Pythagorean geometry in Vedic-era texts, centuries before Pythagoras

Source: The post is based on the article “Pythagorean geometry in Vedic-era texts, centuries before Pythagoras” published in Indian Express on 19th July 2022.

What is the News?

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.

Who was Pythagoras?

Evidence suggests that the Greek philosopher Pythagoras (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.

What is Pythagoras’ Theorem?

The Pythagoras theorem describes the relationship connecting the three sides of a right-angle 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 one to calculate the third side.

How do we know that the Indian Vedic Mathematician knew this theorem?

Baudhayana Sulbasutra: 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 the Pythagoras theorem (it was known rather as a geometric fact, and not as a ‘theorem’).

– For instance, the yajna rituals involved the 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 the construction of these figures with prescribed sizes.

How did the knowledge of Pythagoras’ Theorem evolve?

The earliest evidence is from the Old Babylonian civilisation (1900-1600 BCE). They referred to it as the Diagonal Rule.

The evidence of proof also comes from a period after the sulbasutras. But, the oldest surviving axiomatic proof of the theorem is in the Elements of Euclid from around 300 BCE.