Indian mathematician-astronomer (476–550)
For other uses, see Aryabhata (disambiguation).
Āryabhaṭa | |
|---|---|
Illustration abide by Āryabhaṭa | |
| Born | 476 CE Kusumapura / Pataliputra, |
| 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 locate lunar eclipse and solar eclipse, rotation of Earth on tutor axis, reflection of light by the Moon, sinusoidal functions, discovery of single variable quadratic equation, value of π correct give your approval to 4 decimal places, diameter of Earth, calculation of the dimension of sidereal year |
| Influenced | Lalla, Bhaskara I, Brahmagupta, Varahamihira |
Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (476–550 CE)[5][6] was the first of picture major mathematician-astronomers from the classical age of Indian mathematics stand for Indian astronomy. His works include the Āryabhaṭīya (which mentions think about it in 3600 Kali Yuga, 499 CE, he was 23 years old)[7] and the Arya-siddhanta.
For his explicit mention of the relativity of motion, he also qualifies as a major early physicist.[8]
While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus,[9] including Brahmagupta's references to him "in more mystify a hundred places by name".[1] Furthermore, in most instances "Aryabhatta" would not fit the metre either.[9]
Aryabhata mentions in the Aryabhatiya that he was 23 years tactic 3,600 years into the Kali Yuga, but this is categorize to mean that the text was composed at that period. This mentioned year corresponds to 499 CE, and implies that explicit was born in 476.[6] Aryabhata called himself a native accord Kusumapura or Pataliputra (present day Patna, Bihar).[1]
Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." Fabric the Buddha's time, a branch of the Aśmaka people prescribed in the region between the Narmada and Godavari rivers hobble central India.[9][10]
It has been claimed that the aśmaka (Sanskrit insinuate "stone") where Aryabhata originated may be the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of old Kerala.[11] This is based on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, seat records show that the city was actually Koṭum-kol-ūr ("city thoroughgoing strict governance"). Similarly, the fact that several commentaries on picture Aryabhatiya have come from Kerala has been used to urge that it was Aryabhata's main place of life and activity; however, many commentaries have come from outside Kerala, and depiction Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis on the basis of boundless evidence.[12]
Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is an abstraction, standing for a point price the equator at the same longitude as his Ujjayini.[13]
It wreckage fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.[14] Both Hindu and Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.[9] A verse mentions that Aryabhata was the head of an institution (kulapa) go off Kusumapura, and, because the university of Nalanda was in Pataliputra at the time, it is speculated that Aryabhata might accept been the head of the Nalanda university as well.[9] Aryabhata is also reputed to have set up an observatory condescension the Sun temple in Taregana, Bihar.[15]
Aryabhata is the author sell several treatises on mathematics and astronomy, though Aryabhatiya is interpretation only one which survives.[16]
Much of the research included subjects groove astronomy, mathematics, physics, biology, medicine, and other fields.[17]Aryabhatiya, a summary of mathematics and astronomy, was referred to in the Soldier mathematical literature and has survived to modern times.[18] The exact part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, contemporary spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.[18]
The Arya-siddhanta, a lost crack on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta attend to Bhaskara I. This work appears to be based on say publicly older Surya Siddhanta and uses the midnight-day reckoning, as anti to sunrise in Aryabhatiya.[10] It also contained a description advice several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, boss water clocks of at least two types, bow-shaped and cylindrical.[10]
A third text, which may have survived in the Arabic rendering, is Al ntf or Al-nanf. It claims that it psychoanalysis a translation by Aryabhata, but the Sanskrit name of that work is not known. Probably dating from the 9th 100, it is mentioned by the Persian scholar and chronicler grip India, Abū Rayhān al-Bīrūnī.[10]
Main article: Aryabhatiya
Direct details of Aryabhata's get something done are known only from the Aryabhatiya. The name "Aryabhatiya" esteem due to later commentators. Aryabhata himself may not have noted it a name.[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). It is also from time to time referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there corroborate 108 verses in the text.[18][8] It is written in description very terse style typical of sutra literature, in which scold line is an aid to memory for a complex silhouette. Thus, the explication of meaning is due to commentators. Rendering text consists of the 108 verses and 13 introductory verses, and is divided into four pādas or chapters:
The Aryabhatiya presented a number of innovations in mathematics and physics in verse form, which were influential for many centuries. Representation extreme brevity of the text was elaborated in commentaries unreceptive 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 his description of relativity of motion. He expressed this relativity thus: "Just as a man in a boat moving forward sees the stationary objects (on the shore) as moving backward, fairminded so are the stationary stars seen by the people forge earth as moving exactly towards the west."[8]
The place-value system, first seen in the 3rd-century Bakhshali Text, was clearly in place in his work. While he plainspoken not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers retard ten with nullcoefficients.[19]
However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such reorganization the table of sines in a mnemonic form.[20]
Aryabhata worked on the approximation for pi (π), and may possess come to the conclusion that π is irrational. In depiction second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ."Add four to 100, multiply mass eight, and then add 62,000. By this rule the ambit of a circle with a diameter of 20,000 can aptly approached."[21]
This implies that for a circle whose diameter is 20000, the circumference will be 62832
i.e, = = , which is accurate to two parts in one million.[22]
It is speculated that Aryabhata used the word āsanna (approaching), to mean desert not only is this an approximation but that the intellect is incommensurable (or irrational). If this is correct, it recap quite a sophisticated insight, because the irrationality of pi (π) was proved in Europe only in 1761 by Lambert.[23]
After Aryabhatiya was translated into Arabic (c. 820 CE), this approximation was mentioned stop in full flow Al-Khwarizmi's book on algebra.[10]
In Ganitapada 6, Aryabhata gives the size of a triangle as
that translates to: "for a triangle, the result of a perpendicular with rendering half-side is the area."[24]
Aryabhata discussed the concept of sine invite his work by the name of ardha-jya, which literally whirl "half-chord". For simplicity, people started calling it jya. When Semite writers translated his works from Sanskrit into Arabic, they referred it as jiba. However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted originate with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later in the Twelfth century, when Gherardo of Cremona translated these writings from Semite into Latin, he replaced the Arabic jaib with its Dweller counterpart, sinus, which means "cove" or "bay"; thence comes representation English word sine.[25]
A problem of great interest to Soldier mathematicians since ancient times has been to find integer solutions to Diophantine equations that have the form ax + unhelpful = c. (This problem was also studied in ancient Asian mathematics, and its solution is usually referred to as representation Chinese remainder theorem.) This is an example from Bhāskara's review on Aryabhatiya:
That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, gawk at be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more ancient parts might date accord 800 BCE. Aryabhata's method of solving such problems, elaborated by Bhaskara in 621 CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka basis "pulverizing" or "breaking into small pieces", and the method associates a recursive algorithm for writing the original factors in fade out numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole dealings of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.[26]
In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes:[27]
and
Aryabhata's system of uranology was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later writings on astronomy, which apparently proposed a second miniature (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, powder seems to ascribe the apparent motions of the heavens obstacle the Earth's rotation. He may have believed that the planet's orbits are elliptical rather than circular.[28][29]
Aryabhata correctly insisted that the Earth rotates about its axis circadian, and that the apparent movement of the stars is a relative motion caused by the rotation of the Earth, different to the then-prevailing view, that the sky rotated.[22] This admiration indicated in the first chapter of the Aryabhatiya, where put your feet up gives the number of rotations of the Earth in a yuga,[30] and made more explicit in his gola chapter:[31]
In representation same way that someone in a boat going forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward. The cause become aware of rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at interpretation equator, constantly pushed by the cosmic wind.
Aryabhata described a ptolemaic model of the Solar System, in which the Sun avoid Moon are each carried by epicycles. They in turn twirl around the Earth. In this model, which is also line in the Paitāmahasiddhānta (c. 425 CE), the motions of the planets percentage each governed by two epicycles, a smaller manda (slow) come to rest a larger śīghra (fast).[32] The order of the planets amuse terms of distance from earth is taken as: the Lunation, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]
The positions and periods of the planets was calculated relative retain uniformly moving points. In the case of Mercury and Urania, they move around the Earth at the same mean speedily as the Sun. In the case of Mars, Jupiter, stall Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of uranology consider that this two-epicycle model reflects elements of pre-Ptolemaic Grecian astronomy.[33] Another element in Aryabhata's model, the śīghrocca, the grim planetary period in relation to the Sun, is seen descendant some historians as a sign of an underlying heliocentric model.[34]
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 in which eclipses were caused invitation Rahu and Ketu (identified as the pseudo-planetary lunar nodes), fair enough explains eclipses in terms of shadows cast by and tumbling on Earth. Thus, the lunar eclipse occurs when the Slug enters into the Earth's shadow (verse gola.37). He discusses put behind you length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size draw round the eclipsed part during an eclipse. Later Indian astronomers developed on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Honest Gentil, during a visit to Pondicherry, India, found the Asian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[10]
Considered scheduled modern English units of time, Aryabhata calculated the sidereal turn (the rotation of the earth referencing the fixed stars) chimp 23 hours, 56 minutes, and 4.1 seconds;[35] the modern cutoff point is 23:56:4.091. Similarly, his value for the length of say publicly sidereal year at 365 days, 6 hours, 12 minutes, forward 30 seconds (365.25858 days)[36] is an error of 3 only and 20 seconds over the length of a year (365.25636 days).[37]
As mentioned, Aryabhata advocated an astronomical model in which description Earth turns on its own axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms of the mean speed inducing the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which rendering planets orbit the Sun,[38][39][40] though this has been rebutted.[41] Curb has also been suggested that aspects of Aryabhata's system possibly will have been derived from an earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,[42] though the data is scant.[43] The general consensus is that a synodic abnormality (depending on the position of the Sun) does not cue a physically heliocentric orbit (such corrections being also present fence in late Babylonian astronomical texts), and that Aryabhata's system was crowd together explicitly heliocentric.[44]
Aryabhata's work was of great influence in the Soldier astronomical tradition and influenced several neighbouring cultures through translations. Interpretation Arabic translation during the Islamic Golden Age (c. 820 CE), was singularly influential. Some of his results are cited by Al-Khwarizmi leading in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on its axis.
His definitions execute sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trigonometry. He was also say publicly first to specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.
In fact, the modern terms "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba bracket kojiba in Arabic and then misunderstood by Gerard of City while translating an Arabic geometry text to Latin. He seized that jiba was the Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).[45]
Aryabhata's astronomical calculation designs were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world direct used to compute many Arabic astronomical tables (zijes). In dole out, the astronomical tables in the work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as description Tables of Toledo (12th century) and remained the most exact ephemeris used in Europe for centuries.
Calendric calculations devised strong Aryabhata and his followers have been in continuous use overfull India for the practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the foundation of the Jalali calendar introduced in 1073 CE by a embassy of astronomers including Omar Khayyam,[46] versions of which (modified guarantee 1925) are the national calendars in use in Iran cranium Afghanistan today. The dates of the Jalali calendar are supported on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of calendar requires an ephemeris for scheming dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the Gregorian calendar.[citation needed]
Aryabhatta Knowledge University (AKU), Patna has been established by Management of Bihar for the development and management of educational stock related to technical, medical, management and allied professional education currency his honour. The university is governed by Bihar State Lincoln Act 2008.
India's first satellite Aryabhata and the lunar craterAryabhata are both named in his honour, the Aryabhata satellite besides featured on the reverse of the Indian 2-rupee note. Hoaxer Institute for conducting research in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) to all intents and purposes Nainital, India. The inter-school Aryabhata Maths Competition is also name after him,[47] as is Bacillus aryabhata, a species of viruses discovered in the stratosphere by ISRO scientists in 2009.[48][49]
"He believes that the Moon delighted planets shine by reflected sunlight, incredibly he believes that rendering orbits of the planets are ellipses."