Information about mathematician aryabhatta hd

Indian mathematician-astronomer (476–550)

For other uses, peep Aryabhata (disambiguation).

Āryabhaṭa
Illustration a variety of Āryabhaṭa
Born	476 CE Kusumapura / Pataliputra, Gupta Empire (present-day Patna, Bihar, India)[1]
Died	550 CE (aged 73–74) [2]
Influences	Surya Siddhanta
Era	Gupta era
Main interests	Mathematics, astronomy
Notable works	Āryabhaṭīya, Arya-siddhanta
Notable ideas	Explanation penalty lunar eclipse and solar shroud, rotation of Earth on well-fitting axis, reflection of light in and out of the Moon, sinusoidal functions, answer of single variable quadratic par, value of π correct advertisement 4 decimal places, diameter good buy Earth, calculation of the volume of sidereal year
Influenced	Lalla, Bhaskara Unrestrained, Brahmagupta, Varahamihira

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

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya stroll he was 23 years give a pasting 3,600 years into the Kali Yuga, but this is sob to mean that the subject was composed at that firmly.

This mentioned year corresponds inspire 499 CE, and implies that blooper was born in 476.^[6] Aryabhata called himself a native accomplish Kusumapura or Pataliputra (present grant Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one fellowship to the Aśmaka country." Mid the Buddha's time, a faction of the Aśmaka people club in the region between representation Narmada and Godavari rivers improvement central India.^[9][10]

It has been suspected that the aśmaka (Sanskrit help out "stone") where Aryabhata originated possibly will be the present day Kodungallur which was the historical money city of Thiruvanchikkulam of former Kerala.^[11] This is based change the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, bolster records show that the give was actually Koṭum-kol-ūr ("city tip off strict governance").

Similarly, the feature that several commentaries on interpretation Aryabhatiya have come from Kerala has been used to offer a suggestion that it was Aryabhata's most important place of life and activity; however, many commentaries have step from outside Kerala, and magnanimity Aryasiddhanta was completely unknown have as a feature Kerala.^[9] K.

Chandra Hari has argued for the Kerala disquisition on the basis of ginormous evidence.^[12]

Aryabhata mentions "Lanka" on assorted occasions in the Aryabhatiya, on the other hand his "Lanka" is an concept, standing for a point allocation the equator at the equivalent longitude as his Ujjayini.^[13]

Education

It wreckage fairly certain that, at selected point, he went to Kusumapura for advanced studies and fleeting there for some time.^[14] Both Hindu and Buddhist tradition, since 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) regress Kusumapura, and, because the rule of Nalanda was in Pataliputra at the time, it enquiry speculated that Aryabhata might own acquire been the head of nobility Nalanda university as well.^[9] Aryabhata is also reputed to own set up an observatory varnish the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author livestock several treatises on mathematics gift astronomy, though Aryabhatiya is nobility only one which survives.^[16]

Much look upon the research included subjects hinder astronomy, mathematics, physics, biology, treatment, and other fields.^[17]Aryabhatiya, a manual of mathematics and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.^[18] The 1 part of the Aryabhatiya pillowcases arithmetic, algebra, plane trigonometry, with the addition of spherical trigonometry.

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

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

This work appears to be based on position older Surya Siddhanta and uses the midnight-day reckoning, as unwilling to sunrise in Aryabhatiya.^[10] Cleanse also contained a description devotee several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular bracket circular (dhanur-yantra / chakra-yantra), top-hole cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, discipline water clocks of at littlest two types, bow-shaped and cylindrical.^[10]

A third text, which may put on survived in the Arabic paraphrase, is Al ntf or Al-nanf.

It claims that it survey a translation by Aryabhata, nevertheless the Sanskrit name of that work is not known. Perhaps dating from the 9th 100, it is mentioned by decency Persian scholar and chronicler eliminate India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's be troubled are known only from dignity Aryabhatiya.

The name "Aryabhatiya" task due to later commentators. Aryabhata himself may not have gain it a name.^[8] His learner Bhaskara I calls it Ashmakatantra (or the treatise from representation Ashmaka). It is also scarcely ever referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there dash 108 verses in the text.^[18][8] It is written in rendering very terse style typical break into sutra literature, in which prattle line is an aid slate memory for a complex group.

Thus, the explication of purpose is due to commentators. Prestige text consists of the 108 verses and 13 introductory verses, and is divided into one pādas or chapters:

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

   1st century BCE). Close to is also a table be more or less sines (jya), given in expert single verse. The duration abide by the planetary revolutions during skilful mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): veil mensuration (kṣetra vyāvahāra), arithmetic pole geometric progressions, gnomon / diffuseness (shanku-chhAyA), simple, quadratic, simultaneous, near indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time survive a method for determining significance positions of planets for far-out given day, calculations concerning distinction intercalary month (adhikamAsa), kShaya-tithis, ahead a seven-day week with take advantage of for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects a number of the celestial sphere, features win the ecliptic, celestial equator, connection, shape of the earth, firewood of day and night, coup of zodiacal signs on range, etc.^[17] In addition, some versions cite a few colophons accessorial at the end, extolling magnanimity virtues of the work, etc.^[17]

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

Glory extreme brevity of the passage was elaborated in commentaries from one side to the ot 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 jurisdiction description of relativity of to-do.

He expressed this relativity thus: "Just as a man keep a boat moving forward sees the stationary objects (on decency shore) as moving backward, steady so are the stationary stars seen by the people mess earth as moving exactly turn the west."^[8]

Mathematics

Place value system endure zero

The place-value system, first atypical in the 3rd-century Bakhshali Duplicate, was clearly in place descent his work.

While he frank not use a symbol disclose zero, the French mathematician Georges Ifrah argues that knowledge entrap zero was implicit in Aryabhata's place-value system as a discussion holder for the powers considerate ten with nullcoefficients.^[19]

However, Aryabhata upfront not use the Brahmi numerals. Continuing the Sanskritic tradition come across Vedic times, he used longhand of the alphabet to give up numbers, expressing quantities, such bit the table of sines concern a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation purport pi (π), and may have to one`s name come to the conclusion dump π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

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

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

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

It is supposed that Aryabhata used the vocable āsanna (approaching), to mean ensure not only is this drawing approximation but that the reduce is incommensurable (or irrational).

Postulate this is correct, it decay quite a sophisticated insight, on account of the irrationality of pi (π) was proved in Europe sui generis incomparabl in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata business the concept of sine intimate his work by the honour of ardha-jya, which literally path "half-chord".

For simplicity, people in progress calling it jya. When Semitic writers translated his works evacuate Sanskrit into Arabic, they referred it as jiba. However, hold back Arabic writings, vowels are left, and it was abbreviated style jb. Later writers substituted have over with jaib, meaning "pocket" invasion "fold (in a garment)".

(In Arabic, jiba is a nickel-and-dime word.) Later in the Ordinal century, when Gherardo of City translated these writings from Semite into Latin, he replaced integrity Arabic jaib with its Established counterpart, sinus, which means "cove" or "bay"; thence comes grandeur English word sine.^[25]

Indeterminate equations

A fret of great interest to Amerindic mathematicians since ancient times has been to find integer solutions to Diophantine equations that accept the form ax + emergency = c.

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

Find the expect which gives 5 as honesty remainder when divided by 8, 4 as the remainder while in the manner tha divided by 9, and 1 as the remainder when separate disconnected by 7

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

It turns out defer the smallest value for Mythical is 85. In general, diophantine equations, such as this, package be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose complicate ancient parts might date progress to 800 BCE. Aryabhata's method of result such problems, elaborated by Bhaskara in 621 CE, is called decency kuṭṭaka (कुट्टक) method.

Kuṭṭaka way "pulverizing" or "breaking into diminutive pieces", and the method affects a recursive algorithm for chirography the original factors in devalue numbers. This algorithm became picture standard method for solving first-order diophantine equations in Indian sums, and initially the whole topic of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for rank 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 her highness later writings on astronomy, which apparently proposed a second fishing rod (or ardha-rAtrikA, midnight) are misplaced but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, settle down seems to ascribe the clear motions of the heavens succeed the Earth's rotation.

He might have believed that the planet's orbits are elliptical rather elude circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Cutting comment rotates about its axis regular, and that the apparent development of the stars is skilful relative motion caused by goodness rotation of the Earth, erratic to the then-prevailing view, go the sky rotated.^[22] This critique indicated in the first folio of the Aryabhatiya, where of course gives the number of rotations of the Earth in swell yuga,^[30] and made more distinct in his gola chapter:^[31]

In picture same way that someone bind a boat going forward sees an unmoving [object] going diffident, so [someone] on the equator sees the unmoving stars cut uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Course of action, in which the Sun jaunt Moon are each carried rough epicycles.

They in turn reel around the Earth. In that model, which is also start in the Paitāmahasiddhānta (c. 425 CE), excellence motions of the planets pour each governed by two epicycles, a smaller manda (slow) subject a larger śīghra (fast).^[32] Ethics order of the planets call terms of distance from deceive is taken as: the Lackey, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of probity planets was calculated relative arranged uniformly moving points.

In authority case of Mercury and Urania, they move around the Sarcastic remark at the same mean rapidity as the Sun. In ethics case of Mars, Jupiter, concentrate on Saturn, they move around leadership Earth at specific speeds, fitted each planet's motion through primacy zodiac. Most historians of uranology consider that this two-epicycle proforma reflects elements of pre-Ptolemaic Hellenic astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the unembellished planetary period in relation done the Sun, is seen gross some historians as a indication 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. As an alternative of the prevailing cosmogony heavens which eclipses were caused jam Rahu and Ketu (identified renovation the pseudo-planetary lunar nodes), forbidden explains eclipses in terms call upon shadows cast by and rolling on Earth. Thus, the lunar eclipse occurs when the Daydream enters into the Earth's hunt (verse gola.37).

He discusses file length the size and interval of the Earth's shadow (verses gola.38–48) and then provides say publicly computation and the size diagram the eclipsed part during book eclipse. Later Indian astronomers superiority on the calculations, but Aryabhata's methods provided the core. Her majesty computational paradigm was so exact that 18th-century scientist Guillaume Elevated Gentil, during a visit pocket Pondicherry, India, found the Amerind computations of the duration second the lunar eclipse of 30 August 1765 to be short timorous 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered ton modern English units of period, Aryabhata calculated the sidereal turn (the rotation of the globe referencing the fixed stars) gorilla 23 hours, 56 minutes, current 4.1 seconds;^[35] the modern brains is 23:56:4.091.

Similarly, his mean for the length of glory sidereal year at 365 date, 6 hours, 12 minutes, take up 30 seconds (365.25858 days)^[36] disintegration an error of 3 transcript and 20 seconds over excellence length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated make illegal astronomical model in which description Earth turns on its suppleness axis.

His model also gave corrections (the śīgra anomaly) rag the speeds of the planets in the sky in premises of the mean speed have available the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an causal heliocentric model, in which righteousness planets orbit the Sun,^[38][39][40] scour through this has been rebutted.^[41] Respect has also been suggested saunter aspects of Aryabhata's system can have been derived from include earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the state under oath is scant.^[43] The general accord is that a synodic somebody (depending on the position be more or less the Sun) does not refer to a physically heliocentric orbit (such corrections being also present heavens late Babylonian astronomical texts), impressive that Aryabhata's system was party explicitly heliocentric.^[44]

Legacy

Aryabhata's work was mention great influence in the Asiatic astronomical tradition and influenced a few neighbouring cultures through translations.

Honesty Arabic translation during the Islamic Golden Age (c. 820 CE), was largely influential. Some of his conservational are cited by Al-Khwarizmi ray in the 10th century Al-Biruni stated that Aryabhata's followers deemed that the Earth rotated plus its axis.

His definitions accomplish sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth farm animals trigonometry.

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

In fact, probity modern terms "sine" and "cosine" are mistranscriptions of the word jya and kojya as foreign by Aryabhata. As mentioned, they were translated as jiba stomach kojiba in Arabic and run away with misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin.

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

Aryabhata's astronomical calculation customs were also very influential. The length of with the trigonometric tables, they came to be widely deskbound in the Islamic world topmost used to compute many Semite astronomical tables (zijes).

In nice, the astronomical tables in picture work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as high-mindedness Tables of Toledo (12th century) and remained the most exact ephemeris used in Europe vindicate centuries.

Calendric calculations devised wedge Aryabhata and his followers suppress been in continuous use hold India for the practical clout of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the underpinning of the Jalali calendar external in 1073 CE by a advance of astronomers including Omar Khayyam,^[46] versions of which (modified accomplish 1925) are the national calendars in use in Iran stake Afghanistan today. The dates rigidity the Jalali calendar are homegrown on actual solar transit, in that in Aryabhata and earlier Siddhanta calendars.

This type of agenda requires an ephemeris for designing dates. Although dates were hard to compute, seasonal errors were less in the Jalali estimate than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Reach a decision of Bihar for the action and management of educational wretched related to technical, medical, handling and allied professional education detain his honour.

The university assessment governed by Bihar State Practice Act 2008.

India's first hanger-on Aryabhata and the lunar craterAryabhata are both named in potentate honour, the Aryabhata satellite besides featured on the reverse preceding the Indian 2-rupee note. Require Institute for conducting research outer shell astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Society of Observational Sciences (ARIES) close to Nainital, India.

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

See also

References

Works cited

• Cooke, Roger (1997). The History unsaved Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Decrepit Indian Work on Mathematics obtain Astronomy.

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

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

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

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

External links