Pythagorean geometry in Vedic-era texts and centuries before Pythagoras

Pythagorean geometry in Vedic-era texts and centuries before Pythagoras

Subject: History

Section: Art and Culture

• Sulbasutras described procedures based on knowledge of what we call Pythagoras theorem. While this has long been known, the discussion has been revived after a Karnataka position paper calls the theorem ‘fake news’.
• Madan Gopal, a retired IAS officer who heads Karnataka’s NEP task force, referred to a text called the BaudhayanaSulbasutra, in which a specific shloka refers to the theorem.

Pythagoras theorem

• If any two sides of a right triangle are known, the theorem allows you to calculate the third side.
• Extended to the sides of squares and rectangles and their diagonals, the equation is of immense importance in construction, navigation and astronomy.

Sulbasutras

• The Shulba Sutras or Sulbasutras are sutra texts belonging to the Srauta ritual and containing geometry related to fire-altar construction.
• The ShulbaSutras 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 God 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 Sulva Sutras, which are mathematically the most significant, are those composed by Baudhayana, Manava, Apastamba and Katyayana. Out of them the oldest belongs to Baudhayana and dates back to 600BC. They discuss the cases of the Pythagorean Theorem and Pythagorean triples.

The Baudhayana sutra

• The Baudhāyanasūtras are a group of Vedic Sanskrit texts which cover dharma, daily ritual, mathematics and is one of the oldest Dharma-related texts of Hinduism that have survived into the modern age from the 1st-millennium BCE.
• They belong to the Taittiriya branch of the Krishna Yajurveda school and are among the earliest texts of the genre.
• The Baudhayana sutra consist of six texts:
  • the Srauta sutra, probably in 19 Prasnas (questions),
  • the Karmantasutra in 20 Adhyayas (chapters),
  • the Dwaidhasutra in 4 Prasnas,
  • the Grihyasutra in 4 Prasnas,
  • the Dharmasutra in 4 Prasnas and
  • the Sulbasutra in 3 Adhyayas.