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 = p² - q² \), \ (b = 2pq \), \ (c = p² + q² \). - Plimpton 322 columns: - Column I: \ (² = (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 \) 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
Andrew Stewart Caldin (Tue,) studied this question.