Aryabhata

Page 1

Aryabhata

Darani Vasudevan

Aryabhata

Darani Vasudevan

Preface, Aryabhata is the first Indian Astronomer and Mathematician. He has contributed a lot in these two fields. His works are enormous and astonishing. This book is a short biography of Aryabhata. Hope you will enjoy reading it...

-V. Darani M.Sc., M.Phil., SET

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>>>>>>>>>>>>>><<<<<<<<<<<<<<<<< Aryabhata was the first Indian Astronomer and Mathematician born in 470 CE at Kusumapura (Pataliputra the present day Patna). He was influenced by Surya Siddanta which is a Sanskrit treatise (Hindu text) in Indian Astronomy dating back to the 4th century CE or early 5th century CE. He belonged to the Gupta era. He had vast knowledge and interest in the field of mathematics and astronomy. His major works include Aryabhatia and Arya- Siddhanta. Bhaskara I refers Aryabhata as Asmakiya that is “one belonging to the Asmaka country� that was the present day Kodungallur which was

once

the

capital

city

of

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Thiruvanchikkulam of ancient Kerala. He also mentioned

that

Aryabhata

went

to

Kusumapura for his advanced studies and spent his life there for some years. Many other places were suggested as his birth place by historians. Some mentioned that he was born in Southern India most probably in Kerala, Tamil nadu and Andhra Pradesh while others mentioned North east India especially Bihar as his birth place. Kusumapura is widely accepted to be his birth place because in his work he never mentioned anything related to South India. Moreover all his works are in Sanskrit and Sanskrit was not used in kerala at that time. In Arabic translations,

numerous

mathematicians

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mentioned him as “someone who hailed from Kusumapura.� Hence it appears that he was born,

lived,

flourished

and

worked

in

Magadha. He

was

the

Astronomer

first of

Mathematician

classical

India

and when

Mathematics and Astronomy were still in the nascent stages of development all around the world. The theories put forth by Copernicus and Galileo were suggested by Aryabhata nearly 1500 years ago. Aryabhata completed his education from Nalanda University which was an Ancient Indian University. Later he moved to Bihar to continue his further studies in the great centre

of

learning

located

nearby

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Kusumapura,

Bihar.

The

Gupta

ruler,

Buddhagupta appointed him as the head of the Nalanda University for his extraordinary knowledge and ideas. The University of Nalanda had an Astronomical observatory and it is assumed that Aryabhata might have been

the

head

of

that

department.

Aryabhata is reputed to have set up an observatory at the Sun temple in Tarengana, Bihar. Bhaskara I mentioned “Aryabhata is the master who after reaching the furthest shores and plumbing the in most depths of the

seas

of

ultimate

knowledge

of

mathematics, kinematics and spherics handed over the 3 sciences to the learned world.�

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He is the author of several treatises in Astronomy and Mathematics some of which are lost. His two great works are Aryabhatia and Arya- siddanta. Aryabhatia was the most famous work which was compiled when he was just 23 years old. Aryabhatia written in 499 CE is the direct details of Aryabhata’s work. His disciple Bhaskara I named it as Ashmahatantra which means “the treatise from the Ashmaka.” It is a Sanskrit astronomical treatise and is the only known summary of all the works of Aryabhata. The text consists of 108 versus and 13 introductory versus. The book is divided into 4 chapters namely Gitikapada, Ganitapada,

Kalakriyapada

and

Golapada.

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Gitikapada covers time (kalpa, manvantra and yuga),

table

of

sines

and

duration

of

planetary revolution during a Mahayana is mentioned as 4.32 million years. Ganitapada covers

mathematical

calculations

mensuration,

arithmetic

progressions,

shadows,

and simple,

of

geometric quadratic,

simultaneous and indeterminate equations. Kalakriyapada deals with different units of time and a method for determining the positions

of

planets

for

a

given

day,

calculations concerning the intercalary month and seven days of a week with names for the days. Golapada covers the geometric and trigonometric aspects of the celestial space, features of the ecliptic, celestial equator,

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node, shape of the earth, causes of day and night, rising of zodiac signs on horizon etc. This book presents a number of innovations in the field of Astronomy and Mathematics in verse

form,

which

are

influential

for

centuries. Aryabhatia was translated to Latin in the 13th century.

The

European

Mathematicians

learned to calculate the area of triangles, volume of spheres as well as calculating square

and

cube

roots

through

this

translated version. Arya siddhanta is another great work of Aryabhata. It is a lost work on astronomical computations.

This

circulated

in

the

northwest of India and through the Sasanian

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dynasty (224-651 AD) of Iran, it had a great influence on the development of Islamic Astronomy. Its contents are preserved to some extent in the works of Varahimihira, Bhaskara and Brahmagupta. It is one of the earliest astronomical works to assign the start of each day to midnight. It is a booklet for everyday astronomical calculations and also a guide to examine auspicious times for performing rituals. Till date, the astronomical data provided in these texts are used for preparing Panchangs (Hindu calendar). His notable ideas include, explanations of lunar eclipse and solar eclipse, rotation of earth on its axis, reflection of light by moon, sinusoidal

functions,

solution

of

single

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variable quadratic equations, value of  correct to 4 decimal places, diameter of earth, calculation of the length of sidereal year which is the time taken by the Earth to orbit around the sun once with respect to the fixed stars. He explained the relativity of motions as : “just as a man in a boat moving forward sees the stationary objects on the shore as moving backward, just so are the stationary stars seen by the people on earth as moving exactly towards the west.” Aryabhata’s

system

of

astronomy

was

referred as Audayaka system in whih days are reckoned from Uday, dawn at Lanka or

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equator. He insisted that earth rotates on its own axis daily and the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the belief that sky rotates. He described a geocentric model of the solar system in which the sun and moon are carried by epicycles. He denoted that the sun and moon revolves around the Earth. In his model, the movement of planets are governed by 2 epicycles, a smaller manda and a larger sighra. The order of the planets in terms of distance from earth is moon, mercury, venus, the sun, mars, Jupiter, Saturn and asterisms. He calculated the positions and periods of the planets relative to uniformly moving

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points. According to him, mercury and venus move around the earth at the same mean speed as the sun. Mars, Jupiter and Saturn rotated the earth at specific speeds and he represented the motion of each planet through the zodiac. Another element in Aryabhata’s model is the Sighrocca, the basic planetary period in relation to the sun is considered

as

a

sign

of

underlying

heliocentric model by some historians. Aryabhata scientifically explained the solar and lunar eclipses. He stated that the moon and planets shine by reflection from sun. He explained eclipses in terms of shadows cast by and falling on earth. The lunar eclipse occurs when the moon enters into the earth’s

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shadow. He also provided the computation and the size of the eclipsed part during an eclipse. He 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. His model gave corrections for the speeds of the planets in the sky interms 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. He stated that the correct number of days in a year is 365.

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He also stated that the moon has no light of its own. He concluded that the earth is round and also explained that it rotates on its own axis because of which we have days and nights. He also laid the foundation for the concept of gravitation. Aryabhata gave the pace value system. He didn’t use a symbol for zero. A French Mathematician named George Irfah argues that knowledge of zero was implicit in Aryabhata’s place value system. Some are with the concept that Indians invented numerical system and Aryabhata invented zero whereas some argues that he didn’t

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invent or discover zero because zero as a concept

has

been

mathematicians Aryabhata

just

mentioned

even

before

contributed

by

many

Aryabhata. the

modern

symbol for the value zero. The symbol is a brilliant choice as it has neither a beginning nor an end, there are no sides and the symbol looks

empty

which

signifies

that

it

represents nothingness. Aryabhata didn’t use Brahmi numerals; he used letters of the alphabets to denote numbers, expressing quantities such as the table of sines i a mnemonic form. He worked on the approximation for ď ° (pi) and came to a conclusion that pi is irrational. He mentioned that:

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“Add four to 100, multiply by 8 and then add 62000. By this rule the circumference of a circle with a diameter of 20000 can be approached.” This

means

circumference

that to

the the

ratio

of

diameter

the is

((4+100)×8+62000)/ 20000 = 62832/20000 = 3.1416. When Aryabhatia was translated to Arabic in 820 CE this approximation was accepted and mentioned in Al-khwarizmi’s book on algebra. He gave the area of triangle as “for a triangle, the result of a perpendicular with the half side is the area.” He also discussed the concept of sin.

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He worked on the summation of series of squares and cubes (square root and cube root). He created the “rule of three� which is to find the value of X when three numerals a,b,c is given. He named the initial 10 decimal places and derived methods for extracting square roots, summing

arithmetic

series

and

solving

indeterminate equations of the type ax-by=c. his

method

to

find

a

solution

to

indeterminate equations of this type is recognized world wide.

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He went into extraordinary insight about arithmetic and geometric movements like 2,4,6 and 8 or 2, 10, 50 and 250. He gave a techinique to find the length of chords of circle with half chords as opposed to the full chord strategy utilized by Greeks. Aryabhata

influenced

Lalla,

the

Indian

mathematician and astronomer; Bhaskara I, the mathematician of 7th century who was the first to write numbers in the Hindu decimal system. He was also the author of Aryabhatiyabharya in which he gave an unique and remarkable rational approximation of the sin

function;

Brahmagupta,

the

Indian

mathematician and astronomer; Varahimihira who was one of the nine jewels (navaratnas)

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of the court of Yasodharman Vikramaditya of Malwa. Aryabhata died in 550 CE when he was 74 years old. His work and history are available to modern scholars. The Indian government named its first satellite as Aryabhata (launched in 1975) to honour this wonderful person. There is a statue depicting Aryabhata on the grounds of Inter University centre for Astronomy and Astrophysics (IUCAA), Pune.

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