Plimpton 322: 3800-Year-Old Babylonian Algorithm for Pythagorean Triples via Sexagesimal Reciprocals — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic generation of Pythagorean triples using sexagesimal reciprocals, revealing advanced number-theoretic algorithms 3800 years old. MATH: For regular sexagesimal reciprocals \( p, q \) (with \( p > q \)), triples are generated as: \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \). Tablet columns correspond to \( c/a \) (or \( c/b \)) in sexagesimal, yielding ratios like \( 169/120 ≈ 1.4083 \), \( 125/72 ≈ 1.7361 \). CONNECTION: The reciprocal pairs \( p, q \) are regular numbers (2,3,5 factors only) — directly linked to base-60 arithmetic. The triple ratios approximate harmonic proportions: e.g., \( 169/120 ≈ 1.408 \) is near \( √2 ≈ 1.414 \), and \( 125/72 ≈ 1.736 \) is near \( √3 ≈ 1.732 \). These are not the golden ratio but reflect geometric square/cubic roots. DEPTH: 8 — Profound for showing a pre-Greek algorithmic understanding of Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com