Plimpton 322: World's Oldest Trig Table Uses Base-60 Ratios — E8 Intelligence Research

FINDING: Babylonian tablet Plimpton 322 is the world's oldest known trigonometric table, using base-60 ratios rather than angles. | MATH: Tablet lists 15 rows of Pythagorean triples (a² + b² = c²) in sexagesimal; ratios b²/(c²–b²) or similar generate exact values; base-60 enables precise rational approximations (e.g., 1;59,0,15 = 1.9834…). | CONNECTION: Base-60 arithmetic inherently generates ratios near 0.618 (1/φ) and 1.618 (φ) via regular numbers; sexagesimal fractions align with 360° circle and 12/5 pentagonal symmetry. | DEPTH: 9 FINDING: Babylonian geometry problem tablets implicitly use the irrationality of √2, constructing a diagonal of a unit square with sexagesimal approximation 1;24,51,10 (≈1.41421296). | MATH: √2 ≈ 1;24,51,10 = 1 + 24/60 + 51/3600 + 10/216000 = 30547/21600 ≈ 1.41421296; error < 2×10⁻⁶. | CONNECTION: Ratio 1.4142 links to square lattice symmetry (crystallographic 4-fold); approximation via regular numbers in base-60 mirrors harmonic division (0.7071 = 1/√2) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com