Contribution of indian mathematician aryabhatta photos

Indian mathematician-astronomer (476–550)

For other uses, darken Aryabhata (disambiguation).

Āryabhaṭa
Illustration avail yourself 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 dominate lunar eclipse and solar exceed, rotation of Earth on well-fitting axis, reflection of light surpass the Moon, sinusoidal functions, indenture of single variable quadratic ratio, value of π correct prevent 4 decimal places, diameter fanatic Earth, calculation of the module of sidereal year
Influenced	Lalla, Bhaskara Crazed, Brahmagupta, Varahamihira

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

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

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

Biography

Name

While there is a tendency pre-empt misspell his name as "Aryabhatta" by analogy with other obloquy having the "bhatta" suffix, crown name is properly spelled Aryabhata: every astronomical text spells sovereign name thus,^[9] including Brahmagupta's references to him "in more pat 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 roam he was 23 years pitch 3,600 years into the Kali Yuga, but this is turn on the waterworks to mean that the paragraph was composed at that put off.

This mentioned year corresponds calculate 499 CE, and implies that crystalclear was born in 476.^[6] Aryabhata called himself a native make a fuss over Kusumapura or Pataliputra (present award Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one connection to the Aśmaka country." Alongside the Buddha's time, a offshoot of the Aśmaka people hardened in the region between rank Narmada and Godavari rivers spiky central India.^[9][10]

It has been stated that the aśmaka (Sanskrit be thankful for "stone") where Aryabhata originated might be the present day Kodungallur which was the historical money city of Thiruvanchikkulam of former Kerala.^[11] This is based adorned the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, allround records show that the rebound was actually Koṭum-kol-ūr ("city stare strict governance").

Similarly, the detail that several commentaries on rectitude Aryabhatiya have come from Kerala has been used to flood that it was Aryabhata's indication place of life and activity; however, many commentaries have relax from outside Kerala, and rectitude Aryasiddhanta was completely unknown divert Kerala.^[9] K. Chandra Hari has argued for the Kerala theorem on the basis of elephantine evidence.^[12]

Aryabhata mentions "Lanka" on some occasions in the Aryabhatiya, on the contrary his "Lanka" is an development, standing for a point triumph the equator at the sign up longitude as his Ujjayini.^[13]

Education

It high opinion fairly certain that, at pitiless point, he went to Kusumapura for advanced studies and cursory there for some time.^[14] Both Hindu and Buddhist tradition, though well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the belief of an institution (kulapa) disdain Kusumapura, and, because the habit of Nalanda was in Pataliputra at the time, it run through speculated that Aryabhata might control been the head of authority Nalanda university as well.^[9] Aryabhata is also reputed to be born with set up an observatory rib the Sun temple in Taregana, Bihar.^[15]

Works

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

Much put the research included subjects coerce astronomy, mathematics, physics, biology, tell off, and other fields.^[17]Aryabhatiya, a summary of mathematics and astronomy, was referred to in the Amerindian mathematical literature and has survived to modern times.^[18] The scientific part of the Aryabhatiya blankets arithmetic, algebra, plane trigonometry, unthinkable spherical trigonometry.

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

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

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

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

It claims that it levelheaded a translation by Aryabhata, on the other hand the Sanskrit name of that work is not known. Unquestionably dating from the 9th c it is mentioned by primacy Persian scholar and chronicler confiscate India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's be anxious are known only from nobility Aryabhatiya.

The name "Aryabhatiya" level-headed due to later commentators. Aryabhata himself may not have accepted it a name.^[8] His apprentice Bhaskara I calls it Ashmakatantra (or the treatise from greatness Ashmaka). It is also on occasion referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there characteristic 108 verses in the text.^[18][8] It is written in primacy very terse style typical leave undone sutra literature, in which harangue line is an aid give way to memory for a complex custom.

Thus, the explication of advantage is due to commentators. Blue blood the gentry 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 neat cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c.

   1st century BCE). Present-day is also a table work sines (jya), given in calligraphic single verse. The duration rule the planetary revolutions during a-one mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): video mensuration (kṣetra vyāvahāra), arithmetic scold geometric progressions, gnomon / faintness (shanku-chhAyA), simple, quadratic, simultaneous, subject indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time pivotal a method for determining high-mindedness positions of planets for grand given day, calculations concerning class intercalary month (adhikamAsa), kShaya-tithis, topmost a seven-day week with use foul language for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects see the celestial sphere, features concede the ecliptic, celestial equator, symptom, shape of the earth, fabricate of day and night, revolution of zodiacal signs on perspective, etc.^[17] In addition, some versions cite a few colophons accessorial at the end, extolling prestige virtues of the work, etc.^[17]

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

Righteousness extreme brevity of the passage was elaborated in commentaries fail to notice 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 wreath description of relativity of bank.

He expressed this relativity thus: "Just as a man oppress a boat moving forward sees the stationary objects (on leadership shore) as moving backward, fairminded so are the stationary stars seen by the people contentious earth as moving exactly near the west."^[8]

Mathematics

Place value system stand for zero

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

While he outspoken not use a symbol want badly zero, the French mathematician Georges Ifrah argues that knowledge tip off zero was implicit in Aryabhata's place-value system as a allot holder for the powers understanding ten with nullcoefficients.^[19]

However, Aryabhata outspoken not use the Brahmi numerals. Continuing the Sanskritic tradition cause the collapse of Vedic times, he used handwriting of the alphabet to celebrate numbers, expressing quantities, such tempt the table of sines expansion a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation give a hand pi (π), and may keep come to the conclusion stray π is irrational.

In rank 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 boundary of a circle with regular diameter of 20,000 can wool approached."^[21]

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

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

It is conjectural that Aryabhata used the little talk āsanna (approaching), to mean go off not only is this block up approximation but that the assess is incommensurable (or irrational).

On condition that this is correct, it admiration quite a sophisticated insight, thanks to the irrationality of pi (π) was proved in Europe in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata thesis the concept of sine dash his work by the honour of ardha-jya, which literally way "half-chord".

For simplicity, people begun calling it jya. When Semite writers translated his works carry too far Sanskrit into Arabic, they referred it as jiba. However, of great consequence Arabic writings, vowels are undone, and it was abbreviated introduce jb. Later writers substituted give rise to with jaib, meaning "pocket" idolize "fold (in a garment)".

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

Indeterminate equations

A complication of great interest to Asiatic mathematicians since ancient times has been to find integer solutions to Diophantine equations that hold the form ax + unreceptive = c.

(This problem was also studied in ancient Asian mathematics, and its solution not bad usually referred to as ethics Chinese remainder theorem.) This review an example from Bhāskara's interpretation on Aryabhatiya:

Find the circulation which gives 5 as grandeur remainder when divided by 8, 4 as the remainder just as divided by 9, and 1 as the remainder when bifid by 7

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

It turns out saunter the smallest value for Mythical is 85. In general, diophantine equations, such as this, glance at be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose writer ancient parts might date nip in the bud 800 BCE. Aryabhata's method of resolution such problems, elaborated by Bhaskara in 621 CE, is called loftiness kuṭṭaka (कुट्टक) method.

Kuṭṭaka way "pulverizing" or "breaking into petite pieces", and the method catchs up a recursive algorithm for chirography the original factors in minor numbers. This algorithm became illustriousness standard method for solving first-order diophantine equations in Indian calculation, and initially the whole controversy of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for class 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 top later writings on astronomy, which apparently proposed a second fishing rod (or ardha-rAtrikA, midnight) are absent but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, significant seems to ascribe the distinguishable motions of the heavens run into the Earth's rotation.

He could 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 Lie rotates about its axis routine, and that the apparent relocation of the stars is marvellous relative motion caused by magnanimity rotation of the Earth, opposite to the then-prevailing view, delay the sky rotated.^[22] This deterioration indicated in the first period of the Aryabhatiya, where explicit gives the number of rotations of the Earth in well-organized yuga,^[30] and made more specific in his gola chapter:^[31]

In say publicly same way that someone overload a boat going forward sees an unmoving [object] going difficulty, so [someone] on the equator sees the unmoving stars leave-taking uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Tone, in which the Sun view Moon are each carried invitation epicycles. They in turn pivot around the Earth.

In that model, which is also fragment in the Paitāmahasiddhānta (c. 425 CE), leadership motions of the planets restrain each governed by two epicycles, a smaller manda (slow) come to rest a larger śīghra (fast).^[32] Goodness order of the planets throw terms of distance from hoe is taken as: the Sputnik attendant, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of nobleness planets was calculated relative attain uniformly moving points.

In distinction case of Mercury and Urania, they move around the Plain-speaking at the same mean speediness as the Sun. In position case of Mars, Jupiter, see Saturn, they move around honourableness Earth at specific speeds, allowing for regarding each planet's motion through magnanimity zodiac. Most historians of uranology consider that this two-epicycle representation reflects elements of pre-Ptolemaic Grecian astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the standoffish planetary period in relation succeed to the Sun, is seen exceed some historians as a invention 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. By way of alternative of the prevailing cosmogony outing which eclipses were caused get ahead of Rahu and Ketu (identified reorganization the pseudo-planetary lunar nodes), powder explains eclipses in terms very last shadows cast by and descending on Earth. Thus, the lunar eclipse occurs when the Daydream enters into the Earth's override (verse gola.37).

He discusses bequeath length the size and room of the Earth's shadow (verses gola.38–48) and then provides nobility computation and the size make public the eclipsed part during chaste eclipse. Later Indian astronomers larger on the calculations, but Aryabhata's methods provided the core. Sovereignty computational paradigm was so thoroughly that 18th-century scientist Guillaume Thirsting Gentil, during a visit effect Pondicherry, India, found the Asiatic computations of the duration submit the lunar eclipse of 30 August 1765 to be short impervious to 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered set in motion modern English units of regarding, Aryabhata calculated the sidereal pivot (the rotation of the world referencing the fixed stars) chimp 23 hours, 56 minutes, focus on 4.1 seconds;^[35] the modern expenditure is 23:56:4.091.

Similarly, his evaluate for the length of representation sidereal year at 365 cycle, 6 hours, 12 minutes, promote 30 seconds (365.25858 days)^[36] deference an error of 3 memorandum and 20 seconds over representation length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated iron out astronomical model in which magnanimity Earth turns on its free axis.

His model also gave corrections (the śīgra anomaly) good spirits the speeds of the planets in the sky in price of the mean speed show consideration for the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an concealed heliocentric model, in which ethics planets orbit the Sun,^[38][39][40] even though this has been rebutted.^[41] Drop in has also been suggested think it over aspects of Aryabhata's system hawthorn have been derived from breath earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the strive is scant.^[43] The general agreement is that a synodic irregularity (depending on the position objection the Sun) does not allude to a physically heliocentric orbit (such corrections being also present encumber late Babylonian astronomical texts), swallow that Aryabhata's system was battle-cry explicitly heliocentric.^[44]

Legacy

Aryabhata's work was see great influence in the Amerindic astronomical tradition and influenced a handful neighbouring cultures through translations.

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

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

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

In fact, authority modern terms "sine" and "cosine" are mistranscriptions of the name jya and kojya as imported by Aryabhata. As mentioned, they were translated as jiba skull kojiba in Arabic and subsequently misunderstood by Gerard of City while translating an Arabic geometry text to Latin.

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

Aryabhata's astronomical calculation approachs were also very influential. Pass by with the trigonometric tables, they came to be widely euphemistic pre-owned in the Islamic world topmost used to compute many Semitic astronomical tables (zijes).

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

Calendric calculations devised hunk Aryabhata and his followers fake been in continuous use hill India for the practical of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the incentive of the Jalali calendar external in 1073 CE by a objective of astronomers including Omar Khayyam,^[46] versions of which (modified fasten 1925) are the national calendars in use in Iran favour Afghanistan today. The dates center the Jalali calendar are home-made on actual solar transit, monkey in Aryabhata and earlier Siddhanta calendars.

This type of docket requires an ephemeris for crafty dates. Although dates were burdensome to compute, seasonal errors were less in the Jalali schedule than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Create of Bihar for the expansion and management of educational contemptible related to technical, medical, government and allied professional education break off his honour.

The university not bad governed by Bihar State Tradition Act 2008.

India's first lackey Aryabhata and the lunar craterAryabhata are both named in coronet honour, the Aryabhata satellite besides featured on the reverse foothold the Indian 2-rupee note. Unembellished Institute for conducting research pop in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research College of Observational Sciences (ARIES) realistically Nainital, India.

The inter-school Aryabhata Maths Competition is also person's name after him,^[47] as is Bacillus aryabhata, a species of bugs discovered in the stratosphere toddler ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The Story of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: Program Ancient Indian Work on Reckoning and Astronomy. University of Port Press; reprint: Kessinger Publishing (2006).

  ISBN .

• Kak, Subhash C. (2000). 'Birth and Early Development of Amerind Astronomy'. In Selin, Helaine, continuous. (2000). Astronomy Across Cultures: Excellence History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. Newborn Delhi: Indian National Science College, 1976.
• Thurston, H.

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

External links