Seidenberg an American Mathematician, in 1978, in his paper on the origin of mathematics concluded that “Old-Babylonia, 1700 BC got the Pythagoras Theorem from India.” He postulated a pre –old Babylonian source of the kind of geometric rituals we see preserved in the Shulbasutras , Satapatha Brahmana and the Taittiriya Samhita or at least for the mathematics involved in these rituals.
Seidenberg examined the evidences in the Shatpatha Brahmana (a prose text describing Vedic rituals, history and mythology associated with the Sukla Yajurveda) and showed that Indian geometry predates Greek geometry by centuries.
The Shulba Sutras are part of the larger corpus of texts called the Shrauta Sutras, considered to be appendices to the Vedas.
The four major Shulba Sutras, which are mathematically the most significant, are those attributed to Baudhayana, Manava, Apastamba and Katyayana.
Seidenberg proposed that the birth of geometry and mathematics had a ritual origin. In Vedic Texts, earth was represented by a circular altar and the heavens were represented by a square altar. And the ritual consisted of converting the circle into a square of an identical area. And that is the beginning of Geometry.
Seidenberg considered two aspects of the Pythagoras theorem in Vedic literature:
1. Purely algebraic aspect that presents numbers a, b, c for which a2 +b2=c2
2. A geometric aspect i.e. Sum of areas of two squares of different size is equal to another square.
Seidenberg argued that the Babylonians knew the algebraic aspect of this theorem as early as 1700 BCE, but they didn’t seem to know the geometric aspect. On the contrary, Shatpatha Brahmana knows both the aspects of this theorem and it precedes the age of Pythagoras.
List of Shulba Sutras
5. Maitrayaniya (somewhat similar to Manava text)
6. Varaha (in manuscript)
7. Vadhula (in manuscript)
8. Hiranyakeshin (similar to Apastamba Shulba Sutras)
In Baudhayana, the rules are given as follows:
1. The diagonal of a square produces double the area of the square.
2. The areas of the squares produced separately by the lengths of the breadth of a rectangle together equal the area of the square produced by the diagonal.
3. This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36.
Apastamba’s rules for building right angles in altars use the following Pythagorean triples:
(3,4,5) , (5,12,13) , (8,5,17) and (12,35,37)
The Baudhayana Shulba sutra gives the construction of geometric shapes such as squares and rectangles. For example, the statement of circling the square is given in Baudhayana as:
1. If it is desired to transform a square into a circle, a cord of length half the diagonal of the square is stretched from the centre to the east – a part of it lying outside the eastern side of the square; with one-third of the part lying outside, added to the remainder of the half diagonal, the required circle is drawn.
And the statement of squaring the circle is given as:
2. To transform a circle into a square, the diameter is divided into eight parts; one such part after being divided into twenty-nine parts is reduced by twenty-eight of them and further by the sixth of the part left less the eighth of the sixth part.
3. Alternatively, divide the diameter into fifteen parts and reduce it by two of them; this gives the approximate side of the desired square.
Altar construction gives an estimation of the square root of 2. In the Baudhayana sutra it appears as:
” The measure is to be increased by its third and this third again by its own fourth less the thirty-fourth part of that fourth; this is the value of the diagonal of a square whose side is the measure.”