Plimpton 322: A Ratio-Based Sexagesimal Trigonometric Table — E8 Intelligence Research

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: \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \). - Plimpton 322 uses \( p/q \) as a regular sexagesimal ratio (i.e., \( q \) divides 60^k). - 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