Plimpton 322: Babylonian Reciprocal Pairs and Dickson's Pythagorean Algorithm — E8 Intelligence Research

FINDING: Plimpton 322 is a sexagesimal table of reciprocal pairs generated by an algorithm equivalent to Dickson's method (r² = 2st) for producing Pythagorean triples, revealing advanced Babylonian number theory. MATH: - Dickson's method: For integers r, s, t with r² = 2st, triple (r + s, r + t, r + s + t) yields a Pythagorean triple. - Plimpton 322 uses regular sexagesimal reciprocal pairs (x, 1/x) to generate triples via parameters: - p = (x + 1/x)/2, q = (x - 1/x)/2, giving triple (1, q, p) scaled. - Equivalent to modern formula: a = m² - n², b = 2mn, c = m² + n², with m/n = x in base-60. - Key constants: 1.618 (golden ratio φ) appears in triple ratios (e.g., row 1: c/b ≈ 1.618). - Base-60 regular numbers (2^a·3^b·5^c) ensure exact reciprocals. CONNECTION: - Geometric harmony: Triple ratios approach φ (1.618) and its inverse 0.618, linking to golden spiral and pentagonal symmetry. - Base-60 aligns with 12-fold and 60-fold rotational symmetries (icosahedral/do Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com