Pythagorean Geometry in Vedic-Era

• 20 Jul 2022

For Prelims: Indian Ancient History, Vedic Age, Veda System

For Mains: Significance of Veda System, Significance of Vedic Age

Why in News?

Recently, a position paper by the Karnataka government on the National Education Policy (NEP) 2020 has described Pythagoras’s theorem as “fake news”.

• It has referred to a text called the Baudhayana Sulbasutra, in which a specific shloka refers to the theorem.

What do we need to know about Pythagoras?

• About Pythagoras:
  • Evidence suggests that the Greek philosopher (around 570–490 BC) did exist.
  • There is an element of mystery around him, largely because of the secretive nature of the school/society he founded in Italy.
  • Relatively little is known about his mathematical achievements, because there is nothing today of his own writings.
• About Pythagoras Theorem:
  • The Pythagoras theorem describes the relationship connecting the three sides of a right triangle (one in which one of the angles is 90°).
    • a² + b² = c²
      • If any two sides of a right triangle are known, the theorem allows you to calculate the third side.

How do we know that Vedic Indian Mathematicians knew this?

• There are references of Pythagoras in the Sulbasutras, which are texts pertaining to fire rituals (yajanas) performed by Vedic Indians.
  • The oldest of these is the Baudhayana Sulbasutra.
• The period of Baudhayana Sulbasutra is uncertain. It is estimated based on linguistic and other secondary historical considerations.
  • In recent literature, Baudhayana Sulbasutra is taken to be from around 800 BCE.
• Baudhayana Sulbasutra contains a statement of what is called Pythagoras theorem (it was known rather as a geometric fact, and not as a ‘theorem’).
• The yajna rituals involved construction of altars (vedi) and fireplaces (agni) in a variety of shapes such as isosceles triangles, symmetric trapezia, and rectangles.
  • The sulbasutras describe steps towards construction of these figures with prescribed sizes.

How did the Knowledge of Equation Evolve?

• The earliest evidence is from the Old Babylonian civilisation (1900-1600 BCE).
  • They referred to it as the Diagonal Rule.
• The earliest evidence of a proof comes from a period after the sulbasutras.
• The oldest surviving axiomatic proof of the theorem is in the Elements of Euclid from around 300 BCE.

What are Vedas?

• The word Veda signifies knowledge and the texts are actually about providing mankind knowledge to conduct their entire life on earth and beyond.
• There are four major vedas:
  • Rig Veda:
    • Oldest existing veda among the four.
    • Focus is on worldly prosperity and natural beauty.
    • Text is organised in 10 books known as Mandalas.
    • Prominent gods mentioned in Rig Veda:
      • Lord Indra, Agni, Varuna, Rudra, Aditya etc.
  • Yajur Veda:
    • The name Yaju signifies Sacrifice.
    • It concentrates on rites and mantras of the different types of sacrifices.
    • Two major recensions (samhita) are:
      • Shukla, also called Vajasaneyi Samhita.
      • Krishna, also called Taittiriya Samhita.
  • Sama Veda:
    • It has been named after Saman (melody).
    • It concentrates on Melody or Songs.
    • It is also called the Book of Chants.
  • Atharva Veda:
    • It is also known as Brahma Veda and has been attributed to two rishis called Atharban and Angiras.
    • It concentrates on Peace and Prosperity of human society.
    • Two major recensions (sakhas) are:
      • Paippalada
      • Saunakiya

Source: IE