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Aryabhata the Elder (Aryabhata I)

Born 476 CE

alternate dating (2765 CE)

Aryabhata was India's first satellite, named after the great Indian astronomer of the same name. It was launched by the Soviet Union on 19 April 1975 from Kapustin Yar using a Cosmos-3M launch vehicle. Aryabhata was built by the Indian Space Research Organization (ISRO) to conduct experiments related to astronomy. The satellite reentered the Earth's atmosphere on 11 February 1992

I have included a few important details about just a few of the most famous ancient Indian mathematicians fr
om past years. To my mind, the most important and most influential of these figures were Aryabhata and Panini.


Aryabhata had an excellent understanding of the Keplerian Universe more than a thousand years before Kepler, while Panini made a remarkable analysis of language, namely Sanskrit, which was not matched for 2,500 years, until the modern Bacchus form, in the 20th century.
Some questions we seek to answer in this essay

1.When did he live ?

2. What script did he use, the premise being that sophisticated calculations like the kind he performed cannot be done without the means of a script

3.Did he (or Panini) develop the place value system and the germ of the numerical notation and if so which one ?


Table 12 Comparison of some astronomical constants[i]

Adapted from John Q Jacobs table in

ASTRONOMIC QTY Āryabhața (from Clarke and Kay) Sūrya Siddhānta 2007 (modern)
Years in Cycle ,MY 4,320,000 4,320,000 4,320,000
Rotations,R 1,582,237,500 1,582,237,828 1,582,227,491
Days  in  a MY, DMY=MY-R 1,577,917,500 1,577,917,828 1,577,907,491
Mean Rotations of earth in  SiYr, R/MY=1+DSiYr 366.2586805556 366.2587564815 366.256363634259
Lunar Orbits one MY,LO 57,753,336 57,753,336 57,752,984
Days in a Sidereal month, DSiM = 1577917500/57753336 = 27.32166848
Kaye notes 57,753,339 Lunar orbits rather than 57,753,336 per Clarke. 57,752984
Synodic Months MSyn in a MY= LO-MY 53,433,336 53,433,336 53,430,984  
Days in a synodic month DSynM=DMY/MSyn = 1,577,917,500/53,433,336=29.53058181 days= 29.530588
Mercury orbits in  MY= Nme 17,937,920 17,937,060 17,937,033.867
Orbital Period of Mercury =R/ Nme 88.20631534 88.21054443 87.9686
Venus Orbits in 1 MY=Nv 7,022,388 7,022,376 7,022,260.402
Orbital Period of Venus (days)=R/Nv 225.3133589 225.313744 224.701
Mars Orbits in 1 MY 2,296,824 2,296,832 2,296,876.453
Orbital Period of Mars days

Years= R/Nma







Jupiter Orbits in 1 MY= Nj 364,224 364,220 364,195.066
Orbital Period of Jupiter, Years= R/Nj 11.86083289 years 11.86096315 years 11.86 years
Saturn  Orbits in 1 MY= Ns 146,564 146,568 146,568
Orbital period of   Saturn=R/Ns 10795.54 days =29.47517807 yrs
10795.24745 days =

29.47437367 yrs

10788.8503292 days=

29.4571 yrs

[i] This table was adapted from table that appeared in John Q Jacobs website,

Aryabhata wrote Âryabhatiya , finished in 499 CE ( 2741 BCE), which is a summary of Hindu mathematics up to that time, written in verse. It covers astronomy, spherical trigonometry, arithmetic, algebra and plane trigonometry. Aryabhata gives formulas for the areas of a triangle and a circle which are correct, but the formulas for the volumes of a sphere and a pyramid are wrong.

Âryabhatiya also contains continued fractions, quadratic equations, sums of power series and a table of sines. Aryabhata gave an accurate approximation for pi (equivalent to 3.1416) and was one of the first known to use algebra. He also introduced the versine ( versin = 1 - cos ) into trigonometry.  Incidentally both the words Geometry and Trigonometry are etymologically derived from Sanskrit

Aryabhata also wrote the astronomy text Siddhanta which taught that the apparent rotation of the heavens was due to the axial rotation of the Earth. The work is written in 121 stanzas. It gives  quite a remarkable prescient view of the nature of the solar system as we know it today. Unlike Copernicus and Kepler , he did not stand on the shoulders of giants, but was figuratively speaking one of the giants that bestrode the ancient universe

Aryabhata gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun. He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon.

His value for the length of the year at 365 days 6 hours 12 minutes 30 seconds is an overestimate since the true value is less than 365 days 6 hours.

References (4 books/articles) References for Aryabhata the Elder
from Georges Ifrah Universal History of  Numbers

1.Dictionary of Scientific Biography

2.Biography in Encyclopaedia Britannica

3.B Datta, Two Aryabhatas of al-Biruni, Bull. Calcutta Math. Soc. 17 (1926), 59-74.

4.H-J Ilgauds, Aryabhata I, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).

TheTheme of the RSA Conference 2006,San Jose,CA, February 2006

Every year, the RSA Conference is built around a different historical theme which highlights a significant use, or misuse, of information security. In 2006, the theme is centered on ancient Vedic mathematics, and a mathematical Sage named Aryabhata.

Modern Codes in Ancient Sutras

In 499 CE, in Kusumapura, capital of the Gupta Empire in classical India, a young mathematician named Aryabhata published an astronomical treatise written in 118 Sanskrit verses. A student of the Vedic mathematics tradition that had slowly emerged in India between 1500 and 900 BC, Aryabhata, only 23, intended merely to give a summary of Vedic mathematics up to his time. But his slender volume, the Aaryabhat.iiya, was to become one of the most brilliant achievements in the history of mathematics, with far-ranging implications in the East and West.

Aryabhata correctly determined the axial rotation of the earth. He inferred that planetary orbits were elliptical, and provided a valid explanation of solar and lunar eclipses. His theory of the relativity of motion predated Einstein’s by 1400 years. And his studies in algebra and trigonometry, which laid the foundations for calculus, influenced European mathematicians 1,000 years later, when his texts were translated into European languages from 8th century Arabic translations of the Sanskrit originals.

Today, the work of information security professionals affects the global business community in ways as profound and far-reaching as the seminal calculations of Aryabhata. Join us at the RSA Conference 2006 to celebrate the mathematical achievements of ancient India, and discover unprecedented approaches to securing your business and applications.



            Algebra in Ancient and Modern Times


Edited by V.S. Varadarajan

Price: £17.00 (Paperback)
ISBN-13: 978-0-8218-0989-1
Publication date: 9 July 1998
American Mathematical Society
0 pages, mm
Series: Mathematical World number 12
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  • 'Varadarjan spins a captivating tale, and the mathematics is first-rate. The book belongs on the shelf of any teacher of algebra... The great treasure of this book is the discussion of the work of the great Hindu mathematicians Aryabhata (c.476-550), Brahmagupta (c.598-665), and Bhaskara (c.1114-1185). The book contains many exercises that enhance and supplement the text and that also include historical information. Many of the exercises ask readers to apply the historical techniques. Some of the exercises are quite difficult and will challenge any student.' - The Mathematics Teacher

·                                '"Varadarajan gives us nice treatment of the work of Indian mathematics on the so-called Pell equation as well as a very detailed yet teachable discussion of the standard story of the solution of cubic and quartic equations by del Ferro, Tartaglia, Cardano, and Ferrari in sixteenth-century Italy." Mathematical Reviews' -



This text offers a special account of Indian work in diophantine equations during the 6th through 12th centuries and Italian work on solutions of cubic and biquadratic equations from the 11th through 16th centuries. The volume traces the historical development of algebra and the theory of equations from ancient times to the beginning of modern algebra, outlining some modern themes, such as the fundamental theorem of algebra, Clifford algebras and quarternions. It is geared toward undergraduates who have no background in calculus.
This book is co-published with the Hindustan Book Agency (New Delhi) and is distributed world-wide, except in India, Sri Lanka, Bangladesh, Pakistan, and Nepal, by the American Mathematical Society.

Readership: Undergraduate mathematicians, graduate students, and research mathematicians and historians interested in the history of mathematics.


Some history of early mathematics : Euclid-Diophantus-Archimedes

Pythagoras and the Pythagorean triplets


Irrational numbers: construction and approximation

Arabic mathematics

Beginnigs of algebra in Europe

The cubic and biquadratic equations

Solutions for the cubic and biquadratic equations : Solution of the cubic equation

Solution of the biquadratic equation

Some themes from modern algebra : Numbers, algebra, and the physical world

Complex number systems and the axiomatic treatment of algebra





Authors, editors, and contributors

Edited by V.S. Varadarajan, University of California, Los Angeles


Links to web resources and related information

More in the same subject area:
History of mathematics
History of science
History of engineering & technology
History of medicine
Philosophy of mathematics
Fields & rings

The specification in this catalogue, including without limitation price, format, extent, number of illustrations, and month of publication, was as accurate as possible at the time the catalogue was compiled. Occasionally, due to the nature of some contractual restrictions, we are unable to ship a specific product to a particular territory. Jacket images are provisional and liable to change before publication.









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