Ancient Indian Sulba Sutras: Precise √2 Algorithm and Rope Geometry — E8 Intelligence Research

FINDING: The Sulba Sutras encode a geometric algorithm for √2 with an error of ~0.0000003, plus exact constructions for squares, circles, and altars using rope-and-stake geometry. | MATH: Boudhayana's √2 approximation: \(1 + \frac{1}{3} + \frac{1}{3\cdot4} - \frac{1}{3\cdot4\cdot34} = \frac{577}{408} \approx 1.414215686...\) (true √2 ≈ 1.414213562...; error ≈ 2.12×10⁻⁶). Also the "circle-squaring" ratio: side of square = \( \frac{7}{8} \cdot \text{diagonal}\) (for a circle of diameter d, square side ≈ \( \frac{7}{8}d\sqrt{2} \)), and the "squaring the circle" rule: radius = \( \frac{1}{2} \cdot \text{side} \cdot \left(1 + \frac{1}{3} + \frac{1}{3\cdot4} - \frac{1}{3\cdot4\cdot34}\right) \) — a direct use of the same √2 series. | CONNECTION: The √2 approximation is a convergent of the continued fraction [1;2,2,2,...] — the same root system for the square lattice (Z²). The fraction 577/408 is the 8th convergent; its ratio 577/408 ≈ 1.4142157 is within 0.000002 of √2. The construction use Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com