
Aryabhata (
ISO
ISO is the most common abbreviation for the International Organization for Standardization.
ISO or Iso may also refer to: Business and finance
* Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007
* Is ...
: ) or Aryabhata I
(476–550
CE)
was an Indian mathematician and astronomer of the classical age of
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupt ...
and
Indian astronomy
Astronomy has long history in Indian subcontinent stretching from pre-historic to modern times. Some of the earliest roots of Indian astronomy can be dated to the period of Indus Valley civilisation or earlier. Astronomy later developed as a di ...
. He flourished in the
Gupta Era
The Gupta era is a historical calendar era that begins from c. 318–319 CE. It was used by the Gupta emperors, as well as their vassals and their successors in present-day northern India and Nepal. It is identical to the Vallabhi era (or Valabh ...
and produced works such as the ''
Aryabhatiya
''Aryabhatiya'' ( IAST: ') or ''Aryabhatiyam'' ('), a Sanskrit astronomical treatise, is the ''magnum opus'' and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that ...
'' (which mentions that in 3600 ''
Kali Yuga
''Kali Yuga'', in Hinduism, is the fourth and worst of the four '' yugas'' (world ages) in a '' Yuga Cycle'', preceded by ''Dvapara Yuga'' and followed by the next cycle's '' Krita (Satya) Yuga''. It is believed to be the present age, which ...
'', 499 CE, he was 23 years old)
and the ''Arya-siddhanta.''
Aryabhata created a system of phonemic number notation in which numbers were represented by consonant-vowel monosyllables. Later commentators such as
Brahmagupta
Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the '' Brāhmasphuṭasiddhānta'' (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical tr ...
divide his work into ''Ganita ("Mathematics"), Kalakriya ("Calculations on Time") and Golapada ("Spherical Astronomy")''. His pure mathematics discusses topics such as determination of
square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
and
cube roots, geometrical figures with their properties and
mensuration,
arithmetric progression problems on the
shadow of the gnomon,
quadratic equation
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as
ax^2 + bx + c = 0\,,
where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equati ...
s,
linear
Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...
and
indeterminate equation In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. For example, the equation ax + by =c is a simple indeterminate equation, as is x^2=1. Indeterminate equations cannot be so ...
s. Aryabhata calculated the value of
pi (''π)'' to the fourth decimal digit and was likely aware that
pi (''π)'' is an
irrational number
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two inte ...
, around 1300 years before
Lambert
Lambert may refer to
People
*Lambert (name), a given name and surname
* Lambert, Bishop of Ostia (c. 1036–1130), became Pope Honorius II
*Lambert, Margrave of Tuscany (fl. 929–931), also count and duke of Lucca
*Lambert (pianist), stage-name ...
proved the same. Aryabhata's
sine table
In mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering. The calculation of mathematical tables wa ...
and his work on
trignometry were extremely influential on the
Islamic Golden Age
The Islamic Golden Age was a period of cultural, economic, and scientific flourishing in the history of Islam, traditionally dated from the 8th century to the 14th century. This period is traditionally understood to have begun during the reign ...
; his works were translated into Arabic and influenced
Al-Khwarizmi
Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astrono ...
and
Al-Zarqali. In his spherical astronomy, he applied plane trigonometry to spherical geometry and gave calculations on
solar,
lunar eclipse
A lunar eclipse occurs when the Moon moves into the Earth's shadow. Such alignment occurs during an eclipse season, approximately every six months, during the full moon phase, when the Moon's orbital plane is closest to the plane of the Eart ...
s. He discovered that the apparent westward motion of stars is due to the spherical
Earth's rotation about its own axis. Aryabhata also noted that the
luminosity
Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a s ...
of the Moon and other planets is due to reflected sunlight.
Biography
Name
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,
including
Brahmagupta
Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the '' Brāhmasphuṭasiddhānta'' (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical tr ...
's references to him "in more than a hundred places by name".
Furthermore, in most instances "Aryabhatta" would not fit the metre either.
[
]
Time and place of birth
Aryabhata mentions in the ''Aryabhatiya'' that he was 23 years old 3,600 years into the ''Kali Yuga
''Kali Yuga'', in Hinduism, is the fourth and worst of the four '' yugas'' (world ages) in a '' Yuga Cycle'', preceded by ''Dvapara Yuga'' and followed by the next cycle's '' Krita (Satya) Yuga''. It is believed to be the present age, which ...
'', but this is not to mean that the text was composed at that time. This mentioned year corresponds to 499 CE, and implies that he was born in 476. Aryabhata called himself a native of Kusumapura or Pataliputra
Pataliputra ( IAST: ), adjacent to modern-day Patna, was a city in ancient India, originally built by Magadha ruler Ajatashatru in 490 BCE as a small fort () near the Ganges river.. Udayin laid the foundation of the city of Pataliputra at ...
(present day Patna
Patna (
), historically known as Pataliputra, is the capital and largest city of the state of Bihar in India. According to the United Nations, as of 2018, Patna had a population of 2.35 million, making it the 19th largest city in India. ...
, Bihar
Bihar (; ) is a state in eastern India. It is the 2nd largest state by population in 2019, 12th largest by area of , and 14th largest by GDP in 2021. Bihar borders Uttar Pradesh to its west, Nepal to the north, the northern part of West ...
).
Other hypothesis
Bhāskara I
Bhāskara () (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a ...
describes Aryabhata as ''āśmakīya'', "one belonging to the ''Aśmaka
Ashmaka (Sanskrit: ) or Assaka (Pali: ) was a Mahajanapada in ancient India which existed between 700 BCE and 425 or 345 BCE according to the Buddhist texts '' Anguttara Nikaya'' and '' Puranas''. It was located around and between the Godava ...
'' country." During the Buddha's time, a branch of the Aśmaka people settled in the region between the Narmada and Godavari
The Godavari (International Alphabet of Sanskrit Transliteration, IAST: ''Godāvarī'' Help:IPA/Sanskrit, �od̪aːʋəɾiː is India's second longest river after the Ganges river, Ganga river and drains into the third largest basin in Indi ...
rivers in central India.
It has been claimed that the ''aśmaka'' (Sanskrit for "stone") where Aryabhata originated may be the present day Kodungallur
Kodungallur (; also Cranganore, Portuguese: Cranganor; formerly known as Mahodayapuram, Shingly, Vanchi, Muchiri, Muyirikkode, and Muziris) is a historically significant town situated on the banks of river Periyar on the Malabar Coast in ...
which was the historical capital city of ''Thiruvanchikkulam'' of ancient Kerala. This is based on the belief that Koṭuṅṅallūr 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"). Similarly, the fact that several commentaries on the Aryabhatiya have come from Kerala has been used to suggest that it was Aryabhata's main place of life and activity; however, many commentaries have come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[ K. Chandra Hari has argued for the Kerala hypothesis on the basis of astronomical evidence.
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
Ujjain (, Hindustani pronunciation: �d͡ːʒɛːn is a city in Ujjain district of the Indian state of Madhya Pradesh. It is the fifth-largest city in Madhya Pradesh by population and is the administrative centre of Ujjain district and Ujjain ...
.
Education
It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as Bhāskara I
Bhāskara () (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a ...
(CE 629), identify Kusumapura as Pāṭaliputra
Pataliputra (IAST: ), adjacent to modern-day Patna, was a city in ancient India, originally built by Magadha ruler Ajatashatru in 490 BCE as a small fort () near the Ganges river.. Udayin laid the foundation of the city of Pataliputra at the ...
, modern Patna
Patna (
), historically known as Pataliputra, is the capital and largest city of the state of Bihar in India. According to the United Nations, as of 2018, Patna had a population of 2.35 million, making it the 19th largest city in India. ...
.[ A verse mentions that Aryabhata was the head of an institution (') at Kusumapura, and, because the university of ]Nalanda
Nalanda (, ) was a renowned '' mahavihara'' ( Buddhist monastic university) in ancient Magadha (modern-day Bihar), India.[Taregana
Taregana or Taregna (literally, Counting Stars), is a small town near Masaurhi in Patna district, Bihar, India. It is about from Patna.
History
In Taregna, Aryabhata set up an astronomical observatory in the Sun Temple 6th century. It is bel ...]
, Bihar.
Works
Aryabhata is the author of several treatises on mathematics and astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, a