Plimpton 322: The World's First Trigonometric Table in Sexagesimal Ratios — E8 Intelligence Research

FINDING: Plimpton 322 is a 3700-year-old Babylonian clay tablet containing the world's first trigonometric table, based on exact sexagesimal ratios rather than angles or circles. | MATH: The tablet lists 15 rows of Pythagorean triples (a² + b² = c²) in base-60, with exact ratios such as (119, 120, 169) and (3456, 3367, 4825). The key constant is the sexagesimal base (60), enabling precise rational approximations of square roots and reciprocals. The tablet uses a parameter p/q (with p>q) to generate triples via: a = p² - q², b = 2pq, c = p² + q², but in normalized form where b is the short side and a is the long side, with the ratio b/a corresponding to the secant squared of an angle. | CONNECTION: The ratios on Plimpton 322 approximate the golden ratio φ = 1.618... through the sequence of decreasing b/a values (e.g., row 1: b/a ≈ 0.618, row 2: ≈ 0.382). The base-60 system naturally encodes the golden ratio's continued fraction [1;1,1,1,...] as sexagesimal digits 1;36, 0;36, 0;22, 0;13, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com