By examining the evidence in the Shatapatha Brahmana, we now know that Indian geometry predates Greek geometry by centuries. For example, the earth w… - Abraham Seidenberg
" "By examining the evidence in the Shatapatha Brahmana, we now know that Indian geometry predates Greek geometry by centuries. For example, the 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. There we see the beginnings of geometry! Two aspects of the 'Pythagoras' theorem are described in the Vedic literature. One aspect is purely algebraic that presents numbers a, b, c for which the sum of the squares of the first two equals the square of the third. The second is the geometric, according to which the sum of the areas of two square areas of different size is equal to another square. The Babylonians knew the algebraic aspect of this theorem as early as 1700 BCE, but they did not seem to know the geometric aspect. The Shatapatha Brahmana, which precedes the age of Pythagoras, knows both aspects. Therefore, the Indians could not have learnt it from the Old-Babylonians or the Greeks, who claim to have rediscovered the result only with Pythagoras. India is thus the cradle of the knowledge of geometry and mathematics.
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About Abraham Seidenberg
Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician.
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However, Seidenberg was told by the Indologists that these Sutras, or any Vedic text for that matter, were definitely written later than 1700 BC. But mathematical data cannot be manipulated just like that, and Seidenberg remained convinced of his case: “Whatever the difficulty there may be [concerning chronology], it is small in comparison with the difficulty of deriving the Vedic ritual application of the theorem from Babylonia. (The reverse derivation is easy)… the application involves geometric algebra, and there is no evidence of geometric algebra from Babylonia. And the geometry of Babylonia is already secondary whereas in India it is primary.” [To satisfy the indologists, he said that the Shulba Sutra had conserved an older tradition, and that it is from this one that the Babylonians had learned their mathematics:] “Hence we do not hesitate to place the Vedic (…) rituals, or more exactly, rituals exactly like them, far back of 1700 BC. (…) elements of geometry found in Egypt and Babylonia stem from a ritual system of the kind described in the Sulvasutras.”
Its mathematics was very much like what we see in the Sulvasutras [szulbasu utras]. In the first place, it was associated with ritual. Second, there was no dichotomy between number and magnitude … In geometry it knew the Theorem of Pythagoras and how to convert a rectangle into a square. It knew the isosceles trapezoid and how to compute its area … [and] some number theory centered on the existence of Pythagorean triplets … [and how] to compute a square root. …The arithmetical tendencies here encountered [ie in the SZulbasuutras] were expanded and in connection with observations on the rectangle led to Babylonian mathematics. A contrary tendency, namely, a concern for exactness of thought … together with a recognition that arithmetic methods are not exact, led to Pythagorean mathematics.
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