Plimpton 322: Babylonian Tablets Encoding Pythagorean Triples and Crystallographic Root Ratios — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic list of regular sexagesimal reciprocal pairs (p, q) generating Pythagorean triples, with deep links to root system ratios A₂, B₂, G₂ and crystallographic angles. MATH: - Sexagesimal base-60: regular numbers (2ᵃ·3ᵇ·5ᶜ) yield exact reciprocals. - Triples: (a = p² - q², b = 2pq, c = p² + q²) with p, q regular and p > q. - Key ratios from reciprocal pairs: p/q ≈ 1. 618 (golden ratio), 1. 414 (√2), 1. 732 (√3), 1. 236 (√5 - 1), 0. 618, 0. 786. - Crystallographic angles: 30°, 45°, 60°, 90° appear as slopes from p/q values. CONNECTION: - A₂ root system (hexagonal lattice): angles 60°, 120°; ratio √3 ≈ 1. 732 appears in p/q pairs. - B₂ root system (square lattice): angles 45°, 90°; ratio √2 ≈ 1. 414 appears. - G₂ root system (dodecagonal): angles 30°, 60°, 90°; ratio √3 and 1. 618 (golden) appear. - Base-60 enables exact representation of these ratios via regular numbers, linking to crystallographic symmetry groups. DEPTH: 9 — Direct e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com