Plimpton 322: Oldest Trigonometric Table Using Base-60 Exact Ratios — E8 Intelligence Research

FINDING: Babylonian tablet Plimpton 322 is the world's first trigonometric table, using base-60 (sexagesimal) fractions and exact ratios rather than angles or approximations. MATH: - Base-60 system: divisors include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 — enabling exact fractions (e.g., 1/2 = 0;30, 1/3 = 0;20, 1/4 = 0;15). - Tablet lists 15 pairs of numbers (a, c) from Pythagorean triples, with b implicit (a² + b² = c²). Ratios b²/(c² - b²) or similar yield exact sexagesimal fractions. - Key constants: 1;24,51,10 (≈ √2 in sexagesimal), 1;15 (≈ 5/4), 0;45 (3/4). CONNECTION: - Base-60 directly relates to 360° circle (6×60), enabling exact division of the circle into 6, 10, 12, 15, 20, 30, 60, 90, 120, 180, 360 parts. - Ratios on tablet approximate golden ratio φ = 1.618 (e.g., 1;36 = 1.6, 1;40 = 1.666…), but no exact φ appears. - Geometric harmony: sexagesimal fractions allow exact representation of many regular polygon side ratios (e.g., hexagon side = radius, decagon Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com