Aryabhata
Aryabhata (476–550) was a great astrologer and mathematician of ancient India . He composed the book Aryabhatiya , in which many principles of astrology are presented.
According to another belief, he was born in the Ashmak country of Maharashtra . His
scientific work could be respected only in the capital. Therefore, after a
long journey, he was located in Kusumpur near modern Patna and completed his compositions in
Rajsanidhya. Their origin is believed to be in the Bhatt Brahmbhatt
Brahmin community.
Birth place of
Aryabhata
Although the year of Aryabhata 's
birth is clearly mentioned in the Aryabhatiya, there is controversy about the
actual place of his birth. Some believe that he was born in the
region between the Narmada and
the Godavari , known
as the Ashmaka, and identify Ashmaka with central India, which includes Maharashtra and Madhya Pradesh ,
although early Buddhist texts refer to the Ashmaka as the south. 2 ,
as Dakshinapatha or the Deccan , while other texts state that the
people of Ashmaka must have fought with Alexander , so that Ashmaka should be further
north.
According to a recent study, Aryabhata was a resident of Chamravattam (10
Uttar51, 75E45) in Kerala . According to the study, Asmaka was a Jain region which was spread
around Shravanabelagola and got its name because of the stone pillars
here. Chamravattam was a part of this Jain settlement, the evidence of
this is the Bharatapuzha river which is named after the mythological king
Bharata of the Jains. Aryabhata has also mentioned King Bharata while
defining the eras - in the fifth verse of Dasgitika, the description of the
period that has passed till the time of King Bharat comes. In those days
there was a famous university in Kusumpura where Jains had a decisive influence
and Aryabhata's work thus reached Kusumpura and was also liked.
However, it is fairly certain that he had gone to Kusumpura for
higher education at one point or another and lived there for some time. Bhaskara I (629
AD) identified Kusumpura as Pataliputra (modern Patna ). He used to live there during
the last days of the Gupta Empire . This was the period known as the Golden Age of India, with the Huns invading
the northeast during the empire of Buddhagupta and some minor
kings before Vishnugupta .
Aryabhata used Sri Lanka as a reference for his astronomical systems and the
Aryabhatiya mentions Sri Lanka on
several occasions .
Masterpieces
Information about three texts composed by Aryabhata is available even
today. Dashgitika, Aryabhatiya and
Tantra. But according to experts, he wrote another book - Aryabhata
Siddhanta. At present only 34 of his verses are available. This book
of his was widely used in the seventh century. But there is no definite
information about how such a useful book got lost.
He wrote an important astrological text called Aryabhatiya ,
in which square root , cube root
, parallel
series and
different types of equations are
described. In his book named Aryabhatiya, in 33 verses, which can
accommodate a total of 3 pages, he has described the principles of mathematics
and the principles of astronomy in 75 verses in 5 pages and the instruments for
this. Aryabhata in his small book presented revolutionary concepts
for the principles of his predecessor and later country and also for foreign
countries.
His major work, the Aryabhatiya , a compendium of
mathematics and astronomy, is extensively cited in the Indian mathematical
literature and which continues to exist in modern times. The mathematical
part of Aryabhatiya includes arithmetic, algebra, simple trigonometry and
spherical trigonometry. It includes Continuous Fractions , Quadratic Equations , Sum of Power Series, and a Table
of Sines.
The Arya-siddhanta , a work on astronomical calculations that is now extinct, comes from
the writings of Aryabhata's contemporary Varahamihira , as well as later mathematicians and
commentators, including Brahmagupta and Bhaskara
. I. _ It appears that this work is based on the
old Surya Siddhanta and uses the midnight-day-count rather than Aryabhatiya 's
sunrise. It includes descriptions of a number of astronomical instruments,
such as a nomon ( cone-yantra ),
a shadow instrument ( shaya-yantra ), possibly angle-measuring
instruments, semicircular and circular ( dhanur-yantra / chakra-yantra
).), a cylindrical stick yasti-yantra , a parasol- shaped
instrument called a chhatra- yantra and at least two types
of water clocks —
arched and cylindrical.
A third text that exists as an Arabic translation, Al-Ntf or Al-Nanf ,
claims to be a translation of Aryabhata, but its Sanskrit name is
unknown. It is mentioned by the Persian scholar and Indian historian Abu Rayhan
al-Biruni ,
probably in the 9th century inscriptions.
Aryabhatiya
Direct details of Aryabhata's work are known only from Aryabhatiya
. The name
Aryabhatiya is given by later commentators, Aryabhata himself may not have
named it; This is mentioned by his disciple Bhaskara I in the writings of Ashmakatantra or
Ashmaka. It is also sometimes referred to as Arya-Sata-Ashta (ie
Aryabhata's 108) – which is the number of verses in his text. This sutra is
written in a very concise style similar to literature, where each line helps to
memorize a complex system. Thus, the interpretation of the meaning is due
to the commentators. The entire book consists of 108 verses, plus 13
additional introductory verses, divided into four stanzas or
chapters:
Geetikapada : (13 verses) Large units of time - kalpa , manvantara , yuga , which present a cosmology distinct from early texts such as the Vedanga Jyotish of Lagadha , (1st century BCE, these include the sign of the chords) The table also includes sine which is presented in a single stanza.During a Mahayuga , 4.32 million years are given for the rotation of the planets.
- Ganitapada (33 verses) covers mensuration ( field behavior ), mathematical and geometric progression, cones /shadows ( cone - shadows ), simple, quadratic , simultaneous and indefinite equations ( kutaka ).
- Kalakriyapada (25 verses) : Different units of time and method of determining the positions of the planets for a given day. Regarding the calculation of Adhika Maas (Adhikamas ), Kshaya -Tithis . Presents a seven day week, with the names of the days of the week.
- Golpad (50 verses): Geometric/ trigonometric aspects of the celestial sphere , features of the ecliptic , celestial equator , ecliptic, shape of the earth, causes of day and night, rising of zodiac signs on the horizon, etc.
Additionally, some versions also add some wreaths at the end to compliment the
creations, etc.
Aryabhatiya introduced some innovations in mathematics and astronomy in
verse form, which remained influential for many centuries. The climax of
the text's brevity is described by his disciple Bhaskara I ( Bhashya , 600 and
) in his reviews and by Nilakanta Somayaji in his Aryabhatiya Bhashya (1465) .
Aryabhata's
Contribution
In the history of India, which is known as 'Gupta period' or 'Golden Age',
at that time India made unprecedented progress in the fields of literature, art
and science. At that time, Nalanda University in Magadha was a major and famous
center of knowledge. Students from all over the country used to come here
for learning. There was a special department for the study of astronomy
. According to
an ancient verse, Aryabhata was also the Vice Chancellor of Nalanda University.
Aryabhata has had a great influence on the astrology theory of India and
the world. The greatest influence in India was on the astrology
tradition of Kerala state. Aryabhata holds the most important place among Indian mathematicians
. He has written the principles of astrology and related mathematics in
his Aryabhatiya treatise
in the form of a formula in 120 Aryachandas .
He, on the one hand, represented the value of pi more accurately and precisely
than the preceding Archimedes in mathematics On the
other hand, for the first time in astronomy, it was declared with the example
that the earth itself rotates on its axis .
This is the significance of the discoveries made by Aryabhata without
today's advanced tools of astrology. Aryabhata had discovered what Copernicus (1473
to 1543 AD) had discovered thousand years ago. Aryabhata has written in
"Golpad" "When a man sitting in a boat moves with the flow, then
he understands that the objects like fixed trees, stones, mountains etc. are
going in reverse. They are also seen going in the opposite direction. Thus
Aryabhata first proved that the earth rotates on its axis. He considered
Satyuga, Treta, Dwapara and Kali Yuga to be equal. According to them, 14
Manvantaras in one Kalpa and 72 Mahayugas (Chaturyuga) in one Manvantara and
Satyuga, Dwapar, Treta and Kali Yuga are considered equal in one Chaturyuga.
According to Aryabhata, the relation of circumference and diameter of a
circle comes to 62,832 : 20,000 which is pure up to four decimal
places.
Aryabhata has used a very scientific method of representing big
numbers with a set of letters .
Mathematics
Positional
notation system and the zero
The positional notation system , first seen in the 3rd century Bakhshali Manuscript , was clearly within his work. While he did not use a symbol for zero , French mathematician Georges Ifrah explains that knowledge of zero was implicit in Aryabhata's positional notation system as a placeholder for powers of ten with zero coefficients .
However, Aryabhata did not use brahmi numbering . Continuing the Sanskrit tradition of the Vedic period , he used the letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic way .
Approximation
of π
Aryabhata worked on the approximation of the number π , and may have concluded that it
is irrational . In
the second part of the Aryabhatiyam (gaṇitapāda 10), he
writes:
caturadhikam
śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno
vṛttapariṇāhaḥ.
"Add four to 100, multiply it by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approximated."
This implies that the ratio of circumference to diameter is ((4 + 100) × 8
+ 62,000)/20,000 = 62,832/20,000 = 3.1416, which is accurate to five significant
figures .
It is speculated that Aryabhata used the word āsanna (approximation), to indicate that not only is this an approximation but that the value is immeasurable (or irrational). If this is correct, it is quite a sophisticated understanding, because the irrationality ofit was tested in Europe as late as 1761 by Johann Heinrich Lambert .
After Aryabhatiya was translated into Arabic (c. 820) this approach was mentioned in Al-Khuarismi 's book on algebra.
Trigonometry
In Ganitapada 6, Aryabhata gives the area of a triangle as
- tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ
that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."
Aryabhata discussed the concept of sine in his work by the name of ardha-jya, which literally means "half-chord". For simplicity, people started calling it jya. When Arabic 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 it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later in 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 the English word sine.
Indeterminate equations
A problem of great interest to Indian mathematicians since ancient times has been to find integer solutions to Diophantine equations that have the form ax + by = c. (This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the Chinese remainder theorem.) This is an example from Bhāskara's commentary on Aryabhatiya:
- Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
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,
can be notoriously difficult. They were discussed extensively in ancient Vedic
text Sulba Sutras, whose more ancient parts might date to 800
BCE. Aryabhata's method of solving such problems, elaborated by Bhaskara in 621
CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka means
"pulverizing" or "breaking into small pieces", and the
method involves a recursive algorithm for writing the original factors in
smaller numbers. This algorithm became the standard method for solving
first-order diophantine equations in Indian mathematics, and initially the
whole subject of algebra was called kuṭṭaka-gaṇita or
simply kuṭṭaka.
Astronomy
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.
He may have believed that the planet's orbits as elliptical rather than circular.
Motions of the solar system
Aryabhata
correctly insisted that the earth rotates about its axis daily, and that the
apparent movement of the stars is a relative motion caused by the rotation of
the earth, contrary to the then-prevailing view, that the sky rotated. This is indicated in
the first chapter of the Aryabhatiya, where he gives the number of
rotations of the earth in a yuga, and made more
explicit in his gola chapter:
In the
same way that someone in a boat going forward sees an unmoving going backward, so on the equator sees the unmoving stars going
uniformly westward. The cause of rising and setting the sphere of the stars together with the
planets turns due west at the equator,
constantly pushed by the cosmic wind.
Aryabhata
described a geocentric model
of the solar system, in which the Sun and Moon are each carried by epicycles. They in turn revolve around the
Earth. In this model, which is also found in the Paitāmahasiddhānta (c.
CE 425), the motions of the planets are each governed by two epicycles, a
smaller manda (slow) and a larger śīghra (fast). The
order of the planets in terms of distance from earth is taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms."
The
positions and periods of the planets was calculated relative to uniformly
moving points. In the case of Mercury and Venus, they move around the Earth at
the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they
move around the Earth at specific 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. Another element in
Aryabhata's model, the śīghrocca, the basic planetary period in
relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model.
Eclipses
Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as the pseudo-planetary lunar nodes), 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
30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer,
1752) were long by 68 seconds.
Sidereal periods
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 (365.25858 days) is
an error of 3 minutes and 20 seconds over the length of a year (365.25636 days).
Heliocentrism
As mentioned, Aryabhata advocated an astronomical model in which the 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 of 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, though this has been rebutted.
It has also been suggested that aspects of Aryabhata's system may have been derived from an earlier, likely pre-Ptolemaic Greek, heliocentric model of which Indian astronomers were unaware, though the evidence is scant. The general consensus is that a synodic anomaly (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.
Legacy
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 (c. 820 CE), was
particularly influential. Some of his results are cited by Al-Khwarizmi and
in the 10th century Al-Biruni stated
that Aryabhata's followers believed that the Earth rotated on its axis.
His
definitions of sine (jya), cosine (kojya), versine (utkrama-jya),
and inverse sine (otkram jya) influenced the birth of trigonometry.
He was also the 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, 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
century) 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.
Aryabhatta Knowledge University (AKU),
Patna has been established by Government of Bihar for the development and
management of educational infrastructure related to technical, medical,
management and allied professional education in his honour. The university is
governed by Bihar State University Act 2008.
India's
first satellite Aryabhata and the lunar crater Aryabhata are both named in his honour,
the Aryabhata satellite also featured on the reverse of the Indian 2-rupee note. 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 Aryabhatta Maths Competition is also named
after him, as
is Bacillus aryabhata, a species of bacteria discovered in the stratosphere by ISRO scientists in 2009.
Comments
A. Ayutadvayavishkambhsyasanno
circle-parinaah. (Aryabhatiya, Ganitapada, Verse 10)
B. Achlani bhaani tadvat
sampaschimgani lankayam. (Aryabhatiya, Golapada, Verse 9)
( Earth - When a person sitting in a boat moves
with the flow, then he understands that the objects like fixed trees, stones,
mountains etc. are going in the reverse speed. Similarly, from the moving
earth, the fixed stars are also going in the reverse speed. appear to.)
