Life of perfect irrational π

Bharat Musings

Life of perfect irrational π

Geometry lessons are always incomplete without the use of the unique number 'π'. As complicated as its multiplication is, so is its tradition of coming to the value of 3.1416.....

The earliest reference to this value is found in civilizations of Egyptians, Babylonians, Chinese and many more. But where is the contribution of India in this tradition? Have we read about the contribution of Indic scholars in this life of Pi or do we assume it to be completely a discovery of west? 

Indian Vedic literature's component 'Shulba Sutras' (c.800 BCE)  are ancient texts of Indian Geometry. Written for construction of altars for Yagya with precise measurements, these texts contain the earliest material of Indian Geometry. Each of the 4 Vedas have multiple Shulba Sutras under their domain attributed to various Rishis like Apastambha, Baudhayan, Manava and many more. 

The earliest approximation to the value of π in the Indic context comes in Shulba Sutras. Manava Shulba Sutras (c.750 BCE) has mention of approximate value of π to 3.125. In the Baudhayana Sulbasutra (c. 800 BCE) , various approximate values given are 676/225, 900/289 etc. In different Sulbasutras, the values 2.99, 3.00, 3.004, 3.029, 3.047, 3.088, 3.1141, 3.16049 and 3.2022 can all be found. There are various values of π given in Mahabharat, Shatpath Brahaman as well. 

Aryabhatta ( c. 400 CE) in his text Aryabhatiya gives the the accurate value of upto 4 decimal places and also mentions it to be an approximation ( recognising the never ending decimal places). The verse in Aryabhatiya is as follows :

चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्त्राणाम्।

अयुतद्वयस्य विष्कम्भस्य आसन्नौ वृत्तपरिणाहः॥

Add 4 to 100, multiply by 8 and add to 62,000. This is approximately the circumference of a circle whose diameter is 20,000.

(100 + 4) x 8 + 62,000 = 62,832

62832÷20000= 3.1416 = π

Later in 14th century, Indian Mathematician, Madhav gave the correct value of π upto 11 decimal places. This was about 300 years before Gregory and Lebnitz proposed the series to arrive at the value of π. Therefore many historians now call this series of numbers as Madhav-Gregory-Lebnitz series. 

Bharat always had a rich tradition of Rishis who have contemplated on Philosophy and Science both together. The expert town planning of Indus Valley civilization points to existence of advanced mathematics in some form as well. It's essential that one recognises this rich scientific Indian heritage and takes pride in being one. 

Dr.Karan Mittal 

MBBS, MA (Clinical Psychology), MA (Sanskrit).