FINDING: Plimpton 322 encodes a ratio-based trigonometric table using base-60 reciprocals, not angles or circles, generating exact Pythagorean triples via a generating pair (p, q) with reciprocal pairs in sexagesimal. MATH: - Generating formula: For integers \ (p > q > 0 \) with no common factor, triple sides: \ (a = p² - q² \), \ (b = 2pq \), \ (c = p² + q² \). - Plimpton 322 uses \ (p/q \) as a regular sexagesimal ratio (i. e. , \ (q \) divides 60ᵏ). - Key constant: \ ( (p/q) ² \) yields the ratio \ ( (c/a) ² \) or \ ( (b/a) \) depending on interpretation. - Base-60 reciprocals: \ (1/x \) in sexagesimal is exact only if \ (x \) is regular (factors 2, 3, 5). - Table entries correspond to decreasing \ ( (p/q) ² \) from ~1. 983 to ~1. 387, giving 15 rows. CONNECTION: - Ratio \ (p/q \) approximates \ (2 \) in first row (1. 983 ≈ 2), linking to the diagonal of a square. - The sequence of \ (p/q \) values: 12/5, 64/27, 75/32, 125/54, 9/4, 20/9, 54/25, 32/15, 25/12, 81/40, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Tue,) studied this question.