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

Abstract

FINDING: Sulba Sutras contain explicit geometric constructions for altars (vedi/agni) using Pythagorean triples, square-circle equivalences, and irrational approximations (√2, √3). MATH: - Baudhayana Sulba Sutra (c. 800 BCE) states: *"The diagonal of a square produces double the area"* → side : diagonal = 1 : √2. - Approximation for √2: \( 1 + \frac{1}{3} + \frac{1}{3 \cdot 4} - \frac{1}{3 \cdot 4 \cdot 34} = 1.4142156... \) (error ~2×10⁻⁶). - Pythagorean triple construction: \( 3^2 + 4^2 = 5^2 \) used for right-angle altar bases. - Circle-squaring (caturasra-parināha): ratio of circumference to diameter approximated as \( 3 + \frac{1}{8} = 3.125 \) (or \( \frac{339}{108} \approx 3.1389 \)). - Base-60 influence: altar dimensions in *angula* (finger) units, subdivided into 60 *tilas* (sesame seeds). CONNECTION: - √2 approximation yields ratio 1.4142 → close to 1.414 (√2) but not directly 0.618/1.618. However, the *square-doubling* problem links to geometric mean: side of Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com