AryabhataThe Ancient Mathematician

1. The Approximation of Pi

• Learned pi is irrational
• Wanted to discover an accurate solution for pi
• Wrote in the second part of Aryabhatiyam:
"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."
• This translates to ((4+100)8+62000)/20000=62832/20000=3.1416
• Pi originated in Egypt by the Babylonians and Egyptians

2. Indeterminate Equations

• Wished to find a solution for Diophantine equation "ax+by=c"
• Originated in India where it was a mystery to most mathematicians
• Aryabhata wrote in one of his famous pieces:
"Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7"
• This translates to "N=8x+5=9y+4=7z+1
• Did not find the solution
• Used the kuttaka method to solve the problem
"The universal medicine for the soul is supreme reason and absolute justice, for the mind mathematical and practical truth, for the body quintessence, a combination of light and gold" -Aryabhata