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# Aryabhatta

By Sarah Baghai
by

## Sarah Baghai

on 7 May 2010

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#### Transcript of Aryabhatta

By Sarah Baghai Aryabhatta was born in Kusumapura,India
which is now Patna, India He wrote the Aryabhatiya.Contains mathematical and astronomical hypothesis. They have been found to be very accurate to cotemporary mathematics. He gave an accurate aproximation for pi.In the Aryabhatiya he wrote..
"Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given."
pi=62832/20000= 3.1416 approximately
Actual value-3.14159.... He gave a table of sines. Table had aproximate values at intervals and also intorduced versine in trigonmetry. versine=(1-cosine) He gave the formula for area of a triangle.
"For a triangle, the result of a perpendicular with the half-side is the area"
(also gave the formula for area of a circle) He had the first work that we are aware of that examines
integer solutions to equations.The problem came about from studying a problem in astronomy of determining the periods of the planets. The equations were of the form by=ax+c, and by=ax-c. Aryabhatta was able to use his mathemtical skills to prove that
the earth spins on its axis, rotates around the sun, and the moon rotates around the earth. He was also able to explain correctly the causes for eclipses of the sun and the moon. He calculated the cicumference of the earth
to be 24,835 miles which was a great approximation to the
currently accepted value which is 24,902 miles. Aryabhatta's value for the length of a year was 365 days 6 hours 12 minutes and 30 seconds. This was an overestimation but a good aproximation. the true value is 365 days and 6 hours. He knew the sign and added the sign of zero.
without the sign of zero and the place value system it
would have been impossible for him to carry out calculations like square or cubic roots. Aryabhatta By Sarah Baghai Most of his work lost and very little known
about his personal life Mathematical Astronomical Aryabhatta died in the year 550 but they place is unknown Works Cited

"Aryabhatta the Elder." Aryabhatta the Elder. J J O'Connor and E F Robertson, Nov.-Dec. 200. Web. 1 May 2010. <http://www-history.mcs.st-andrews.ac.uk/history/Biographies/Aryabhata_I.html>.

"Aryabhatta the Elder." Aryabhatta the Elder. J J O'Connor and E F Robertson, Nov.-Dec. 200. Web. 1 May 2010. <http://www-history.mcs.st-andrews.ac.uk/history/Biographies/Aryabhata_I.html>.

GREAT ANCIENT MATHEMATICIAN- ARYABHATTA. Hiranmaya Kar. Web. 1 May 2010. <http://www.indiastudychannel.com/projects/4789-GREAT-ANCIENT-MATHEMATICIAN-ARYABHATTA.aspx>.

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