Baudhayana Theorem: Pythagoras, 800 Years Early
The Indian origin of the world's most famous geometric theorem
Examine the Sulbasutra verse stating the relationship between the sides of a right triangle, centuries before Pythagoras.
Baudhayana Theorem: Pythagoras, 800 Years Early
Sometime around 800 BCE, on a strip of cleared land near the banks of the Sarasvatī, a Vedic priest named Baudhāyana sits down with a stylus and a stack of palm leaves. The knot-counted cord he has been using all morning is still coiled at his side. The smell of damp earth and cattle dung from the neighbouring fields hangs in the air. Two of his students sit cross-legged in front of him, ready to memorise. What he is about to dictate is a few lines of very compressed Sanskrit, each a standing rule for how a cord behaves when you stretch it from corner to corner of a rectangle on the ground. One of those lines, Sūtra 1.48 in the text later called the Baudhāyana Śulbasūtra, will survive twenty-eight centuries. It will travel through Greek, Arabic, Latin, and English schoolrooms, acquire the name of a Greek mystic born three hundred years after Baudhāyana's death, and be taught to every schoolchild on earth as a² + b² = c². The attribution to Pythagoras of Samos is one of the most famous misattributions in the history of mathematics. This lesson is the story of what the sūtra actually says, and of who said it first.
What the Sūtra Actually Says
Baudhāyana's exact words are these: 'dīrghacaturasrasyākṣaṇayārajjuḥ pārśvamānī tiryaṅmānī ca yatpṛthagbhūte kurutas tadubhayaṃ karoti'. The rope stretched along the diagonal of a rectangle produces an area that the vertical and horizontal sides produce together. Translated into modern algebra, this is precisely a² + b² = c². It is not a hint, not a precursor, not a partial form. It is the statement. Baudhāyana then goes further. In the very next sūtra, he lists specific integer solutions so that ritual builders could lay out right angles without any computation at all: 3 and 4 and 5, 5 and 12 and 13, 8 and 15 and 17, 7 and 24 and 25, 12 and 35 and 37. These are Pythagorean triples, tabulated three hundred years before Pythagoras.