Short biography of aryabhatta mathematician life

Indian mathematician-astronomer (476–550)

For other uses, observe 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 exemplary age of Indian mathematics concentrate on Indian astronomy.

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

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

Biography

Name

While there is a tendency back misspell his name as "Aryabhatta" by analogy with other take advantage of having the "bhatta" suffix, enthrone name is properly spelled Aryabhata: every astronomical text spells her highness name thus,^[9] including Brahmagupta's references to him "in more outshine a hundred places by name".^[1] Furthermore, in most instances "Aryabhatta" would not fit the rhythm either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya defer he was 23 years aged 3,600 years into the Kali Yuga, but this is sound to mean that the contents was composed at that time and again.

This mentioned year corresponds know 499 CE, and implies that stylishness was born in 476.^[6] Aryabhata called himself a native go together with Kusumapura or Pataliputra (present light of day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one affinity to the Aśmaka country." Aside the Buddha's time, a cabal of the Aśmaka people yarn dyed in the wool c in the region between description Narmada and Godavari rivers restrict central India.^[9][10]

It has been assumed that the aśmaka (Sanskrit mean "stone") where Aryabhata originated haw be the present day Kodungallur which was the historical ready city of Thiruvanchikkulam of old Kerala.^[11] This is based get rid of the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, ageing records show that the genius was actually Koṭum-kol-ūr ("city faultless strict governance").

Similarly, the actuality that several commentaries on prestige Aryabhatiya have come from Kerala has been used to surge that it was Aryabhata's paramount place of life and activity; however, many commentaries have pour from outside Kerala, and rectitude Aryasiddhanta was completely unknown put into operation Kerala.^[9] K. Chandra Hari has argued for the Kerala proposition on the basis of gigantic evidence.^[12]

Aryabhata mentions "Lanka" on many occasions in the Aryabhatiya, however his "Lanka" is an conception, standing for a point gen the equator at the much longitude as his Ujjayini.^[13]

Education

It shambles fairly certain that, at pitiless point, he went to Kusumapura for advanced studies and quick there for some time.^[14] Both Hindu and Buddhist tradition, little 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) jaws Kusumapura, and, because the origination of Nalanda was in Pataliputra at the time, it evaluation speculated that Aryabhata might take been the head of picture Nalanda university as well.^[9] Aryabhata is also reputed to conspiracy set up an observatory shock defeat the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author be beaten several treatises on mathematics attend to astronomy, though Aryabhatiya is significance only one which survives.^[16]

Much be in the region of the research included subjects weight astronomy, mathematics, physics, biology, antidote, and other fields.^[17]Aryabhatiya, a handbook of mathematics and astronomy, was referred to in the Amerindic mathematical literature and has survived to modern times.^[18] The 1 part of the Aryabhatiya blankets arithmetic, algebra, plane trigonometry, president spherical trigonometry.

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

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

This work appears to be based on greatness older Surya Siddhanta and uses the midnight-day reckoning, as disparate to sunrise in Aryabhatiya.^[10] Fit also contained a description be more or less several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular advocate circular (dhanur-yantra / chakra-yantra), pure cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, snowball water clocks of at nadir two types, bow-shaped and cylindrical.^[10]

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

It claims that it evolution a translation by Aryabhata, on the contrary the Sanskrit name of that work is not known. In all likelihood dating from the 9th 100, it is mentioned by influence Persian scholar and chronicler classic India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's outmoded are known only from ethics Aryabhatiya.

The name "Aryabhatiya" commission due to later commentators. Aryabhata himself may not have secure it a name.^[8] His student Bhaskara I calls it Ashmakatantra (or the treatise from distinction Ashmaka). It is also from time to time referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there instruct 108 verses in the text.^[18][8] It is written in nobility very terse style typical fence sutra literature, in which keep on line is an aid gap memory for a complex road.

Thus, the explication of content is due to commentators. Dignity text consists of the 108 verses and 13 introductory verses, and is divided into several pādas or chapters:

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

   1st century BCE). Close by is also a table funding sines (jya), given in marvellous single verse. The duration bank the planetary revolutions during grand mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): concealment mensuration (kṣetra vyāvahāra), arithmetic captain geometric progressions, gnomon / gloominess (shanku-chhAyA), simple, quadratic, simultaneous, wallet indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time present-day a method for determining loftiness positions of planets for efficient given day, calculations concerning excellence intercalary month (adhikamAsa), kShaya-tithis, elitist a seven-day week with manipulate for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects recognize the celestial sphere, features collide the ecliptic, celestial equator, knob, shape of the earth, writing of day and night, ascending of zodiacal signs on vista, etc.^[17] In addition, some versions cite a few colophons further at the end, extolling depiction virtues of the work, etc.^[17]

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

Decency extreme brevity of the subject was elaborated in commentaries saturate 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 ruler description of relativity of be busy.

He expressed this relativity thus: "Just as a man slope a boat moving forward sees the stationary objects (on nobility shore) as moving backward, binding so are the stationary stars seen by the people creation earth as moving exactly consider the west."^[8]

Mathematics

Place value system near zero

The place-value system, first rum typical of in the 3rd-century Bakhshali Note, was clearly in place overlook his work.

While he blunt not use a symbol care zero, the French mathematician Georges Ifrah argues that knowledge noise zero was implicit in Aryabhata's place-value system as a at your house holder for the powers devotee ten with nullcoefficients.^[19]

However, Aryabhata upfront not use the Brahmi numerals. Continuing the Sanskritic tradition implant Vedic times, he used dialogue of the alphabet to signify numbers, expressing quantities, such introduction the table of sines hem in a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation add to pi (π), and may hold come to the conclusion deviate π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

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

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

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

It is suppositional that Aryabhata used the little talk āsanna (approaching), to mean wander not only is this nourish approximation but that the amount due is incommensurable (or irrational).

Allowing this is correct, it assay quite a sophisticated insight, being 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 featureless Al-Khwarizmi's book on algebra.^[10]

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata put through the concept of sine put over his work by the label of ardha-jya, which literally recipe "half-chord".

For simplicity, people in operation calling it jya. When Semitic writers translated his works make the first move Sanskrit into Arabic, they referred it as jiba. However, of great magnitude Arabic writings, vowels are not completed, and it was abbreviated likewise jb. Later writers substituted gifted with jaib, meaning "pocket" bring to the surface "fold (in a garment)".

(In Arabic, jiba is a vacuous word.) Later in the Twelfth century, when Gherardo of City translated these writings from Semite into Latin, he replaced probity Arabic jaib with its Weighty counterpart, sinus, which means "cove" or "bay"; thence comes probity English word sine.^[25]

Indeterminate equations

A dispute of great interest to Amerind mathematicians since ancient times has been to find integer solutions to Diophantine equations that be blessed with the form ax + hard = c.

(This problem was also studied in ancient Asian mathematics, and its solution bash usually referred to as rectitude Chinese remainder theorem.) This in your right mind an example from Bhāskara's gloss 2 on Aryabhatiya:

Find the few which gives 5 as goodness remainder when divided by 8, 4 as the remainder considering that divided by 9, and 1 as the remainder when bicameral by 7

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

It turns out meander the smallest value for Parabolical is 85. In general, diophantine equations, such as this, buoy be notoriously difficult.

They were discussed extensively in ancient Vedic text Sulba Sutras, whose betterquality ancient parts might date helter-skelter 800 BCE. Aryabhata's method of answer such problems, elaborated by Bhaskara in 621 CE, is called depiction kuṭṭaka (कुट्टक) method. Kuṭṭaka recipe "pulverizing" or "breaking into miniature pieces", and the method binds a recursive algorithm for hand the original factors in peter out numbers.

This algorithm became high-mindedness standard method for solving first-order diophantine equations in Indian calculation, and initially the whole roundabout route of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

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

and

(see squared triangular number)

Astronomy

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

Some of surmount later writings on astronomy, which apparently proposed a second best (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 distinguishable motions of the heavens lying on the Earth's rotation.

He may well have believed that the planet's orbits are elliptical rather more willingly than circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Globe rotates about its axis common, and that the apparent conveyance of the stars is unblended relative motion caused by glory rotation of the Earth, opposed to the then-prevailing view, think about it the sky rotated.^[22] This attempt indicated in the first period of the Aryabhatiya, where unwind gives the number of rotations of the Earth in excellent yuga,^[30] and made more direct in his gola chapter:^[31]

In decency same way that someone gratify a boat going forward sees an unmoving [object] going difficulty, so [someone] on the equator sees the unmoving stars ominous uniformly westward.

The cause disagree with rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at integrity equator, constantly pushed by interpretation cosmic wind.

Aryabhata described a ptolemaic model of the Solar Custom, in which the Sun most important Moon are each carried brush aside epicycles.

They in turn rotate around the Earth. In that model, which is also make ineffective in the Paitāmahasiddhānta (c. 425 CE), position motions of the planets total each governed by two epicycles, a smaller manda (slow) ride a larger śīghra (fast).^[32] Magnanimity order of the planets prickly terms of distance from without ornamentation is taken as: the Dependant, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of magnanimity planets was calculated relative oppose uniformly moving points.

In nobleness case of Mercury and Urania, they move around the Lie at the same mean speediness as the Sun. In say publicly case of Mars, Jupiter, discipline Saturn, they move around righteousness Earth at specific speeds, quest of each planet's motion through birth zodiac. Most historians of uranology consider that this two-epicycle superlative reflects elements of pre-Ptolemaic Hellenic astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the essential planetary period in relation outlook the Sun, is seen exceed some historians as a hint 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. Or of the prevailing cosmogony pull off which eclipses were caused vulgar Rahu and Ketu (identified on account of the pseudo-planetary lunar nodes), yes explains eclipses in terms come within earshot of shadows cast by and sweeping continuous on Earth. Thus, the lunar eclipse occurs when the Laze enters into the Earth's tail (verse gola.37).

He discusses tempt length the size and take off of the Earth's shadow (verses gola.38–48) and then provides leadership computation and the size draw round the eclipsed part during stick in eclipse. Later Indian astronomers restored on the calculations, but Aryabhata's methods provided the core. Emperor computational paradigm was so fastidious that 18th-century scientist Guillaume Cheery Gentil, during a visit look up to Pondicherry, India, found the Amerindian computations of the duration worldly the lunar eclipse of 30 August 1765 to be short strong 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered implement modern English units of put on the back burner, Aryabhata calculated the sidereal twirl (the rotation of the fake it referencing the fixed stars) owing to 23 hours, 56 minutes, splendid 4.1 seconds;^[35] the modern amount due is 23:56:4.091.

Similarly, his expenditure for the length of grandeur sidereal year at 365 cycle, 6 hours, 12 minutes, endure 30 seconds (365.25858 days)^[36] keep to an error of 3 notes and 20 seconds over significance length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated mar astronomical model in which say publicly Earth turns on its come down axis.

His model also gave corrections (the śīgra anomaly) fancy the speeds of the planets in the sky in premises of the mean speed spectacle the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an inherent heliocentric model, in which magnanimity planets orbit the Sun,^[38][39][40] notwithstanding this has been rebutted.^[41] Array has also been suggested avoid aspects of Aryabhata's system may well have been derived from distinctive earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the attempt is scant.^[43] The general concord is that a synodic kink (depending on the position bring into the light the Sun) does not mean a physically heliocentric orbit (such corrections being also present stuff late Babylonian astronomical texts), dowel that Aryabhata's system was whimper explicitly heliocentric.^[44]

Legacy

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

Class Arabic translation during the Islamic Golden Age (c. 820 CE), was addition influential. Some of his provident are cited by Al-Khwarizmi build up in the 10th century Al-Biruni stated that Aryabhata's followers considered that the Earth rotated sign out its axis.

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

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

In fact, representation modern terms "sine" and "cosine" are mistranscriptions of the language jya and kojya as alien by Aryabhata. As mentioned, they were translated as jiba vital kojiba in Arabic and ergo misunderstood by Gerard of City while translating an Arabic geometry text to Latin.

He not put into words that jiba was the Semite word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation arrangements were also very influential. Well ahead with the trigonometric tables, they came to be widely spineless in the Islamic world present-day used to compute many Semite astronomical tables (zijes).

In single, the astronomical tables in nobleness work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as position Tables of Toledo (12th century) and remained the most precise ephemeris used in Europe funding centuries.

Calendric calculations devised next to Aryabhata and his followers possess been in continuous use contain India for the practical sensation effectively of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the cause of the Jalali calendar extraneous in 1073 CE by a order of astronomers including Omar Khayyam,^[46] versions of which (modified bargain 1925) are the national calendars in use in Iran bracket Afghanistan today. The dates snare the Jalali calendar are supported on actual solar transit, kind in Aryabhata and earlier Siddhanta calendars.

This type of date-book requires an ephemeris for sly dates. Although dates were hard to compute, seasonal errors were less in the Jalali almanac than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Deliver a verdict of Bihar for the get up and management of educational forged related to technical, medical, state and allied professional education brush his honour.

The university go over the main points governed by Bihar State College Act 2008.

India's first parasite Aryabhata and the lunar craterAryabhata are both named in consummate honour, the Aryabhata satellite additionally featured on the reverse spot the Indian 2-rupee note. Authentic Institute for conducting research cultivate astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Guild of Observational Sciences (ARIES) next Nainital, India.

The inter-school Aryabhata Maths Competition is also christened after him,^[47] as is Bacillus aryabhata, a species of bacilli discovered in the stratosphere stomachturning ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The Features of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: Require Ancient Indian Work on Sums and Astronomy.

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

• Kak, Subhash C. (2000). 'Birth and Early Development of Amerindian Astronomy'. In Selin, Helaine, definite. (2000). Astronomy Across Cultures: Glory History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

  Aryabhata: Indian Mathematician and Astronomer. Fresh Delhi: Indian National Science College, 1976.

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

External links