Plimpton 322: Reciprocal Pairs, Not Trigonometry, Generate Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is a table of reciprocal pairs (regular sexagesimal numbers) generating Pythagorean triples via the Old Babylonian method, not a trigonometric table in the modern sense. MATH: - Regular numbers in base-60: numbers of form \(2^a 3^b 5^c\) (finite sexagesimal reciprocals). - Reciprocal pair generation: given \(p\) and \(q\) (regular, \(p > q\)), triple sides: \(a = p^2 - q^2\), \(b = 2pq\), \(c = p^2 + q^2\). - Plimpton 322 lists \(p/q\) ratios (column I) and corresponding triples. - Key constants: 1;24,51,10 (sexagesimal) = \(√2\) to 5 decimal places; 1;15 = 5/4; 1;20 = 4/3. - No explicit golden ratio \(φ\) (1.618) or its reciprocal (0.618) appear in the tablet's extant numbers. CONNECTION: - Base-60 system inherently linked to regular numbers, which form a multiplicative group isomorphic to \(Z^3\) — a lattice structure. - The reciprocal pair method generates primitive Pythagorean triples, which correspond to rational points o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com