Pythagorean Geometry in Vedic-era Texts

Context

The position paper, part of Karnataka’s submissions to the NCERT for a National Curriculum Framework, has revived discussion on what we call the Pythagoras theorem was already known to Indians from the Vedic times.

Dispute

• The Pythagoras theorem is disputed in many international forums. Not the content, but Pythagoras claiming it as his own.
• A retired IAS officer who heads Karnataka’s NEP task force, has referred to a text called the BaudhayanaSulbasutra, in which a specific shloka refers to the theorem.

Pythagoras History

• 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.
  

What is the evidence that Sulbasutra contains?

• In the first chapter in the BaudhayanaSulbasutra contains, the (areas of the squares) produced separately by the length and the breadth of a rectangle together equal the area (of the square) produced by the diagonal.
• This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36.

Uses

• 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.

What is the similarity between Sulbasutra’s equation and Pythagoras?

• The Pythagorean equation comes into play in these procedures, which involve drawing perpendiculars.
• These perpendiculars were based on triangles whose sides were in the ratio 3:4:5 or 5:12:13.
• These sides follow the Pythagorean relation, because 3² + 4² = 5², and 5² + 12² = 13². Such combinations are called Pythagorean triples.