Bodayana.

Baudhayana was an ancient Indian sage, traditionally dated several centuries before Pythagoras. In his work, the Baudhayana Sulba Sutra, he described a geometric rule equivalent to what is now known as the Pythagorean theorem.

A famous translation of Baudhayana's statement is:

"The diagonal of a rectangle produces the areas produced separately by its two sides."

In modern notation:

where  is the diagonal (hypotenuse) of a right-angled triangle.

Why was Baudhayana interested in geometry?

The Sulba Sutras were manuals for constructing Vedic fire altars. Priests needed precise geometric methods to create squares, rectangles, circles, and other shapes of equal area. This practical need led to remarkably advanced geometry.

Did Baudhayana discover the theorem before Pythagoras?

Many historians agree that the theorem was known in India and Babylon before Pythagoras lived. What remains uncertain is whether Pythagoras himself discovered it independently or learned ideas that were already circulating. The theorem is named after Pythagoras because of its central place in later Greek mathematics and the tradition that his school provided a proof.

A simple example

For a right triangle with sides 3 and 4:

So the diagonal is 5.

Baudhayana's work is a reminder that sophisticated mathematical ideas arose in several ancient civilizations, including Vedic India, long before the modern era.