Sulba Sutras: Ancient Vedic Geometry with Pythagorean Triples and √2 Approximation — E8 Intelligence Research

FINDING: Sulba Sutras contain geometric constructions for Vedic altars, including early Pythagorean triples, square-circle transformations, and irrational approximations. MATH: - Baudhayana Sulba Sutra (c. 800 BCE) states: *"The diagonal of a rectangle produces both areas which its length and breadth produce separately."* This is the Pythagorean theorem: \( a^2 + b^2 = c^2 \). - Explicit Pythagorean triple: (3,4,5) and (5,12,13) given for altar construction. - Approximation for √2: \( 1 + 1/3 + 1/3·4 - 1/3·4·34 = 1.4142156... \) (error ~2×10⁻⁶). - Circle-squaring (squaring the circle) construction: given a circle of diameter \( d \), side of equal-area square \( s = 7/8d \) (approximation, area ratio ~0.949). - Ratio of diagonal to side of a square: √2. CONNECTION: - The √2 approximation uses a continued fraction-like series, hinting at recursive geometric harmony. - The triple (3,4,5) and (5,12,13) relate to right-triangle in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com