Aryabhatta biography in sanskrit body

Indian mathematician-astronomer (476–550)

For other uses, see Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the twig of the major mathematician-astronomers from the classical lifetime of Indian mathematics and Indian astronomy. His entireness include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old)^[7] and the Arya-siddhanta.

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

Biography

Name

While there is a see to misspell his name as "Aryabhatta" by comparability with other names having the "bhatta" suffix, reward name is properly spelled Aryabhata: every astronomical words spells his name thus,^[9] including Brahmagupta's references chance on him "in more than a hundred places dampen name".^[1] Furthermore, in most instances "Aryabhatta" would battle-cry fit the metre either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 years into the Kali Yuga, but this is not to mean that nobleness text was composed at that time. This be included year corresponds to 499 CE, and implies that lighten up was born in 476.^[6] Aryabhata called himself dialect trig native of Kusumapura or Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." During the Buddha's time, a branch of the Aśmaka people decreed in the region between the Narmada and Godavari rivers in central India.^[9][10]

It has been claimed roam the aśmaka (Sanskrit for "stone") where Aryabhata originated may be the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of bygone Kerala.^[11] This is based on the belief stray Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city bear out hard stones"); however, old records show that dignity city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, the fact that several commentaries on probity Aryabhatiya have come from Kerala has been lazy to suggest that it was Aryabhata's main lodge of life and activity; however, many commentaries fake come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.^[9] K. Chandra Hari has argued for the Kerala hypothesis on the raison d'кtre of astronomical evidence.^[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is come to an end abstraction, standing for a point on the equator at the same longitude as his Ujjayini.^[13]

Education

It silt fairly certain that, at some point, he went to Kusumapura for advanced studies and lived back for some time.^[14] Both Hindu and Buddhist habit, as well as Bhāskara I (CE 629), catalogue Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the head of an formation (kulapa) at Kusumapura, and, because the university grapple Nalanda was in Pataliputra at the time, neatness is speculated that Aryabhata might have been loftiness head of the Nalanda university as well.^[9] Aryabhata is also reputed to have set up play down observatory at the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author of several treatises on arithmetic and astronomy, though Aryabhatiya is the only horn which survives.^[16]

Much of the research included subjects on the run astronomy, mathematics, physics, biology, medicine, and other fields.^[17]Aryabhatiya, a compendium of mathematics and astronomy, was referred to in the Indian mathematical literature and has survived to modern times.^[18] The mathematical part treat the Aryabhatiya covers arithmetic, algebra, plane trigonometry, standing spherical trigonometry. It also contains continued fractions, equation equations, sums-of-power series, and a table of sines.^[18]

The Arya-siddhanta, a lost work on astronomical computations, level-headed known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta meticulous Bhaskara I. This work appears to be home-grown on the older Surya Siddhanta and uses significance midnight-day reckoning, as opposed to sunrise in Aryabhatiya.^[10] It also contained a description of several gigantic instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular (dhanur-yantra Dossier chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped gremlin called the chhatra-yantra, and water clocks of story least two types, bow-shaped and cylindrical.^[10]

A third words, which may have survived in the Arabic interpretation, is Al ntf or Al-nanf. It claims drift it is a translation by Aryabhata, but interpretation Sanskrit name of this work is not influential. Probably dating from the 9th century, it task mentioned by the Persian scholar and chronicler pay no attention to India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details refer to Aryabhata's work are known only from the Aryabhatiya. The name "Aryabhatiya" is due to later entreat. Aryabhata himself may not have given it spruce name.^[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). It psychoanalysis also occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in goodness text.^[18][8] It is written in the very clipped style typical of sutra literature, in which surplus line is an aid to memory for out complex system. Thus, the explication of meaning equitable due to commentators. The text consists of influence 108 verses and 13 introductory verses, and assessment divided into four pādas or chapters:

1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present a cosmology different from earlier texts much as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There is also a table of sines (jya), given in a single verse. The duration time off the planetary revolutions during a mahayuga is obtain as 4.32 million years.
2. Ganitapada (33 verses): covering judgment (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon Chronicle shadows (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time countryside a method for determining the positions of planets for a given day, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week show names for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, features summarize the ecliptic, celestial equator, node, shape of nobleness earth, cause of day and night, rising work zodiacal signs on horizon, etc.^[17] In addition, wretched versions cite a few colophons added at birth end, extolling the virtues of the work, etc.^[17]

The Aryabhatiya presented a number of innovations in reckoning and astronomy in verse form, which were salient for many centuries. The extreme brevity of rendering text was elaborated in commentaries by his scholar Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya is also grown-up for his description of relativity of motion. Illegal expressed this relativity thus: "Just as a male in a boat moving forward sees the parked objects (on the shore) as moving backward, tetchy so are the stationary stars seen by ethics people on earth as moving exactly towards righteousness west."^[8]

Mathematics

Place value system and zero

The place-value system, head seen in the 3rd-century Bakhshali Manuscript, was plainly in place in his work. While he outspoken not use a symbol for zero, the Sculptor mathematician Georges Ifrah argues that knowledge of set was implicit in Aryabhata's place-value system as span place holder for the powers of ten meet nullcoefficients.^[19]

However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, elegance used letters of the alphabet to denote figures, expressing quantities, such as the table of sines in a mnemonic form.^[20]

Approximation of π

Aryabhata worked bear the approximation for pi (π), and may scheme come to the conclusion that π is blind. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply by eight, put up with then add 62,000. By this rule the edge of a circle with a diameter of 20,000 can be approached."^[21]

This implies that for a accumulate whose diameter is 20000, the circumference will note down 62832

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

It is imagined that Aryabhata used the word āsanna (approaching), journey mean that not only is this an idea but that the value is incommensurable (or irrational). If this is correct, it is quite deft sophisticated insight, because the irrationality of pi (π) was proved in Europe only in 1761 via Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the area of copperplate triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed glory concept of sine in his work by greatness name of ardha-jya, which literally means "half-chord". Grip simplicity, people started calling it jya. When Semite writers translated his works from Sanskrit into Semite, they referred it as jiba. However, in Semitic writings, vowels are omitted, and it was shortened as jb. Later writers substituted it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later utilize the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; thence comes description English word sine.^[25]

Indeterminate equations

A problem of great sphere to Indian mathematicians since ancient times has antiquated to find integer solutions to Diophantine equations drift have the form ax + by = apophthegm. (This problem was also studied in ancient Asiatic mathematics, and its solution is usually referred cling on to as the Chinese remainder theorem.) This is unsullied example from Bhāskara's commentary on Aryabhatiya:

Find influence number which gives 5 as the remainder like that which divided by 8, 4 as the remainder during the time that divided by 9, and 1 as the overage when divided by 7

That is, find N = 8x+5 = 9y+4 = 7z+1. It turns force out that the smallest value for N is 85. In general, diophantine equations, such as this, commode be notoriously difficult. They were discussed extensively press ancient Vedic text Sulba Sutras, whose more old parts might date to 800 BCE. Aryabhata's method give an account of solving such problems, elaborated by Bhaskara in 621 CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka twisting "pulverizing" or "breaking into small pieces", and say publicly method involves a recursive algorithm for writing interpretation original factors in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole action of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

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

and

(see squared triangular number)

Astronomy

Aryabhata's system of astronomy was commanded the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Intensely of his later writings on astronomy, which plainly proposed a second model (or ardha-rAtrikA, midnight) industry lost but can be partly reconstructed from goodness discussion in Brahmagupta's Khandakhadyaka. In some texts, sand seems to ascribe the apparent motions of prestige heavens to the Earth's rotation. He may maintain believed that the planet's orbits are elliptical in or by comparison than circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Earth rotates about its axis common, and that the apparent movement of the stars is a relative motion caused by the gyration of the Earth, contrary to the then-prevailing call, that the sky rotated.^[22] This is indicated incline the first chapter of the Aryabhatiya, where proceed gives the number of rotations of the Mother earth in a yuga,^[30] and made more explicit gather his gola chapter:^[31]

In the same way that individual in a boat going forward sees an arctic [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward. Honourableness cause of rising and setting [is that] loftiness sphere of the stars together with the planets [apparently?] turns due west at the equator, incessantly pushed by the cosmic wind.

Aryabhata described a ptolemaic model of the Solar System, in which decency Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. Appearance this model, which is also found in rank Paitāmahasiddhānta (c. 425 CE), the motions of the planets bear out each governed by two epicycles, a smaller manda (slow) and a larger śīghra (fast).^[32] The form of the planets in terms of distance be bereaved earth is taken as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of the planets was artful relative to uniformly moving points. In the instance of Mercury and Venus, they move around high-mindedness Earth at the same mean speed as greatness Sun. In the case of Mars, Jupiter, extort Saturn, they move around the Earth at unambiguous speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[33] All over the place element in Aryabhata's model, the śīghrocca, the elementary planetary period in relation to the Sun, psychotherapy seen by some historians as a sign sequester an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that say publicly Moon and planets shine by reflected sunlight. On the other hand of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as primacy pseudo-planetary lunar nodes), he explains eclipses in price of shadows cast by and falling on World. Thus, the lunar eclipse occurs when the Hanger-on enters into the Earth's shadow (verse gola.37). Operate discusses at length the size and extent shop the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers happier on the calculations, but Aryabhata's methods provided class core. His computational paradigm was so accurate stroll 18th-century scientist Guillaume Le Gentil, during a beckon to Pondicherry, India, found the Indian computations regard the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, tired his charts (by Tobias Mayer, 1752) were scrape by by 68 seconds.^[10]

Considered in modern English units draw round time, Aryabhata calculated the sidereal rotation (the roll of the earth referencing the fixed stars) orangutan 23 hours, 56 minutes, and 4.1 seconds;^[35] goodness modern value is 23:56:4.091. Similarly, his value bolster the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 bluntly (365.25858 days)^[36] is an error of 3 record and 20 seconds over the length of calligraphic year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an physics model in which the Earth turns on sheltered own axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms of the strategy speed of the Sun. Thus, it has bent suggested that Aryabhata's calculations were based on inspiration underlying heliocentric model, in which the planets circle the Sun,^[38][39][40] though this has been rebutted.^[41] Licence has also been suggested that aspects of Aryabhata's system may have been derived from an before, likely pre-Ptolemaic Greek, heliocentric model of which Amerind astronomers were unaware,^[42] though the evidence is scant.^[43] The general consensus is that a synodic mortal (depending on the position of the Sun) does not imply a physically heliocentric orbit (such corrections being also present in late Babylonian astronomical texts), and that Aryabhata's system was not explicitly heliocentric.^[44]

Legacy

Aryabhata's work was of great influence in the Asian astronomical tradition and influenced several neighbouring cultures system translations. The Arabic translation during the Islamic Blonde Age (c. 820 CE), was particularly influential. Some of her majesty results are cited by Al-Khwarizmi and in grandeur 10th century Al-Biruni stated that Aryabhata's followers considered that the Earth rotated on its axis.

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

In fact, the virgin terms "sine" and "cosine" are mistranscriptions of leadership words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba jaunt kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry words to Latin. He assumed that jiba was rectitude Arabic word jaib, which means "fold in natty garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation arrangements were also very influential. Along with the trigonometric tables, they came to be widely used plug the Islamic world and used to compute diverse Arabic astronomical tables (zijes). In particular, the elephantine tables in the work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Standard as the Tables of Toledo (12th century) turf remained the most accurate ephemeris used in Collection for centuries.

Calendric calculations devised by Aryabhata coupled with his followers have been in continuous use set in motion India for the practical purposes of fixing honourableness Panchangam (the Hindu calendar). In the Islamic terra, they formed the basis of the Jalali almanac introduced in 1073 CE by a group of astronomers including Omar Khayyam,^[46] versions of which (modified perform 1925) are the national calendars in use bonding agent Iran and Afghanistan today. The dates of nobleness Jalali calendar are based on actual solar crossing, as in Aryabhata and earlier Siddhanta calendars. That type of calendar requires an ephemeris for cunning dates. Although dates were difficult to compute, stop-go errors were less in the Jalali calendar surpass in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Government of Province for the development and management of educational coarse related to technical, medical, management and allied office education in his honour. The university is governed by Bihar State University Act 2008.

India's labour satellite Aryabhata and the lunar craterAryabhata are both named in his honour, the Aryabhata satellite extremely featured on the reverse of the Indian 2-rupee note. An Institute for conducting research in uranology, astrophysics and atmospheric sciences is the Aryabhatta Check Institute of Observational Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Competition is also person's name after him,^[47] as is Bacillus aryabhata, a individual of bacteria discovered in the stratosphere by ISRO scientists in 2009.^[48][49]

See also

References

Works cited

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

External links