# Pi in Indian Mathematics

Pi or Π is the most interesting number in mathematics. Its history is one of the most fascinating stories mathematics has to offer. Π finds its usage in geometry, trigonometry, analysis. Π generally is associated with a circle. Indians were the first to observe that the perimeter (circumference) of a circle increases in proportion to its diameter. Therefore, our ancestors established the relation- perimeter / diameter = constant. They didn’t call it Pi though.

Since the Indus Valley script is not deciphered, it will be incorrect to claim that Π was known in the subcontinent in 3000 BC. But they did know the value of Pi by the time Rigveda was written. The Vedangas and Sulabasutras also mention the value of Π. The oldest of them, the Baudhayayana Sulabasutra claims that the perimeter of a pit is 3 times its diameter- therefore approximating the value of Π at 3. Many other texts, including the Mahabharata (Bhishmaparva, XII: 44) and many Puranas approximate Π at the value of 3.

Later, many other Sulabasutras mention the value of Π to be 18 * (3 – 2 √2) = 3.088. The Manava Sulabasutra approximates the value of Π to be 28/5= 3.125. The ancient Jaina school of mathematics preferred the approximation Π = √10. This value of Π has been used not only by Jainas, but also by the greats like Varahamihira, Brahmagupta and Sridhara.

With Aryabhatta (476 AD), a new era of mathematics dawned in India. Aryabhatta approximated Π = 62832/20000 = 3.1416. This was astonishingly correct to 4 decimal places (better than 22/7, which is correct only to 2 places). The Indian values of Π (√10, 62832/20000) were later included in Chinese and Arabs literature.

Many years later, another great mathematician of the Aryabhatta School of mathematics, named Madhava (1340 AD). Madhava gave the value of Π to be 2827,4333,8823,3 / 9*1011. This approximation yields correct value of Π to 11 decimal places. This value of Π is still in use in modern mathematics. Madhava also knew the Madhava series of Π/4, which was rediscovered in Europe by Leibniz in 1673.

The fascination behind Pi has lasted longer than any civilization. Such is the power of curiosity and knowledge.

### 4 responses to “Pi in Indian Mathematics”

1. Vijay

Hi.
Thanks for the info.
Do you have any literature proof with regards to use of golden proportions to create face dimensions in ancient India.