Plimpton 322: The Old Babylonian Exact-Ratio Trigonometry Tablet — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Old Babylonian clay tablet containing 15 rows of Pythagorean triples, now understood as a sophisticated trigonometric table based on exact ratios, not angles. MATH: The tablet lists pairs (a, c) from triples a² + b² = c², with a < b. Key ratios: b²/(c² - b²) = b²/a² = (b/a)². The entries correspond to sec²(θ) = (c/b)², with θ decreasing from ~45° to ~30°. Base-60 sexagesimal system used throughout. No explicit π or φ, but ratios like 1;59,15 (≈1.983) and 2;49,56 (≈2.831) appear. CONNECTION: The tablet's structure aligns with base-60 fractions, which naturally produce ratios near 0.618 (1/φ) and 1.618 (φ) when inverted. The decreasing secant values (1.983 to 1.414) span the range where φ-related ratios (1.618) appear. The 15 rows may encode a regular 15-sided polygon (pentadecagon) symmetry, linking to crystallographic 15-fold rotational symmetry (though not periodic in 2D). The exact rational triples avoid irrationals, mirroring the Babylonian Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com