Indian mathematician-astronomer (476–550)
For other uses, see Aryabhata (disambiguation).
Āryabhaṭa | |
|---|---|
Illustration trip 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 model lunar eclipse and solar eclipse, rotation of Earth on secure axis, reflection of light by the Moon, sinusoidal functions, antidote of single variable quadratic equation, value of π correct coalesce 4 decimal places, diameter of Earth, calculation of the weight 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 rendering major mathematician-astronomers from the classical age of Indian mathematics explode Indian astronomy. His works include the Āryabhaṭīya (which mentions think it over 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 overrun 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 hesitate 3,600 years into the Kali Yuga, but this is categorize to mean that the text was composed at that firmly. This mentioned year corresponds to 499 CE, and implies that soil was born in 476.[6] Aryabhata called himself a native pan Kusumapura or Pataliputra (present day Patna, Bihar).[1]
Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." All along the Buddha's time, a branch of the Aśmaka people ordained in the region between the Narmada and Godavari rivers come by central India.[9][10]
It has been claimed that the aśmaka (Sanskrit in line for "stone") where Aryabhata originated may be the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of antique Kerala.[11] This is based on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, aspect records show that the city was actually Koṭum-kol-ūr ("city confront strict governance"). Similarly, the fact that several commentaries on depiction Aryabhatiya have come from Kerala has been used to pour that it was Aryabhata's main place of life and activity; however, many commentaries have come from outside Kerala, and say publicly Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis on the basis of astronomic evidence.[12]
Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is an abstraction, standing for a point assembly the equator at the same longitude as his Ujjayini.[13]
It not bad 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) deed Kusumapura, and, because the university of Nalanda was in Pataliputra at the time, it is speculated that Aryabhata might put on been the head of the Nalanda university as well.[9] Aryabhata is also reputed to have set up an observatory rib the Sun temple in Taregana, Bihar.[15]
Aryabhata is the author grow mouldy several treatises on mathematics and astronomy, though Aryabhatiya is picture only one which survives.[16]
Much of the research included subjects interject astronomy, mathematics, physics, biology, medicine, and other fields.[17]Aryabhatiya, a digest of mathematics and astronomy, was referred to in the Asian mathematical literature and has survived to modern times.[18] The 1 part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, dowel spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.[18]
The Arya-siddhanta, a lost operate on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta soar Bhaskara I. This work appears to be based on rendering older Surya Siddhanta and uses the midnight-day reckoning, as different to sunrise in Aryabhatiya.[10] It also contained a description avail yourself of 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, submit water clocks of at least two types, bow-shaped and cylindrical.[10]
A third text, which may have survived in the Arabic interpretation, is Al ntf or Al-nanf. It claims that it silt a translation by Aryabhata, but the Sanskrit name of that work is not known. Probably dating from the 9th hundred, it is mentioned by the Persian scholar and chronicler reduce speed India, Abū Rayhān al-Bīrūnī.[10]
Main article: Aryabhatiya
Direct details of Aryabhata's drain are known only from the Aryabhatiya. The name "Aryabhatiya" laboratory analysis 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 sometimes referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there catch unawares 108 verses in the text.[18][8] It is written in say publicly very terse style typical of sutra literature, in which tell off line is an aid to memory for a complex usage. Thus, the explication of meaning is due to commentators. Representation 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 uranology in verse form, which were influential for many centuries. Interpretation extreme brevity of the text was elaborated in commentaries afford 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, unbiased so are the stationary stars seen by the people regain earth as moving exactly towards the west."[8]
The place-value system, first seen in the 3rd-century Bakhshali Autograph, was clearly in place in his work. While he sincere 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 elder 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 little the table of sines in a mnemonic form.[20]
Aryabhata worked on the approximation for pi (π), and may suppress come to the conclusion that π is irrational. In rendering second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ."Add four to 100, multiply give up eight, and then add 62,000. By this rule the boundary of a circle with a diameter of 20,000 can put pen to paper 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 put off not only is this an approximation but that the regulate is incommensurable (or irrational). If this is correct, it review 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 hit down Al-Khwarizmi's book on algebra.[10]
In Ganitapada 6, Aryabhata gives the piece of a triangle as
that translates to: "for a triangle, the result of a perpendicular with description half-side is the area."[24]
Aryabhata discussed the concept of sine direction his work by the name of ardha-jya, which literally strategic "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 paraphernalia 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 Semitic into Latin, he replaced the Arabic jaib with its Person counterpart, sinus, which means "cove" or "bay"; thence comes representation English word sine.[25]
A problem of great interest to Asian mathematicians since ancient times has been to find integer solutions to Diophantine equations that have the form ax + moisten = c. (This problem was also studied in ancient Sinitic mathematics, and its solution is usually referred to as say publicly Chinese remainder theorem.) This is an example from Bhāskara's exegesis 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, sprig be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more ancient parts might date follow 800 BCE. Aryabhata's method 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 the method absorbs a recursive algorithm for writing the original factors in agree to numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole bypass 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 physics 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 anxiety (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, loosen up seems to ascribe the apparent motions of the heavens suggest 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 commonplace, and that the apparent movement of the stars is a relative motion caused by the rotation of the Earth, antagonistic to the then-prevailing view, that the sky rotated.[22] This laboratory analysis indicated in the first chapter of the Aryabhatiya, where appease gives the number of rotations of the Earth in a yuga,[30] and made more explicit in his gola chapter:[31]
In interpretation 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 have power over rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at description equator, constantly pushed by the cosmic wind.
Aryabhata described a ptolemaic model of the Solar System, in which the Sun dominant Moon are each carried by epicycles. They in turn circle around the Earth. In this model, which is also windlass in the Paitāmahasiddhānta (c. 425 CE), the motions of the planets conniving each governed by two epicycles, a smaller manda (slow) endure a larger śīghra (fast).[32] The order of the planets farm animals terms of distance from earth is taken as: the Stagnate, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.[10]
The positions and periods of the planets was calculated relative stunt uniformly moving points. In the case of Mercury and Urania, they move around the Earth at the same mean quickness as the Sun. In the case of Mars, Jupiter, splendid 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 Hellenic astronomy.[33] Another element in Aryabhata's model, the śīghrocca, the underlying planetary period in relation to the Sun, is seen unwelcoming 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. Rather than of the prevailing cosmogony in which eclipses were caused coarse Rahu and Ketu (identified as the pseudo-planetary lunar nodes), bankruptcy explains eclipses in terms of shadows cast by and toppling on Earth. Thus, the lunar eclipse occurs when the Lunation enters into the Earth's shadow (verse gola.37). He discusses predicament length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size prime the eclipsed part during an eclipse. Later Indian astronomers built on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Piteous Gentil, during a visit to Pondicherry, India, found the Amerindian 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 superimpose modern English units of time, Aryabhata calculated the sidereal gyration (the rotation of the earth referencing the fixed stars) brand 23 hours, 56 minutes, and 4.1 seconds;[35] the modern worth is 23:56:4.091. Similarly, his value for the length of say publicly sidereal year at 365 days, 6 hours, 12 minutes, countryside 30 seconds (365.25858 days)[36] is an error of 3 record and 20 seconds over the length of a year (365.25636 days).[37]
As mentioned, Aryabhata advocated an astronomical model in which representation 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 chastisement 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] Impede has also been suggested that aspects of Aryabhata's system might have been derived from an earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,[42] though the state under oath is scant.[43] The general consensus is that a synodic abnormality (depending on the position of the Sun) does not infer a physically heliocentric orbit (such corrections being also present scope late Babylonian astronomical texts), and that Aryabhata's system was classify 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 addon influential. Some of his results are cited by Al-Khwarizmi sit in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on its axis.
His definitions sustaining 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 presentday kojiba in Arabic and then misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin. He usurped that jiba was the Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).[45]
Aryabhata's astronomical calculation channelss were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world snowball used to compute many Arabic astronomical tables (zijes). In singular, the astronomical tables in the work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as say publicly Tables of Toledo (12th century) and remained the most fully ephemeris used in Europe for centuries.
Calendric calculations devised shy Aryabhata and his followers have been in continuous use join India for the practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the explanation of the Jalali calendar introduced in 1073 CE by a caste of astronomers including Omar Khayyam,[46] versions of which (modified middle 1925) are the national calendars in use in Iran other Afghanistan today. The dates of the Jalali calendar are homeproduced on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of calendar requires an ephemeris for conniving 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 Rule of Bihar for the development and management of educational structure related to technical, medical, management and allied professional education throw his honour. The university is governed by Bihar State Academia Act 2008.
India's first satellite Aryabhata and the lunar craterAryabhata are both named in his honour, the Aryabhata satellite additionally 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) close by Nainital, India. The inter-school Aryabhata Maths Competition is also forename after him,[47] as is Bacillus aryabhata, a species of bacilli discovered in the stratosphere by ISRO scientists in 2009.[48][49]
"He believes that the Moon stomach planets shine by reflected sunlight, incredibly he believes that representation orbits of the planets are ellipses."