Sulvasutras

Geometry in Vedic Age- Sulvasutras or Sulbasutras

Some scholars have shown on the basis of evidence in Shatapatha Brahmana that Indian geometry predates Greek geometry by centuries. It has been argued that Geometry and Mathematics had a ritualistic beginning in India centuries before Greeks or Babylon. In these rituals, Earth was represented by Circular altar and heavens were represented in Squar altar. There were eagle shaped altars also. The examples are as follows:

The Ritual consisted of coverting the Circle into a square of identical area. As per a paper by Seidenberg: Babylonia [1700 BC] got the theorem of Pythagoras from India or that both Old-Babylonia and India got it from a third source. The source quoted was Sulvasutras.

Sulvasutras deal with complex fire altars of various shapes constructed with bricks of specific shapes and area: the total area of the altar must always be carefully respected. This proves that despite of no existance of algebra, there was an awareness of precise purely geometrical calculations.

Seidenberg’s conclusion of India being the source of the geometric and mathematical knowledge of the ancient world has been included now in chronology of the texts. Please note that Sulva sutras belong to a bigger text Shrauta Sutras. The four major Sulva Sutras, which are mathematically the most significant, are those composed by Baudhayana, Manava, Apastamba and Katyayana. Out of them the oldest belongs to Baudhayana and dates back to 600BC. They discuss the cases of the Pythagorean Theorem and Pythagorean triples.

The Baudhayan Sulbasutra 1.48 says: The diagonal of a rectangle produces both areas produced seperately by its two sides.It is represented as follows

In the Baudhayan’s Sulva Sutras we should note that the Right angles were made by ropes marked to give the triads 3, 4, 5 and 5, 12, 13 (3² + 4² = 5², 5² + 12² = 13²) J

Sulva Sutra also mentions a ritual which included “Squaring the circle” (and vice-versa), thus geometrically constructing a square having the same area as a given area. It has worked out the square root of 2 to 1.414215, up to last 5 decimals.