Sumerian Base-60 and Plimpton 322: Exact Rational Trigonometry — E8 Intelligence Research

FINDING: Sumerian sexagesimal (base-60) system encodes a highly composite, factor-rich arithmetic framework; Plimpton 322 reveals a proto-trigonometric table based on exact rational ratios (Pythagorean triples), not angle approximations. MATH: Base-60 prime factorization: 60 = 2² × 3 × 5 → 12 divisors (1,2,3,4,5,6,10,12,15,20,30,60). Plimpton 322: columns of (a, c) pairs satisfying a² + b² = c², with b = (p² − q²)/2, a = pq, c = (p² + q²)/2 for coprime p>q (standard parameterization). Ratios on tablet: e.g., line 1: b=119, c=169 → b/c ≈ 0.7041; line 11: b=45, c=75 → 0.6; line 15: b=56, c=106 → 0.5283. These yield exact sexagesimal reciprocals (1/b, 1/c) — the tablet is a table of secant² (or cotangent²) values, not angles. CONNECTION: Base-60's divisibility by 3 and 5 directly supports geometric ratios: 0.618 = (√5−1)/2 arises from 5; 0.786 = √(0.618) — both expressible in sexagesimal as finite or repeating but exact fractions (0.618 = 37/60 + 0.008 → 37;4,48 in base-60). The 12 di Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com