Sulba Sutras: Earliest Pythagorean Theorem and Vedic Altar Geometry — E8 Intelligence Research

FINDING: The Sulba Sutras contain the earliest known explicit statement of the Pythagorean theorem (Baudhayana, ~800 BCE), plus geometric constructions for altars (agni) using exact square-circle equivalences and irrational approximations. | MATH: Baudhayana's theorem: *dīrghasyākṣṇayā rajjuḥ pārśvamānī, tiryaḍmānī, yatpṛthagbhūte kurutastadubhayaṅ karoti* — "The diagonal of a rectangle produces both [areas] which the sides separately produce." Explicitly: \(c^2 = a^2 + b^2\). Also, Baudhayana gives \(\sqrt{2} \approx 1 + \frac{1}{3} + \frac{1}{3\cdot4} - \frac{1}{3\cdot4\cdot34} = \frac{577}{408} \approx 1.414215686\) (error ~2×10⁻⁶). For circle-squaring: \( \text{side of square} = \frac{7}{8} \times \text{circle diameter} + \frac{1}{8} \times \frac{\text{diameter}}{29} \) (Baudhayana), implying \(\pi \approx 3.088\) (crude but structural). More refined: \( \pi \approx 3.1416\) via \( \frac{13}{15} \) diagonal method in later sutras. | CONNECTION: The \(\sqrt{2}\) approximation \(577/ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com