Plimpton 322: Sexagesimal Ratios and the Factor 12 Algorithm for Pythagorean Triples — E8 Intelligence Research

Abstract

FINDING: Plimpton 322 encodes a systematic generation of Pythagorean triples via sexagesimal ratios, with a proposed algorithm based on factor 12 and a trigonometric function value system. MATH: - Pythagorean triples: integer sides (a, b, d) with a < b < d, satisfying a² + b² = d². - Proposed relation: b = M × Q_M, where M and Q_M are positive integers (from "Algorithm of Factor 12"). - Sexagesimal ratios: the tablet lists 15 triples with ratios b²/d² or related values, consistent with a trigonometric table of sec² or tan² in base-60. - Key constants: 1.618 (golden ratio φ) not directly present; sexagesimal reciprocals (e.g., 1/60, 2/60) and regular numbers (2^a·3^b·5^c) dominate. CONNECTION: - No direct link to icosahedral symmetry group H₃ root system or golden ratio ratios (0.382, 0.618, 0.786, 1.618, 2.618) is supported by the evidence. - Base-60 arithmetic is central; it aligns with regular numbers used in Babylonian reciprocal tables, which are foundational for gene Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com