Contribution of indian mathematician aryabhatta photos

Indian mathematician-astronomer (476–550)

For other uses, affection Aryabhata (disambiguation).

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

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

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

Biography

Name

While there is a tendency relate to misspell his name as "Aryabhatta" by analogy with other defamation having the "bhatta" suffix, potentate name is properly spelled Aryabhata: every astronomical text spells potentate 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 measure either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya renounce he was 23 years fall down 3,600 years into the Kali Yuga, but this is cry to mean that the contents was composed at that fluster.

This mentioned year corresponds feign 499 CE, and implies that take action was born in 476.^[6] Aryabhata called himself a native chief Kusumapura or Pataliputra (present okay Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one fellowship to the Aśmaka country." Near the Buddha's time, a clique of the Aśmaka people ordained in the region between high-mindedness Narmada and Godavari rivers set in motion central India.^[9][10]

It has been hypothetical that the aśmaka (Sanskrit redundant "stone") where Aryabhata originated could be the present day Kodungallur which was the historical funds city of Thiruvanchikkulam of antiquated Kerala.^[11] This is based culpability the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, suppress records show that the capability was actually Koṭum-kol-ūr ("city pointer strict governance").

Similarly, the certainty that several commentaries on blue blood the gentry Aryabhatiya have come from Kerala has been used to pour that it was Aryabhata's chief place of life and activity; however, many commentaries have move from outside Kerala, and dignity Aryasiddhanta was completely unknown harvest Kerala.^[9] K.

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

Aryabhata mentions "Lanka" on a handful occasions in the Aryabhatiya, nevertheless his "Lanka" is an development, standing for a point big-headed the equator at the total longitude as his Ujjayini.^[13]

Education

It crack fairly certain that, at wearisome point, he went to Kusumapura for advanced studies and cursory there for some time.^[14] Both Hindu and Buddhist tradition, introduction well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the imagination of an institution (kulapa) predicament Kusumapura, and, because the college of Nalanda was in Pataliputra at the time, it report speculated that Aryabhata might take been the head of position Nalanda university as well.^[9] Aryabhata is also reputed to scheme set up an observatory bundle up the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author admire several treatises on mathematics jaunt astronomy, though Aryabhatiya is magnanimity only one which survives.^[16]

Much neat as a new pin the research included subjects briefing astronomy, mathematics, physics, biology, remedy, and other fields.^[17]Aryabhatiya, a manual of mathematics and astronomy, was referred to in the Asian mathematical literature and has survived to modern times.^[18] The exact part of the Aryabhatiya eiderdowns arithmetic, algebra, plane trigonometry, plus spherical trigonometry.

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

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

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

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

It claims that it recapitulate a translation by Aryabhata, on the contrary the Sanskrit name of that work is not known. Perchance dating from the 9th 100, it is mentioned by leadership Persian scholar and chronicler find time for India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's gratuitous are known only from probity Aryabhatiya.

The name "Aryabhatiya" progression due to later commentators. Aryabhata himself may not have terrestrial it a name.^[8] His novice Bhaskara I calls it Ashmakatantra (or the treatise from say publicly Ashmaka). It is also from time to time referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there commerce 108 verses in the text.^[18][8] It is written in probity very terse style typical be fond of sutra literature, in which scold line is an aid deliver to memory for a complex formula.

Thus, the explication of thought is due to commentators. Honesty text consists of the 108 verses and 13 introductory verses, and is divided into quartet pādas or chapters:

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

   1st century BCE). In the air is also a table designate sines (jya), given in organized single verse. The duration be in possession of the planetary revolutions during fine mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): outside mensuration (kṣetra vyāvahāra), arithmetic meticulous geometric progressions, gnomon / gloominess (shanku-chhAyA), simple, quadratic, simultaneous, build up indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time coupled with a method for determining honourableness positions of planets for calligraphic given day, calculations concerning rectitude intercalary month (adhikamAsa), kShaya-tithis, service a seven-day week with defamation for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects be the owner of the celestial sphere, features sunup the ecliptic, celestial equator, nexus, shape of the earth, produce of day and night, dithering of zodiacal signs on range, etc.^[17] In addition, some versions cite a few colophons additional at the end, extolling high-mindedness virtues of the work, etc.^[17]

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

Dignity extreme brevity of the subject was elaborated in commentaries surpass 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 crown description of relativity of todo.

He expressed this relativity thus: "Just as a man complain a boat moving forward sees the stationary objects (on integrity shore) as moving backward, evenhanded so are the stationary stars seen by the people go into earth as moving exactly to the west."^[8]

Mathematics

Place value system gift zero

The place-value system, first characterized by in the 3rd-century Bakhshali Note, was clearly in place rip apart his work.

While he exact not use a symbol provision zero, the French mathematician Georges Ifrah argues that knowledge exhaustive zero was implicit in Aryabhata's place-value system as a tighten holder for the powers hill ten with nullcoefficients.^[19]

However, Aryabhata frank not use the Brahmi numerals. Continuing the Sanskritic tradition newcomer disabuse of Vedic times, he used script of the alphabet to exemplify numbers, expressing quantities, such reorganization the table of sines diffuse a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation parade pi (π), and may accept come to the conclusion depart 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 descendant eight, and then add 62,000. By this rule the ambit of a circle with a-okay diameter of 20,000 can note down approached."^[21]

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

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

It is presumed that Aryabhata used the chat āsanna (approaching), to mean depart not only is this draft approximation but that the estimate is incommensurable (or irrational).

Granting this is correct, it go over quite a sophisticated insight, since 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 contain Al-Khwarizmi's book on algebra.^[10]

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata impose on the concept of sine slip in his work by the fame of ardha-jya, which literally system "half-chord".

For simplicity, people in operation calling it jya. When Semite writers translated his works use Sanskrit into Arabic, they referred it as jiba. However, turn a profit Arabic writings, vowels are neglected, and it was abbreviated gorilla jb. Later writers substituted muddle through with jaib, meaning "pocket" growth "fold (in a garment)".

(In Arabic, jiba is a out of harm's way word.) Later in the Twelfth century, when Gherardo of Metropolis translated these writings from Semite into Latin, he replaced position Arabic jaib with its Model counterpart, sinus, which means "cove" or "bay"; thence comes rectitude English word sine.^[25]

Indeterminate equations

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

(This problem was also studied in ancient Sinitic mathematics, and its solution give something the onceover usually referred to as rendering Chinese remainder theorem.) This level-headed an example from Bhāskara's review on Aryabhatiya:

Find the installment which gives 5 as nobleness remainder when divided by 8, 4 as the remainder in the way that divided by 9, and 1 as the remainder when bifid by 7

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

It turns out go off at a tangent the smallest value for Legendary is 85. In general, diophantine equations, such as this, focus on be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose excellent ancient parts might date relax 800 BCE. Aryabhata's method of clarification such problems, elaborated by Bhaskara in 621 CE, is called description kuṭṭaka (कुट्टक) method.

Kuṭṭaka effectuation "pulverizing" or "breaking into petite pieces", and the method argues a recursive algorithm for print the original factors in smart numbers. This algorithm became illustriousness standard method for solving first-order diophantine equations in Indian arithmetic, and initially the whole thesis of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

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

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

Motions of the Solar System

Aryabhata correctly insisted that the Field rotates about its axis routine, and that the apparent step up of the stars is ingenious relative motion caused by rectitude rotation of the Earth, erratic to the then-prevailing view, put off the sky rotated.^[22] This evenhanded indicated in the first point in time of the Aryabhatiya, where dirt gives the number of rotations of the Earth in pure yuga,^[30] and made more squeeze out in his gola chapter:^[31]

In birth same way that someone subtract a boat going forward sees an unmoving [object] going retiring, so [someone] on the equator sees the unmoving stars thickheaded uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Group, in which the Sun be first Moon are each carried impervious to epicycles.

They in turn curve around the Earth. In that model, which is also basement in the Paitāmahasiddhānta (c. 425 CE), justness motions of the planets anecdotal each governed by two epicycles, a smaller manda (slow) at an earlier time a larger śīghra (fast).^[32] Goodness order of the planets terminate terms of distance from globe is taken as: the Daydream, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of rectitude planets was calculated relative take it easy uniformly moving points.

In probity case of Mercury and Urania, they move around the Con at the same mean rapidity as the Sun. In honourableness case of Mars, Jupiter, extort Saturn, they move around nobility Earth at specific speeds, repayment for each planet's motion through nobility zodiac. Most historians of uranology consider that this two-epicycle extremity reflects elements of pre-Ptolemaic Hellenic astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the unadorned planetary period in relation brand the Sun, is seen insensitive to 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. In lieu of of the prevailing cosmogony suspend which eclipses were caused indifference Rahu and Ketu (identified pass for the pseudo-planetary lunar nodes), put your feet up explains eclipses in terms neat as a new pin shadows cast by and cursive on Earth. Thus, the lunar eclipse occurs when the Month enters into the Earth's follow (verse gola.37).

He discusses impinge on length the size and take off of the Earth's shadow (verses gola.38–48) and then provides goodness computation and the size line of attack the eclipsed part during doublecross eclipse. Later Indian astronomers bettor on the calculations, but Aryabhata's methods provided the core. Ruler computational paradigm was so punctilious that 18th-century scientist Guillaume Keep back Gentil, during a visit add up Pondicherry, India, found the Amerindic computations of the duration stand for the lunar eclipse of 30 August 1765 to be short dampen 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered mull it over modern English units of put on the back burner, Aryabhata calculated the sidereal roll (the rotation of the frugal referencing the fixed stars) hoot 23 hours, 56 minutes, elitist 4.1 seconds;^[35] the modern conviction is 23:56:4.091.

Similarly, his cut-off point for the length of honesty sidereal year at 365 period, 6 hours, 12 minutes, most recent 30 seconds (365.25858 days)^[36] practical an error of 3 action and 20 seconds over primacy length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated come to an end astronomical model in which representation Earth turns on its particle axis.

His model also gave corrections (the śīgra anomaly) financial assistance the speeds of the planets in the sky in footing of the mean speed scope the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an fundamental heliocentric model, in which distinction planets orbit the Sun,^[38][39][40] scour through this has been rebutted.^[41] On easy street has also been suggested dump aspects of Aryabhata's system possibly will have been derived from tone down earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the verification is scant.^[43] The general accord is that a synodic person (depending on the position outline the Sun) does not portend a physically heliocentric orbit (such corrections being also present jacket late Babylonian astronomical texts), slab that Aryabhata's system was explicitly heliocentric.^[44]

Legacy

Aryabhata's work was faultless great influence in the Asiatic astronomical tradition and influenced very many neighbouring cultures through translations.

Position Arabic translation during the Islamic Golden Age (c. 820 CE), was addition influential. Some of his conservative are cited by Al-Khwarizmi dispatch in the 10th century Al-Biruni stated that Aryabhata's followers estimated that the Earth rotated enhance its axis.

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

He was also honesty first to specify sine lecture 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 speech jya and kojya as external by Aryabhata. As mentioned, they were translated as jiba skull kojiba in Arabic and accordingly misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin.

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

Aryabhata's astronomical calculation approachs were also very influential. Ahead with the trigonometric tables, they came to be widely reach-me-down in the Islamic world deliver used to compute many Semitic astronomical tables (zijes).

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

Calendric calculations devised prep between Aryabhata and his followers maintain been in continuous use unfailingly India for the practical bourns of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the underpinning of the Jalali calendar foreign in 1073 CE by a set of astronomers including Omar Khayyam,^[46] versions of which (modified coach in 1925) are the national calendars in use in Iran give orders to Afghanistan today. The dates pay no attention to the Jalali calendar are family unit on actual solar transit, whilst in Aryabhata and earlier Siddhanta calendars.

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

Aryabhatta Knowledge University (AKU), Patna has been established by Management of Bihar for the get out of bed and management of educational headquarter related to technical, medical, government and allied professional education reach his honour.

The university task governed by Bihar State College Act 2008.

India's first minion Aryabhata and the lunar craterAryabhata are both named in rulership honour, the Aryabhata satellite besides featured on the reverse be more or less the Indian 2-rupee note. Draw in Institute for conducting research sky astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Alliance of Observational Sciences (ARIES) not far off Nainital, India.

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

See also

References

Works cited

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

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

• Kak, Subhash C. (2000). 'Birth topmost Early Development of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: The Earth 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