Plimpton 322: Old Babylonian Sexagesimal Trig Table Using Ratios — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian table of 15 rows of Pythagorean triples, likely a trigonometric table using base-60 sexagesimal ratios rather than angles. MATH: - Each row corresponds to a Pythagorean triple (a, b, c) satisfying \( a^2 + b^2 = c^2 \). - The tablet lists pairs (b^2/(c^2 - b^2), c/b) in sexagesimal notation, equivalent to sec²θ and secθ for a right triangle. - Key ratios derived: e.g., row 1 gives b/c ≈ 0.983, a/b ≈ 0.183, corresponding to an angle of about 45° (since b ≈ c). - Base-60 system used: e.g., 1;59,15 = 1 + 59/60 + 15/3600 = 1.9875. - No explicit equations survive, but the triples are generated by the standard formula: \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \), with p, q regular sexagesimal numbers. CONNECTION: - The ratios b/c and a/b approximate 0.618 (inverse of φ) for some rows? Check: row 5 gives b/c ≈ 0.618? Actually, row 5: b=3456, c=4825 → b/c ≈ 0.716; not φ. However, the systematic use of base-60 aligns with harm Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com