Shulba Sutras

[1] The four major Shulba Sutras, which are mathematically the most significant, are those attributed to Baudhayana, Manava, Apastamba and Katyayana.

[2] Their language is late Vedic Sanskrit, pointing to a composition roughly during the 1st millennium BCE.

[2] Pingree says that the Apastamba is likely the next oldest; he places the Katyayana and the Manava third and fourth chronologically, on the basis of apparent borrowings.

[3] According to mathematical historian Kim Plofker, the Katyayana was composed after "the great grammatical codification of Sanskrit by Pāṇini in probably the mid-fourth century BCE", but she places the Manava in the same period as the Baudhayana.

With regard to the composition of Vedic texts, Plofker writes,The Vedic veneration of Sanskrit as a sacred speech, whose divinely revealed texts were meant to be recited, heard, and memorized rather than transmitted in writing, helped shape Sanskrit literature in general.

Thus texts were composed in formats that could be easily memorized: either condensed prose aphorisms (sūtras, a word later applied to mean a rule or algorithm in general) or verse, particularly in the Classical period.

[citation needed] The Satapatha Brahmana and the Taittiriya Samhita, whose contents date to the late second millennium or early first millennium BCE, describe altars whose dimensions appear to be based on the right triangle with legs of 15 pada and 36 pada, one of the triangles listed in the Baudhayana Shulba Sutra.

It is possible, as proposed by mathematical historian Radha Charan Gupta, that the geometry was developed to meet the needs of ritual.

[13] Some scholars go farther: Staal hypothesizes a common ritual origin for Indian and Greek geometry, citing similar interest and approach to doubling and other geometric transformation problems.

[14] Seidenberg, followed by Bartel Leendert van der Waerden, sees a ritual origin for mathematics more broadly, postulating that the major advances, such as discovery of the Pythagorean theorem, occurred in only one place, and diffused from there to the rest of the world.

[15][16] Van der Waerden mentions that author of Sulbha sutras existed before 600 BCE and could not have been influenced by Greek geometry.

[20] In contrast, Pingree cautions that "it would be a mistake to see in [the altar builders'] works the unique origin of geometry; others in India and elsewhere, whether in response to practical or theoretical problems, may well have advanced as far without their solutions having been committed to memory or eventually transcribed in manuscripts.

"[21] Plofker also raises the possibility that "existing geometric knowledge [was] consciously incorporated into ritual practice".

The assertion that each procedure produces a square of the desired area is equivalent to the statement of the Pythagorean theorem.

Alternatively, divide [the diameter] into fifteen parts and reduce it by two of them; this gives the approximate side of the square [desired].