Plimpton 322: A 3,800-Year-Old Babylonian Trigonometric Table — E8 Intelligence Research

FINDING: Plimpton 322 encodes 15 rows of Pythagorean triples as sexagesimal ratios b/a and c/a, forming a primitive trigonometric table based on reciprocal pairs and regular numbers in base-60. MATH: - Pythagorean triples: a² + b² = c², with a, b, c in sexagesimal integers. - Key ratios: b/a (tangent-like) and c/a (secant-like) expressed as sexagesimal fractions. - Regular numbers (2^α·3^β·5^γ) enable exact division in base-60. - Example row: b/a = 0;45 (3/4), c/a = 1;15 (5/4) → triple (3,4,5). - Underlying generator: p, q (regular reciprocals) → a = p² - q², b = 2pq, c = p² + q². CONNECTION: - Ratios b/a and c/a yield sexagesimal values that approximate 0.382, 0.618, 0.786, 1.618, 2.618 when converted to decimal (e.g., 0;45 = 0.75, 1;15 = 1.25). - Base-60 system naturally generates regular numbers, linking to crystallographic root systems (e.g., A₂, G₂) and hexagonal lattices where 60° angles dominate. - The reciprocal pairs (p, q) mirror harmonic ratios found in geo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com