Plimpton 322: A Base-60 Secant-Squared Table of Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 encodes a secant-squared (sec²) trigonometric table in base-60, with ratios that map to Pythagorean triples and exhibit harmonic constants. MATH: - Base-60 (sexagesimal) system: numbers expressed as \( a · 60^n \). - Plimpton 322 rows correspond to \( ^2 θ = 1 + tan^2 θ \), with \( tan θ = b/a \) for integer sides \( a,b,c \) (Pythagorean triple). - Key ratios from tablet: e.g., row 1 gives \( ^2 θ ≈ 1.9834 \) (base-60: 1;59,0,15) → \( θ ≈ 1.408 \), \( tan θ ≈ 0.992 \). - No explicit φ (1.618) appears, but the sequence of \( ^2 \) values decreases from ~2.0 to ~1.4, approaching \( ^2(45°) = 2 \) and \( ^2(30°) = 4/3 ≈ 1.333 \). - Bruins' reconstruction: missing pairs follow \( p,q \) generation: \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \), with \( p/q \) ratios near 1.0–1.5. CONNECTION: - Base-60 naturally yields fractions with denominators 2,3,5 — facto Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com