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ARYABHATA BIOGRAPHYADICHUNCHANAGIRI POLYTECHNIC

Aryabhata (476550 CE) was the first in the line of great

mathematician-astronomers from the classical age of Indian

mathematics and Indian astronomy. His most famous works are

the Aryabhatiya (499 CE, when he was 23 years old) and the

Arya-siddhanta.

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

Dept. of CS & E 1
http://en.wikipedia.org/wiki/Mathematicianhttp://en.wikipedia.org/wiki/Astronomerhttp://en.wikipedia.org/wiki/Indian_mathematicshttp://en.wikipedia.org/wiki/Indian_mathematicshttp://en.wikipedia.org/wiki/Indian_astronomyhttp://en.wikipedia.org/wiki/Aryabhatiyahttp://en.wikipedia.org/wiki/Siddhantahttp://en.wikipedia.org/wiki/Bhattahttp://en.wikipedia.org/wiki/Mathematicianhttp://en.wikipedia.org/wiki/Astronomerhttp://en.wikipedia.org/wiki/Indian_mathematicshttp://en.wikipedia.org/wiki/Indian_mathematicshttp://en.wikipedia.org/wiki/Indian_astronomyhttp://en.wikipedia.org/wiki/Aryabhatiyahttp://en.wikipedia.org/wiki/Siddhantahttp://en.wikipedia.org/wiki/Bhatta


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properly spelled Aryabhata: every astronomical text spells his

name thus,[1] including Brahmagupta's references to him "in more

than a hundred places by name".[2] Furthermore, in most

instances "Aryabhatta" does not fit the metre either. [1]

Birth

Aryabhata mentions in the Aryabhatiya that it was composed

3,600 years into the Kali Yuga, when he was 23 years old. This

corresponds to 499 CE, and implies that he was born in 476 CE. [1]

Aryabhata provides no information about his place of birth. The

only information comes from Bhskara I, who describes Aryabhata

as makya, "one belonging to the amaka country." It is widely

attested that, during the Buddha's time, a branch of the Amaka

people settled in the region between the Narmada and Godavari

rivers in central India, today the South GujaratNorth Maharashtraregion. Aryabhata is believed to have been born there.[1][3]

However, early Buddhist texts describe Ashmaka as being further

south, in dakshinapath or the Deccan, while other texts describe

the Ashmakas as having fought Alexander, which would put them

further north.[3]

Work

It is fairly certain that, at some point, he went to Kusumapura for

advanced studies and that he lived there for some time. [4] Both

Hindu and Buddhist tradition, as well as Bhskara I (CE 629),

Dept. of CS & E 2
http://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-1http://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Kali_Yugahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Bh%C4%81skara_Ihttp://en.wikipedia.org/wiki/A%C5%9Bmakahttp://en.wikipedia.org/wiki/Narmada_Riverhttp://en.wikipedia.org/wiki/Godavarihttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2http://en.wikipedia.org/wiki/Deccanhttp://en.wikipedia.org/wiki/Alexanderhttp://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2http://en.wikipedia.org/wiki/Aryabhata#cite_note-3http://en.wikipedia.org/wiki/Bh%C4%81skara_Ihttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-1http://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Kali_Yugahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Bh%C4%81skara_Ihttp://en.wikipedia.org/wiki/A%C5%9Bmakahttp://en.wikipedia.org/wiki/Narmada_Riverhttp://en.wikipedia.org/wiki/Godavarihttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2http://en.wikipedia.org/wiki/Deccanhttp://en.wikipedia.org/wiki/Alexanderhttp://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2http://en.wikipedia.org/wiki/Aryabhata#cite_note-3http://en.wikipedia.org/wiki/Bh%C4%81skara_I


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identify Kusumapura as P aliputra, modern Patna.[1] 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.[1] Aryabhata is also reputed to have

set up an observatory at the Sun temple inTaregana, Bihar.[5]

Italic textOther hypotheses suggested that Aryabhata may

have been from Kerala, but K. V. Sarma, an authority on Kerala'sastronomical tradition, disagreed and pointed out several errors in

this hypothesis.[6]

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.

Works

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

Dept. of CS & E 3
http://en.wikipedia.org/wiki/P%C4%81%E1%B9%ADaliputrahttp://en.wikipedia.org/wiki/Patnahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Nalandahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Tareganahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-4http://en.wikipedia.org/wiki/K._V._Sarmahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-5http://en.wikipedia.org/wiki/Ujjayinihttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/P%C4%81%E1%B9%ADaliputrahttp://en.wikipedia.org/wiki/Patnahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Nalandahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-sarma-0http://en.wikipedia.org/wiki/Tareganahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-4http://en.wikipedia.org/wiki/K._V._Sarmahttp://en.wikipedia.org/wiki/Aryabhata#cite_note-5http://en.wikipedia.org/wiki/Ujjayinihttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Astronomy


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covers arithmetic, algebra, plane trigonometry, and spherical

trigonometry. It also contains continued fractions, quadratic

equations, sums-of-power series, and a table of sines.

TheArya-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 containeda 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.

[3]

A third text, which may have survived in the Arabic translation, is

Al ntforAl-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, Ab Rayhn al-Brn.[3]

Mathematics

Place value system and zero

Dept. of CS & E 4
http://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Spherical_trigonometryhttp://en.wikipedia.org/wiki/Spherical_trigonometryhttp://en.wikipedia.org/wiki/Fraction_(mathematics)http://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Aryabhata's_sine_tablehttp://en.wikipedia.org/wiki/Varahamihirahttp://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Bhaskara_Ihttp://en.wikipedia.org/wiki/Surya_Siddhantahttp://en.wikipedia.org/wiki/Gnomonhttp://en.wikipedia.org/wiki/Water_clockhttp://en.wikipedia.org/wiki/Water_clockhttp://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2http://en.wikipedia.org/wiki/Arabic_languagehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Ab%C5%AB_Rayh%C4%81n_al-B%C4%ABr%C5%ABn%C4%ABhttp://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2http://en.wikipedia.org/wiki/Arithmetichttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Spherical_trigonometryhttp://en.wikipedia.org/wiki/Spherical_trigonometryhttp://en.wikipedia.org/wiki/Fraction_(mathematics)http://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Aryabhata's_sine_tablehttp://en.wikipedia.org/wiki/Varahamihirahttp://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Bhaskara_Ihttp://en.wikipedia.org/wiki/Surya_Siddhantahttp://en.wikipedia.org/wiki/Gnomonhttp://en.wikipedia.org/wiki/Water_clockhttp://en.wikipedia.org/wiki/Water_clockhttp://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2http://en.wikipedia.org/wiki/Arabic_languagehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Ab%C5%AB_Rayh%C4%81n_al-B%C4%ABr%C5%ABn%C4%ABhttp://en.wikipedia.org/wiki/Aryabhata#cite_note-Ansari-2


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The place-value system, first seen in the 3rd century Bakhshali

Manuscript, was clearly in place in his work. While he did 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 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 thetable of sines in a mnemonic form[

Approximation ofpi

Aryabhata worked on the approximation for pi (), and may have

come to the conclusion that is irrational. In the second part of

theAryabhatiyam (gaitapda 10), he writes:

caturadhikam atamaaguam dvaistath sahasrm

ayutadvayavikambhasysanno vttapariha

"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 canbe approached."[10]

Dept. of CS & E 5
http://en.wikipedia.org/wiki/Place-valuehttp://en.wikipedia.org/wiki/Bakhshali_Manuscripthttp://en.wikipedia.org/wiki/Bakhshali_Manuscripthttp://en.wikipedia.org/wiki/Georges_Ifrahhttp://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/Vedic_periodhttp://en.wikipedia.org/wiki/Mnemonichttp://en.wikipedia.org/wiki/Pihttp://en.wikipedia.org/wiki/Aryabhata#cite_note-9http://en.wikipedia.org/wiki/Place-valuehttp://en.wikipedia.org/wiki/Bakhshali_Manuscripthttp://en.wikipedia.org/wiki/Bakhshali_Manuscripthttp://en.wikipedia.org/wiki/Georges_Ifrahhttp://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/Vedic_periodhttp://en.wikipedia.org/wiki/Mnemonichttp://en.wikipedia.org/wiki/Pihttp://en.wikipedia.org/wiki/Aryabhata#cite_note-9


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This implies that the ratio of the circumference to the diameter is

((4+100)8+62000)/20000 = 62832/20000 = 3.1416, which is

accurate to five significant figures.

Dept. of CS & E 6
http://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Significant_figures

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