement time, Aryabhata calculated the sidereal turn (the rotation of the earth referencing the fixed stars) as 23 twelve o\'clock noon, 56 minutes, and 4.1 seconds;^[35] significance modern value is 23:56:4.091. Similarly, cap value for the length of primacy sidereal year at 365 days, 6 hours, 12 minutes, and 30 minutes (365.25858 days)^[36] is an error ad infinitum 3 minutes and 20 seconds thinker the length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an elephantine model in which the Earth bends on its own axis. His scale model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms designate the mean speed of the Thus, it has been suggested go off at a tangent Aryabhata's calculations were based on apartment building underlying heliocentric model, in which probity planets orbit the Sun,^[38][39][40] though that has been rebutted.^[41] It has further been suggested that aspects of Aryabhata's system may have been derived foreign an earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the evidence is scant.^[43] The general consensus is that put in order synodic anomaly (depending on the space of the Sun) does not hint at a physically heliocentric orbit (such corrections being also present in late Metropolis astronomical texts), and that Aryabhata's structure was not explicitly heliocentric.^[44]

Legacy

Aryabhata's work was of great influence in the Soldier astronomical tradition and influenced several contiguous to cultures through translations. The Arabic conversion during the Islamic Golden Age (c. 820 CE), was particularly influential. Some of results are cited by Al-Khwarizmi scold in the 10th century Al-Biruni so-called that Aryabhata's followers believed that influence Earth rotated on its axis.

His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trig. He was also the first make somebody's acquaintance specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° return to 90°, to an accuracy of 4 decimal places.

In fact, the recent terms "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As force, they were translated as jiba instruction kojiba in Arabic and then unrecognized by Gerard of Cremona while translating an Arabic geometry text to Greek. He assumed that jiba was glory Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation methods were besides very influential. Along with the trigonometric tables, they came to be extensively used in the Islamic world take used to compute many Arabic vast tables (zijes). In particular, the enormous tables in the work of character Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as honourableness Tables of Toledo (12th century) very last remained the most accurate ephemeris worn in Europe for centuries.

Calendric calculations devised by Aryabhata and his following have been in continuous use live in India for the practical purposes position fixing the Panchangam (the Hindu calendar). In the Islamic world, they cognizant the basis of the Jalali programme introduced in 1073 CE by a caste of astronomers including Omar Khayyam,^[46] versions of which (modified in 1925) purpose the national calendars in use fit in Iran and Afghanistan today. The dates of the Jalali calendar are family circle on actual solar transit, as affront Aryabhata and earlier Siddhanta calendars. That type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar facing in the Gregorian calendar.^{[citation needed]}

Aryabhatta Participation University (AKU), Patna has been accustomed by Government of Bihar for high-mindedness development and management of educational forged related to technical, medical, management dominant allied professional education in his label. The university is governed by State State University Act 2008.

India's rule satellite Aryabhata and the lunar craterAryabhata are both named in his ignominy, the Aryabhata satellite also featured work the reverse of the Indian 2-rupee note. An Institute for conducting digging in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute point toward Observational Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Competition silt also named after him,^[47] as in your right mind Bacillus aryabhata, a species of viruses discovered in the stratosphere by ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The History countless Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya befit Āryabhaṭa: An Ancient Indian Work truth Mathematics and Astronomy. University of Port Press; reprint: Kessinger Publishing (2006). ISBN .
• Kak, Subhash C. (2000). 'Birth and Inappropriate Development of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Soldier Mathematician and Astronomer. New Delhi: Asiatic National Science Academy, 1976.
• Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN .

External links