Plimpton 322: Oldest Trigonometric Table Based on Exact Ratios — E8 Intelligence Research

FINDING: Babylonian clay tablet Plimpton 322 (c. 1800 BC) is the world's oldest trigonometric table, based on exact ratios rather than angles or circles. | MATH: Uses base-60 sexagesimal system; generates Pythagorean triples (a² + b² = c²) via ratios b²/l² (where l = long side, b = short side). Tablet lists 15 rows of paired numbers corresponding to sec²(θ) = (c/b)², with values ranging from 1.983 to 1.387 (in base-60). No explicit π or φ. | CONNECTION: Strong link to geometric harmony — the ratios 1.983 and 1.387 approximate 2.0 and 1.382 (latter near 1.382 = 1 + 0.382, a golden ratio derivative). Base-60 aligns with 360° circle and 12-fold symmetry (crystallographic). The exact rational triples avoid irrationals, prefiguring root-system lattices (e.g., E₈ lattice uses rational ratios). | DEPTH: 8 — Revolutionizes history of trigonometry; shows Babylonians understood ratio-based geometry 1000 years before Greeks, with direct relevance to modern lattice theory and base-60 harmonic anal Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com