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CONTRIBUTOR PERSONALITY

DEVELOPMENT

ARYABHATA

By: Chintan Panchal

090410116059

09-ITG-53

L.Y.(I.T)

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Who was Aryabhata??

Aryabhata] 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 when

he was 23 years old and theArya-siddhanta.

http://en.wikipedia.org/wiki/Aryabhatahttp://en.wikipedia.org/wiki/Aryabhata

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Early Life of Aryabhata.

Aryabhata provides no information about his place of

birth.

Some evidence said that Aryabhata was born in Taregna

(literally, song of the stars), which is a small town inBihar, India.

In other side some archeological evidence suggests that

Aryabhata could have originated from the present

day Kodungallur which was the historical capital cityof Thiruvanchikkulam of ancient Kerala.

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Contribution of Aryabhata.

IN MATHEMATICS

Place value system and zero.

The place-value system, first seen in the 3rdcentury Bakhshali Manuscript, was clearly in place in

his work. While he did not use a symbol for zero, the

French mathematician Georges Ifrah explains that

knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten

with null coefficients.

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Approximation of. Aryabhata worked on the approximation for pi (), and may

have come to the conclusion that is irrational. In thesecond part of theAryabhatiyam (gaitapda 10).

He writes:

caturadhikam atamaaguamdvaistathsahasrmayutadvayavikambhasysannovttapariha.("Add four to 100, multiply by eight, andthen add 62,000. By this rule the circumference of a circlewith 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= 62832/20000= 3.1416,

which is accurate to five significant figures.

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Trigonometry

In Ganitapada 6, Aryabhata gives the area of a triangle

as :

tribhujasya phalashariram samadalakoti

bhujardhasamvargahthat

translates to: "for a triangle, the result of a

perpendicular

with the half-side is the area."

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Algebra

InAryabhatiya Aryabhata provided elegant results for

the summation of series of squares and cubes:

For Cube

For Square

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In Astronomy

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 in other parts

of the world, that the sky rotated.

This is indicated in the first chapter of theAryabhatiya,

where he gives the number of rotations of the earth in

ayuga, and made more explicit in his gola chapter. Aryabhata described a geocentric model of the solar

system, in which the Sun and Moon are each carriedby epicycles.

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Eclipses

Solar and lunar eclipses were scientifically explained byAryabhata. 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.

He discusses at length the size and extent of the Earth's

shadow and then provides the computation and the size

of the eclipsed part during an eclipse.

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Sidereal periods

Considered in modern English units of time, Aryabhatacalculated the sidereal rotation(the rotation of theearth referencing the fixed stars) as 23 hours, 56

minutes, and 4.1 seconds. The modern value is23:56:4.091.

Similarly, his value for the length of the sidereal yearat 365 days, 6 hours, 12 minutes, and 30 seconds

(365.25858 days) is an error of 3 minutes and 20seconds over the length of a year (365.25636 days).

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Some Achievements ofAryabhata.

Calendric calculations devised by Aryabhata and his followershave been in continuous use in India for the practical purposes

of fixing the Panchangam(the Hindu calendar).

Aryabhata's astronomical calculation methods were also veryinfluential. Along with the trigonometric tables, they came to be

widely used in the Islamic world and used to compute

many Arabic astronomical tables (zijes).

His definitions of sine(jya),cosine (kojya), versine (utkrama-

jya), and inverse sine (otkram jya) influenced the birth

oftrigonometry. 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.

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In Memories of Aryabhata.

India's first satellite Aryabhata and the lunarcrater Aryabhata are named in his honour.

An Institute for conducting research in astronomy,astrophysics and atmospheric sciences is the AryabhattaResearch Institute of Observational Sciences(ARIOS) nearNainital, India.

The inter-school Aryabhata Maths Competition is alsonamed after him, as is Bacillus aryabhata, a species ofbacteria discovered by ISRO scientists in 2009.

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