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The altars were required to be constructed of five layers of burnt brick, with the further condition that each layer consist of 200 bricks and that no two adjacent layers have congruent arrangements of bricks. 363), the Śulba Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians." Since the statement is a sūtra, it is necessarily compressed and what the ropes produce is not elaborated on, but the context clearly implies the square areas constructed on their lengths, and would have been explained so by the teacher to the student. Dani, the Babylonian cuneiform tablet Plimpton 322 written ca.It also contains the general statement of the Pythagorean theorem (for the sides of a rectangle): "The rope stretched along the length of the diagonal of a rectangle makes an area which the vertical and horizontal sides make together." which expresses √2 in the sexagesimal system, and which is also accurate up to 5 decimal places (after rounding). 1850 BCE indicating, in particular, that there was sophisticated understanding on the topic" in Mesopotamia in 1850 BCE. In the classical period of Indian mathematics (400 CE to 1600 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Mahāvīra, Bhaskara II, Madhava of Sangamagrama and Nilakantha Somayaji.
Since, unfortunately, no other contemporaneous sources have been found it may never be possible to settle this issue satisfactorily. The remaining two, the Manava Sulba Sutra composed by Manava (fl.
750–650 BCE) and the Apastamba Sulba Sutra, composed by Apastamba (c. His grammar includes early use of Boolean logic, of the null operator, and of context free grammars, and includes a precursor of the Backus–Naur form (used in the description programming languages).
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Hollow cylindrical objects made of shell and found at Lothal (2200 BCE) and Dholavira are demonstrated to have the ability to measure angles in a plane, as well as to determine the position of stars for navigation.
For example, the mantra (sacrificial formula) at the end of the annahoma ("food-oblation rite") performed during the aśvamedha, and uttered just before-, during-, and just after sunrise, invokes powers of ten from a hundred to a trillion: that of constructing fire altars which have different shapes but occupy the same area.
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