Plimpton 322: Oldest Trigonometric Table Using 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) and (c/a) correspond to sec²(θ) in modern terms. Constants: 1;59,0,15 = 1.9834... (close to √4 = 2), 1;24,51,10 = 1.41421296... (√2 to six decimal places). | CONNECTION: Base-60 arithmetic naturally generates ratios 0.618 (1/φ) and 1.618 (φ) via reciprocal pairs; sexagesimal fractions align with 360° circle and 12-fold symmetry. | DEPTH: 8 — Reveals advanced geometric understanding 1,000 years before Greek trigonometry, with exact ratios and systematic computation. FINDING: Two Babylonian geometry tablets (YBC 7289, MS 3052) contain a proof-like procedure for √2 irrationality, using reciprocal pairs and geometric iteration. | MATH: YBC 7289 gives √2 = 1;24,51,10 (1.41421296) and its reciprocal 0;42,25,35 (0.7071065); MS 3052 shows a "squaring the diagonal" a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com