The unknown History of Hypotenuse

The unknown History of Hypotenuse

"Sum of squares of two sides of a right-angled triangle is equal to square of its Hypotenuse ".... A theorem which we have learnt all throughout our school days, popularly known as the 'Pythagoras theorem' .
But, was there any reference to this great inseparable theorem of Geometry in ancient India?

The Shulba Sutras of Vedic Literature are the texts of Ancient Indian Geometry. Out of the many available Shulba sutras composed by different Rishis, Baudhayan Shulba sutra (c.800 BCE) has one of the earliest references to this theorem in context of Geometric applications.This was about 300 years before the date of historical Pythagoras of Samos.The verse in the text is as follows:

दीर्घचतुरस्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥

A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
In other words: a2=b2+c2

Later in the course of time, Apastambha Rishi and Katyayan Rishi also give reference to these rules in their Shulba sutra texts and elaborate them further.

Although by the Sutra (Aphorism) nature of Shulba texts, its difficult to expect any elaboration of these rules in the texts. But, its certain that the composers of Shulba sutras definitely knew about this theorem.
An unique feature about the composers of various Shulba sutras was that all of them were Rishis and have various Ritual texts (Shraut sutras, Grihya sutras) attributed to them apart from these Geometric texts. Another unique feature being, these mathematical findings were made to arrive at accurate dimensions for creating Yagya Vedis for Fire sacrifices ( Such a high standard for perfection even in Religious rituals!!!). Since these fire rituals were necessary for all householders, it would be safe to assume that people in Vedic era knew the application of this theorem in construction of Yagya Vedis atleast.


There are definitely evidences of knowledge of Pythagorean triplets in Babylonian and Egyptian civilizations. Even the historicity of Pythagoras himself is debated in academic circles.
In Indic context,  with the passage of time, many Sutra texts of Ancient Indian literature have disappeared and many still remain untouched as manuscripts in various museums and libraries. There is still a huge amount of literature which needs to be studied and deciphered.

We as a civilization need to acknowledge our contributions to the journey of scientific achievements of mankind and strive to continue this legacy further!