Shulba Sutras

The Shulva Sutras or Śulbasūtras (Sanskrit: शुल्बसूत्र; : "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction. The Shulba Sutras are part of the larger corpus of texts called the Shrauta Sutras, considered to be appendices to the Vedas. They are the only sources of knowledge of Indian mathematics from the Vedic period. Unique fire-altar shapes were associated with unique gifts from the Gods. For instance, "he who desires heaven is to construct a fire-altar in the form of a falcon"; "a fire-altar in the form of a tortoise is to be constructed by one desiring to win the world of Brahman" and "those who wish to destroy existing and future enemies should construct a fire-altar in the form of a rhombus". The four major Shulba Sutras, which are mathematically the most significant, are those attributed to Baudhayana, Manava, Apastamba and Katyayana. Their language is late Vedic Sanskrit, pointing to a composition roughly during the 1st millennium BCE. The oldest is the sutra attributed to Baudhayana, possibly compiled around 800 BCE to 500 BCE. 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. According to 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.