Plimpton 322: A Sexagesimal Secant-Squared Table Generating 15 Perfect Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is a sexagesimal table of normalized secant-squared ratios (1;59,15,0,0 to 1;55,7,41,15,0) derived from reciprocal pairs, generating 15 Pythagorean triples with no errors, revealing a proto-trigonometric method based on base-60 arithmetic. MATH: - Base-60 (sexagesimal) system: place-value notation with 59 digits. - Pythagorean triple generation: for regular sexagesimal reciprocals \( p, q \) (with \( p > q \), both having only 2,3,5 prime factors), triple sides: \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \). - Plimpton 322 columns: - Column I: \( ^2 θ = (c/b)^2 \) (normalized to 1;59,15,0,0 down to 1;55,7,41,15,0). - Column II: short side \( a \) (e.g., 1,59 = 119). - Column III: diagonal \( c \) (e.g., 2,49 = 169). - Key ratios: \( ^2 θ \) values decrease linearly in steps of ~0.001 to 0.002 in base-60, corresponding to angles from ~44.76° to ~31.89°. - No explicit use of golden ratio or harmonic ratios (0.382, 0 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com