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How Baudhayana stated a² + b² = c² in ~800 BCE – three centuries before Pythagoras was born – in a Vedic fire altar manual, with √2 accurate to 5 decimal places
a² + b² = c². Taught in every school worldwide as 'Pythagoras's theorem.' But the earliest known statement of this result appears not in Greece, but in India – in the Baudhayana Sulba Sutra, written ~800 BCE. Pythagoras was born ~570 BCE – roughly 230 years later.
The Sulba Sutras are Vedic appendices giving the geometry for fire altar construction. "Sulba" means rope – literally rope-and-peg geometry manuals. Altars had to be specific shapes (falcon, tortoise, wheel) with exact areas – ritual law demanded mathematical precision. Any deviation was considered invalid.
दीर्घचतुरश्रस्याक्ष्णयारज्जुः पार्श्वमानी तिर्यङ्मानी च यत्पृथग्भूते कुरुतस्तदुभयं करोति
"The diagonal of a rectangle produces both [areas] which its length and breadth produce separately."
= a² + b² = c² – a general rule for ALL rectangles