Sulba Sutras: Early Pythagorean Theorem and Irrational Number Geometry — E8 Intelligence Research

FINDING: Sulba Sutras contain precise geometric constructions for ritual altars, including early formulations of the Pythagorean theorem and irrational numbers. MATH: Key results from Baudhayana and Apastamba Sulba Sutras: - Pythagorean theorem: *dīrghasyākṣṇayā rajjuḥ pārśvamānī tiryagmānī ca yat pṛthagbhūte kurutastadubhayaṃ saṃkaroti* (The diagonal of a rectangle produces both areas which the sides produce separately). Equivalent to a² + b² = c². - Approximation for √2: *saviśeṣaḥ* (increase by) 1 + 1/3 + 1/(3·4) - 1/(3·4·34) = 1.4142156... (error ~2×10⁻⁶). - Circle-squaring: Construction of a square equal in area to a circle, using ratio 7/8 of diameter for side (approximation of π ≈ 3.088, later refined). - Altar area ratios: Fire altars (agni) scaled by factors 1, 2, 3, ... using geometric transformations preserving area. CONNECTION: Strong geometric harmony links: - √2 approximation uses a continued-fraction-like series (1, 3, 4, 34) — related to Pell's equation x² - 2y² = ±1, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com