This is what I know of Aryabhatta I (with two 't')
 

The man was born somewhere in south-central India in the year 476 AD and as a
boy, went to study  astonomy at the Univrsity of Nalanda (near the eastern
city of Patna). He made significant contributions to the field of astronomy
and probably propounded or came close to the Heliocentric theory of
gravitation, almost a thausand years before Copernicus.
 

Aryabhatta's Magnum Opus, the "Aryabhattiya" was translated into Latin in the
13th century (about 700 years after his death). The book explained methods for
calculating the areas of triangles, volumes and surface areas of spheres as
well as square and cube root. Aryabhatta's ideas about eclipses and the sun
being the source of moonlight did not have much of an impression on European
astronomers as by then they were coming to know of these facts through
independent observations of scientists such as Copernicus and Galileo.
However, one can appreciate his contribution when considering that the works
were done 700 years before the "translation", and much before Copernicus or
Galileo came into being.
 

In that book, Aryabhatta is said to have written "Just as a person travelling
in a boat feels that the trees on the bank are moving, people on the Earth
feel that the Sun is moving".
 

Aryabhatta's biggest problem was he could not make a good telescope with the
technology at hand in the 5th and 6th century AD. This hindered further
advancement of ancient Indian astronomy. Though it should be admitted that
with his unaided observations with crude instruments, he was able to arrive at
sufficiently accurate measurement of astronomical movements and movement of
the earth and moon around the sun to predict eclipses.
 

Aryabhatta's methods of astronomical calculations expounded in his
"Aryabhatta-siddhanta" were reliable enough for practical purposes of fixing
the Panchanga (Hindu calendar). Thus, eclipses were also forecast and their
true nature was perceived at least by other astronomers that prepared the
Indian calendars.
 

I am not sure if concept of zero and the "decimal" system was his. I thought
that happened in India centuries before Aryabhatta - I could be wrong though
(needs looking into, this one).
 

I believe Indians in the first century BC had words for each number to the
power of ten (10, 100, 1000 etc) going up to 10 to the power of 53 as
"Tallakshanam". First archaeological proof of inscription explaining the
meaning of the number "zero" was found on a copper plate in Gujarat, India,
from 585 CE.
 

Likewise, the concept of "pi" as the ratio of the circumference to the
diameter of a circle might be older than Aryabhatta, although he calculated
that value upto the forth decimal. The old Sanskrit text Baudhayana Shulba
Sutra of the 6th Century BCE mentions this ratio as approximately equal to 3.
Aryabhatta in 499 BCE worked out the value to Pi to the 4th decimal place, as
3(177/1250) = 3.1416. A few centuries later, in 825 CE, the Arab
mathematician, Mohammed Ibna Musa, said that "this value 62832/20000 has been
given by the Hindus (Indians)".
 

Aparrt from that, there is some opinion that the earlier mentioned Sanskrit
book of 6th century BC, called "Budhayana Sulba Sutra" (literally - knowledge
about the rule of the rope) explained a variant of the Pythagoras theorem. The
book explained how to construct geometrically perfect structures (such as
complicated fire alters with concentric circles and squeares expanding out
from the centre, where each outer square will tangetially touch the inner
circle) and has text which translates roughly as the square of the area
produced by the diagonal of a rectangle is equal to the sum of the squares of
areas produced by its two sides (dealing with diagonals of a rectangle rather
than a right angle triangle - but essentially meaning the same). Measurements
in construction of gemetric shapes were apparently done with lengths of rope
those days, hence the name of the book. If this is true, the theorem predates
Pythagorus by nearly two millenia !!
 

A few other Indian astronomers might merit mention, such as Bhaskaracharya, of
almost the same time as Aryabhatta. Bhaskaracharya calculated the length of a
solar year as 365.2587 days, against the current accepted figure of 365.2596
days. Bhaskaracharya, in his ‘Surya Siddhanta’ (i.e. study of the Sun) notes
"objects fall on the Earth due to a force of attraction by the Earth.
Therefore, the Earth, planets, constellations, moons and sun are all
influenced in their respective motion by this mutual attraction".
 

Using various search engines on the net, once should be able to find most of
the topics above, and perhaps even more, as more and more info is made
available almost by the day.
 

Best rgds
Santanu Mitra
 

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 Search for titles in the same series           Reviews   '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' -   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 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.   Contents Some history of early mathematics : Euclid-Diophantus-Archimedes Pythagoras and the Pythagorean triplets Aryabhata-Brahmagupta-Bhaskarsa 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   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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