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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
Cosmos3M 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 from 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 http://www.jqjacobs.net/astro/aryabhata.html 
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=MYR 
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. 
57,752, 984 
Synodic Months MSyn in a MY= LOMY 
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 
688.8807449
1.880858089 
688.8783455
1.880851538 
686.2
1.88 
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 
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
alBiruni, Bull. Calcutta Math. Soc. 17 (1926), 5974.
4.HJ 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
farranging 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 farreaching 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
http://www.oup.com/uk/catalogue/?ci=9780821809891http://www.oup.com/uk/catalogue/?ci=9780821809891
Price: £17.00
(Paperback)
ISBN13: 9780821809891
Publication date: 9 July 1998
American Mathematical Society
0 pages, mm
Series: Mathematical World number 12
Search for titles in the same series
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Reviews

'Varadarjan
spins a captivating tale, and the mathematics is
firstrate. 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.476550),
Brahmagupta (c.598665), and Bhaskara
(c.11141185). 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 socalled 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 sixteenthcentury Italy."
Mathematical Reviews' 
Description
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 copublished with the Hindustan Book
Agency (New Delhi) and is distributed worldwide,
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.
Contents
Some history of early mathematics
: EuclidDiophantusArchimedes
Pythagoras and the Pythagorean triplets
AryabhataBrahmaguptaBhaskarsa
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
References
Chronology
Index
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
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