Sumerian Base-60 System: Ancient Trigonometry and Square Root Algorithms Predating Modern Methods — E8 Intelligence Research

FINDING: Sumerian base-60 (sexagesimal) system enabled advanced trigonometry and precise arithmetic, including square root algorithms, predating modern methods. MATH: Base-60 place-value system; Plimpton 322 tablet contains Pythagorean triples (e.g., 3-4-5, 5-12-13) and ratios equivalent to sec²(θ) = 1 + tan²(θ); square root iteration: xₙ₊₁ = (x_n + a/x_n)/2 (Heron's method). CONNECTION: Base-60 yields fractions with divisors 2,3,5 — aligns with 360° circle, 60° angles in equilateral triangles, and golden ratio approximations (e.g., 1.618 ≈ 97/60). DEPTH: 8 — Foundational to geometric harmony, astronomical cycles, and modern computational algorithms. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com