Arya Bhatta (5th century CE, Kaliyuga's 36th century) was a Hindu teacher and writer on mathematics and astronomy in Bharat (ancient India). Through his text, the Aryabhatiya, details of Indian arithmetic, algebra, and plane and spherical trigonometry have survived to the modern day. Fractions, quadratic equations, sums of powers, and even sine tables formed a part of this body of knowledge.
Regarding pi, Arya Bhatta wrote, in the Aryabhatiya:
"Add four to 100, multiply by eight and then add 62,000. By this rule the circumference of a circle of diameter 20,000 can be approached."
The value calculated for pi was the square root of 9.8684 (= 3.1414...).
Arya Bhatta was careful, in his writing, to state that using his rule the value of the circumference "can be approached". His statement the value can only be 'approached' and is an approximation, suggests an insight that the value of pi was irrational, only proven more than 1,000 years later in Europe, by Lambert in 1761.
