### 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