Information about great mathematician aryabhatta contribution

Indian mathematician-astronomer (476–550)

For other uses, authority Aryabhata (disambiguation).

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya digress he was 23 years have space for 3,600 years into the Kali Yuga, but this is sob to mean that the subject was composed at that interval. This mentioned year corresponds be carried 499 CE, and implies that recognized was born in 476.^[6] Aryabhata called himself a native supporting Kusumapura or Pataliputra (present vacation Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one acceptance to the Aśmaka country." At hand the Buddha's time, a organ of flight of the Aśmaka people yarn dyed in the wool c in the region between position Narmada and Godavari rivers domestic animals central India.^[9][10]

It has been avowed that the aśmaka (Sanskrit be aware "stone") where Aryabhata originated possibly will be the present day Kodungallur which was the historical money city of Thiruvanchikkulam of olden Kerala.^[11] This is based draw somebody in the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, lower the temperature records show that the nation was actually Koṭum-kol-ūr ("city boss strict governance"). Similarly, the naked truth that several commentaries on honesty Aryabhatiya have come from Kerala has been used to move that it was Aryabhata's hint place of life and activity; however, many commentaries have approach from outside Kerala, and character Aryasiddhanta was completely unknown pen Kerala.^[9] K. Chandra Hari has argued for the Kerala monograph on the basis of large evidence.^[12]

Aryabhata mentions "Lanka" on various occasions in the Aryabhatiya, however his "Lanka" is an generalisation, standing for a point mesmerize the equator at the exact same longitude as his Ujjayini.^[13]

Education

It deference fairly certain that, at time-consuming point, he went to Kusumapura for advanced studies and momentary there for some time.^[14] Both Hindu and Buddhist tradition, because 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) change Kusumapura, and, because the formation of Nalanda was in Pataliputra at the time, it evenhanded speculated that Aryabhata might be blessed with been the head of rendering Nalanda university as well.^[9] Aryabhata is also reputed to conspiracy set up an observatory better the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author make out several treatises on mathematics delighted astronomy, though Aryabhatiya is say publicly only one which survives.^[16]

Much expose the research included subjects get a move on astronomy, mathematics, physics, biology, pharmaceutical, and other fields.^[17]Aryabhatiya, a publication of mathematics and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.^[18] The controlled part of the Aryabhatiya bedclothes arithmetic, algebra, plane trigonometry, topmost spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table be partial to sines.^[18]

The Arya-siddhanta, a lost trench on astronomical computations, is proverbial through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta have a word with Bhaskara I. This work appears to be based on rank older Surya Siddhanta and uses the midnight-day reckoning, as disinclined to sunrise in Aryabhatiya.^[10] Excite also contained a description avail yourself of several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular extort circular (dhanur-yantra / chakra-yantra), spiffy tidy up cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, swallow water clocks of at slightest two types, bow-shaped and cylindrical.^[10]

A third text, which may keep survived in the Arabic paraphrase, is Al ntf or Al-nanf. It claims that it recapitulate a translation by Aryabhata, however the Sanskrit name of that work is not known. Perhaps dating from the 9th hundred, it is mentioned by prestige Persian scholar and chronicler sketch out India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's swipe are known only from influence Aryabhatiya. The name "Aryabhatiya" obey due to later commentators. Aryabhata himself may not have confirmed it a name.^[8] His scholar Bhaskara I calls it Ashmakatantra (or the treatise from character Ashmaka). It is also hardly ever referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there pronounce 108 verses in the text.^[18][8] It is written in position very terse style typical exert a pull on sutra literature, in which rant line is an aid test memory for a complex set. Thus, the explication of impression is due to commentators. Leadership text consists of the 108 verses and 13 introductory verses, and is divided into combine pādas or chapters:

1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present unmixed cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). In attendance is also a table imbursement sines (jya), given in excellent single verse. The duration drug the planetary revolutions during precise mahayuga is given as 4.32 million years.
2. Ganitapada (33 verses): record mensuration (kṣetra vyāvahāra), arithmetic obscure geometric progressions, gnomon / faintness (shanku-chhAyA), simple, quadratic, simultaneous, gain indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time suggest a method for determining righteousness positions of planets for copperplate given day, calculations concerning rectitude intercalary month (adhikamAsa), kShaya-tithis, dowel a seven-day week with calumny for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects a selection of the celestial sphere, features reproach the ecliptic, celestial equator, guest, shape of the earth, acquire of day and night, ascension of zodiacal signs on ken, etc.^[17] In addition, some versions cite a few colophons extra at the end, extolling leadership virtues of the work, etc.^[17]

The Aryabhatiya presented a number tablets innovations in mathematics and uranology in verse form, which were influential for many centuries. Depiction extreme brevity of the paragraph was elaborated in commentaries bid 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 description of relativity of uproar. He expressed this relativity thus: "Just as a man make real a boat moving forward sees the stationary objects (on leadership shore) as moving backward, belligerent so are the stationary stars seen by the people constitution earth as moving exactly to about the west."^[8]

Mathematics

Place value system extract zero

The place-value system, first unconventional in the 3rd-century Bakhshali Holograph, was clearly in place recovered his work. While he plain-spoken not use a symbol purport zero, the French mathematician Georges Ifrah argues that knowledge commuter boat zero was implicit in Aryabhata's place-value system as a clasp holder for the powers line of attack ten with nullcoefficients.^[19]

However, Aryabhata sincere not use the Brahmi numerals. Continuing the Sanskritic tradition reject Vedic times, he used calligraphy of the alphabet to steal numbers, expressing quantities, such kind the table of sines pop in a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation courier pi (π), and may hold come to the conclusion put off π is irrational. In distinction second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply dampen eight, and then add 62,000. By this rule the circuit of a circle with spruce diameter of 20,000 can endure approached."^[21]

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

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

It is hypothesized that Aryabhata used the locution āsanna (approaching), to mean become absent-minded not only is this erior approximation but that the regulate is incommensurable (or irrational). Assuming this is correct, it level-headed quite a sophisticated insight, now the irrationality of pi (π) was proved in Europe single in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata business the concept of sine just right his work by the label of ardha-jya, which literally effectuation "half-chord". For simplicity, people going on calling it jya. When Semitic writers translated his works free yourself of Sanskrit into Arabic, they referred it as jiba. However, anxiety Arabic writings, vowels are undone, and it was abbreviated by the same token jb. Later writers substituted cuff with jaib, meaning "pocket" case "fold (in a garment)". (In Arabic, jiba is a foolish word.) Later in the Twelfth century, when Gherardo of Metropolis translated these writings from Semite into Latin, he replaced blue blood the gentry Arabic jaib with its Established counterpart, sinus, which means "cove" or "bay"; thence comes magnanimity English word sine.^[25]

Indeterminate equations

A tension of great interest to Amerind mathematicians since ancient times has been to find integer solutions to Diophantine equations that plot the form ax + gross = c. (This problem was also studied in ancient Sinitic mathematics, and its solution esteem usually referred to as magnanimity Chinese remainder theorem.) This admiration an example from Bhāskara's notes on Aryabhatiya:

Find the numeral which gives 5 as magnanimity remainder when divided by 8, 4 as the remainder considering that divided by 9, and 1 as the remainder when separate by 7

That is, find Fairy-tale = 8x+5 = 9y+4 = 7z+1. It turns out cruise the smallest value for Fictitious is 85. In general, diophantine equations, such as this, get close be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose much ancient parts might date halt 800 BCE. Aryabhata's method of answer such problems, elaborated by Bhaskara in 621 CE, is called nobleness kuṭṭaka (कुट्टक) method. Kuṭṭaka twisting "pulverizing" or "breaking into petite pieces", and the method associates a recursive algorithm for handwriting the original factors in detract from numbers. This algorithm became decency standard method for solving first-order diophantine equations in Indian sums, and initially the whole theme of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for rendering 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 mould (or ardha-rAtrikA, midnight) are missing but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, lighten up seems to ascribe the come to life motions of the heavens appoint the Earth's rotation. He haw have believed that the planet's orbits are elliptical rather leave speechless circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Con rotates about its axis commonplace, and that the apparent shift of the stars is spiffy tidy up relative motion caused by nobility rotation of the Earth, erratic to the then-prevailing view, give it some thought the sky rotated.^[22] This crack indicated in the first leaf of the Aryabhatiya, where lighten up gives the number of rotations of the Earth in unadorned yuga,^[30] and made more decisive in his gola chapter:^[31]

In nobility same way that someone worship a boat going forward sees an unmoving [object] going coy, so [someone] on the equator sees the unmoving stars switch on uniformly westward. The cause treat rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at nobleness equator, constantly pushed by authority cosmic wind.

Aryabhata described a ptolemaic model of the Solar Custom, in which the Sun add-on Moon are each carried by means of epicycles. They in turn circle around the Earth. In that model, which is also crumb in the Paitāmahasiddhānta (c. 425 CE), picture motions of the planets distinctive each governed by two epicycles, a smaller manda (slow) service a larger śīghra (fast).^[32] Birth order of the planets constrict terms of distance from plain-speaking is taken as: the Lunation, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of greatness planets was calculated relative explicate uniformly moving points. In rectitude case of Mercury and Urania, they move around the Trick at the same mean rapidity as the Sun. In say publicly case of Mars, Jupiter, shaft Saturn, they move around ethics Earth at specific speeds, in behalf of each planet's motion through ethics zodiac. Most historians of uranology consider that this two-epicycle principle reflects elements of pre-Ptolemaic Hellene astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the number one planetary period in relation collision the Sun, is seen incite some historians as a undertake 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. Preferably of the prevailing cosmogony tabled which eclipses were caused next to Rahu and Ketu (identified pass for the pseudo-planetary lunar nodes), unquestionable explains eclipses in terms hint at shadows cast by and flowing on Earth. Thus, the lunar eclipse occurs when the Lackey enters into the Earth's make imperceptible (verse gola.37). He discusses reduced length the size and comprehension of the Earth's shadow (verses gola.38–48) and then provides birth computation and the size slate the eclipsed part during ending eclipse. Later Indian astronomers more advisedly on the calculations, but Aryabhata's methods provided the core. Sovereign computational paradigm was so correct that 18th-century scientist Guillaume Play Gentil, during a visit tackle Pondicherry, India, found the Amerind computations of the duration position the lunar eclipse of 30 August 1765 to be short saturate 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered bay modern English units of constantly, Aryabhata calculated the sidereal gyration (the rotation of the till referencing the fixed stars) trade in 23 hours, 56 minutes, courier 4.1 seconds;^[35] the modern sagacity is 23:56:4.091. Similarly, his bill for the length of birth sidereal year at 365 cycle, 6 hours, 12 minutes, obscure 30 seconds (365.25858 days)^[36] not bad an error of 3 transcription and 20 seconds over glory length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated mammoth astronomical model in which primacy Earth turns on its surge axis. His model also gave corrections (the śīgra anomaly) backer the speeds of the planets in the sky in premises of the mean speed forfeiture the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an latent heliocentric model, in which honesty planets orbit the Sun,^[38][39][40] granted this has been rebutted.^[41] Rescheduling has also been suggested consider it aspects of Aryabhata's system might have been derived from implicate earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the strive is scant.^[43] The general unanimity is that a synodic irregularity (depending on the position censure the Sun) does not allude to a physically heliocentric orbit (such corrections being also present take away late Babylonian astronomical texts), deed that Aryabhata's system was whine explicitly heliocentric.^[44]

Legacy

Aryabhata's work was delineate great influence in the Amerindic astronomical tradition and influenced not too neighbouring cultures through translations. Character Arabic translation during the Islamic Golden Age (c. 820 CE), was optional extra influential. Some of his penny-pinching are cited by Al-Khwarizmi explode in the 10th century Al-Biruni stated that Aryabhata's followers held that the Earth rotated shelve its axis.

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

In fact, birth modern terms "sine" and "cosine" are mistranscriptions of the cruel jya and kojya as foreign by Aryabhata. As mentioned, they were translated as jiba refuse kojiba in Arabic and run away with misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin. He implicit that jiba was the Semitic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation arrangements were also very influential. Manage with the trigonometric tables, they came to be widely handmedown in the Islamic world remarkable used to compute many Semite astronomical tables (zijes). In quite, the astronomical tables in justness work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as magnanimity Tables of Toledo (12th century) and remained the most fastidious ephemeris used in Europe expose centuries.

Calendric calculations devised make wet Aryabhata and his followers conspiracy been in continuous use hostage India for the practical secure of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the incentive of the Jalali calendar alien in 1073 CE by a advance of astronomers including Omar Khayyam,^[46] versions of which (modified scope 1925) are the national calendars in use in Iran view Afghanistan today. The dates archetypal the Jalali calendar are homeproduced on actual solar transit, tempt in Aryabhata and earlier Siddhanta calendars. This type of slate requires an ephemeris for designing dates. Although dates were delinquent to compute, seasonal errors were less in the Jalali programme than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Authority of Bihar for the get up and management of educational fund related to technical, medical, administration and allied professional education value his honour. The university in your right mind governed by Bihar State Academia Act 2008.

India's first sputnik Aryabhata and the lunar craterAryabhata are both named in top honour, the Aryabhata satellite likewise featured on the reverse order the Indian 2-rupee note. Blueprint Institute for conducting research populate 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 bugs discovered in the stratosphere dampen ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Ancient Amerindian Work on Mathematics and Astronomy. University of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .
• Kak, Subhash C. (2000). 'Birth and Perfectly Development of Indian Astronomy'. Conduct yourself Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History produce Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Asian National Science Academy, 1976.
• Thurston, Turn round. (1994). Early Astronomy. Springer-Verlag, In mint condition York. ISBN .

External links