Aryabhata

Nama

Sungguhpun terdapat kecenderungan bagi salah mengeja sebagai "Aryabhatta" menurut analogi dengan nama-nama lain yang mempunyai akhiran "bhatta", namanya secara sesuai dieja Aryabhata: tiap teks astronomi mengeja namanya oleh itu, termasuk rujukan Brahmagupta padanya "dalam lebih daripada seratus tempat mengikut nama". Lebih lanjutnya, dalam kebanyakan contoh "Aryabhatta" tidak muatkan meter juga.

Kelahiran

Aryabhata menyebut dalam Aryabhatiya bahawa ia dikarang 3,600 tahun ke dalam Kali Yuga, ketika dia berusia 23 tahun. Ini bersamaan dengan 499 AM, dan bermakna bahawa dia dilahirkan pada 476 AM.
Aryabhata tidak memberikan maklumat tentang tempat kelahirannya. Satu-satunya maklumat datang dari Bhāskara I, yang menggambarkan wAryabhata sebagai āśmakīya, "seseorang yang datangnya dari negeri aśmaka." Sungguhpun aśmaka pada adalnya terletak di barat laut India, ia dibukti ramai bahawa, ketika zaman Buddha, satu cabang suku Aśmaka menetap di kawasan antara sungai Narmada dan sungai Godavari, di selatan Gujarat–Utara kawasan Maharashtra tengah India. Aryabhata dipercayai dilahirka di sana. Bagaimanapun, teks awal Buddha menggambarkan Ashmaka sebelai lebih jauh keselatan, di dakshinapath atau Deccan, sementara teks lain menggambarkan Ashmakas sebagai menentang Alexander, yang akan meletakkan mereka lebih jauh ke utara.

Karya

It is fairly certain that, at some point, he went to Kusumapura for advanced studies and that he lived there for some time. Both Hindu and Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna. A verse mentions that Aryabhata was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well.

Hipotesis Kerala

It has also been suggested that aśmaka (Sanskrit for "stone") might be the region in Kerala that is now known as Koṭuṅṅallūr, based on the belief that it was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, old records show that the city was actually Koṭum-kol-ūr ("city of strict governance"). It is also claimed that the fact that several commentaries on the Aryabhatiya have come from Kerala suggest that it was Aryabhata's main place of life and activity. But K. V. Sarma, the authority on Kerala's astronomical tradition, disagrees and cites many commentaries that have come from outside Kerala and the Aryasiddhanta's being completely unknown in Kerala. In recent (2007) papers, K. Chandra Hari uses a discrepancy in Aryabhata's astronomical values to deduce that he carried out his calculations from a place in Kerala at the same meridian as Ujjayini, possibly Chamravattam (10°N51, 75°E45) in central Kerala. He further hypothesizes that Asmaka was the Jain country surrounding Shravanabelagola, taking its name from the stone monoliths there.
Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is an abstraction, standing for a point on the equator at the same longitude as his Ujjayini.

Karya

Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost. His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.
The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya. It also contained a description 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, and water clocks of at least two types, bow-shaped and cylindrical.
A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf. It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known. Probably dating from the 9th century, it is mentioned by the Persian scholar and chronicler of India, Abū Rayhān al-Bīrūnī.

Menempatkan sistem nilai dan kosong

The place-value system, first seen in the 3rd century Bakhshali Manuscript, was clearly in place in his work. ; he certainly did not use the symbol, but French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients
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 as the table of sines in a mnemonic form.

Pi sebagai tidak rasional

Aryabhata worked on the approximation for Pi (), and may have come to the conclusion that  is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
chaturadhikam śatamaśṭaguṇam dvāśaśṭistathā sahasrāṇām
 Ayutadvayaviśkambhasyāsanno vrîttapariṇahaḥ.

"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."
This implies that the ratio of the circumference to the diameter is ((4+100)×8+62000)/20000 = 3.1416, which is accurate to five significant figures.
It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by Lambert).
After Aryabhatiya was translated into Arabic (ca. 820 CE) this approximation was mentioned in Al-Khwarizmi's book on algebra.

Astronomi

Aryabhata's system of astronomy 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 model (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's khanDakhAdyaka. In some texts, he seems to ascribe the apparent motions of the heavens to the Earth's rotation.

Gerhana

Aryabhata states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by pseudo-planetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the moon enters into the Earth's shadow (verse gola.37). He discusses at length the size and extent of 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 improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 1765-08-30 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.
Aryabhata's computation of the Earth's circumference as 39,968.0582 kilometres was only 0.2% smaller than the actual value of 40,075.0167 kilometres. This approximation was a significant improvement over the computation by Greek mathematician Eratosthenes (c. 200 BCE), whose exact computation is not known in modern units but his estimate had an error of around 5–10%.

Tempoh sidereal

Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 seconds is an error of 3 minutes and 20 seconds over the length of a year. The notion of sidereal time was known in most other astronomical systems of the time, but this computation was likely the most accurate of the period.

Heliosentrisme

As mentioned, Aryabhata claimed that the Earth turns on its own axis, and some elements of his planetary epicyclic models rotate at the same speed as the motion of the Earth around the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which the planets orbit the Sun. A detailed rebuttal to this heliocentric interpretation is in a review that describes B. L. van der Waerden's book as "show[ing] a complete misunderstanding of Indian planetary theory [that] is flatly contradicted by every word of Aryabhata's description." However, some concede that Aryabhata's system stems from an earlier heliocentric model, of which he was unaware. It has even been claimed that he considered the planet's paths to be elliptical, but no primary evidence for this has been found. Though Aristarchus of Samos (3rd century BCE) and sometimes Heraclides of Pontus (4th century BCE) are usually credited with knowing the heliocentric theory, the version of Greek astronomy known in ancient India as the Paulisa Siddhanta (possibly by a Paul of Alexandria) makes no reference to a heliocentric theory.

Legasi

Aryabhata's work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age (ca. 820 CE), was particularly influential. Some of his results are cited by Al-Khwarizmi, and he is mentioned by the 10th century Arabic scholar Al-Biruni, who states that Aryabhata's followers believed that the Earth rotated on its axis.
His definitions of sine (jya), cosine (kojya), versine (ukramajya), and inverse sine (otkram jya) influenced the birth of trigonometry. He was also the first to specify sine and versine (1 - cosx) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.
In fact, modern names "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry text to Latin. He assumed that jiba was the Arabic word jaib, which means "fold in a garment", L. sinus (c.1150).
Aryabhata's astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables (zijes). In particular, the astronomical tables in the work of the Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th c.) and remained the most accurate ephemeris used in Europe for centuries.
Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the basis of the Jalali calendar introduced in 1073 CE by a group of astronomers including Omar Khayyam, versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today. The dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the Gregorian calendar.
India's first satellite Aryabhata and the lunar crater Aryabhata are named in his honour. An Institute for conducting research in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute of observational sciences (ARIES) near Nainital, India. The inter-school Aryabhata Maths Competition is also named after him, as is Bacillus aryabhata, a species of bacteria discovered by ISRO scientists in 2009.