Plimpton 322: Oldest Trigonometric Table, Encoding Secant-Squared Values (30°–45°) in Base-60 — E8 Intelligence Research

FINDING: Plimpton 322 encodes a decreasing sequence of secant-squared values (1/cos²θ) for angles 30° to 45°, representing the world's oldest known trigonometric table in base-60. MATH: - Sec²θ = (c/b)² for Pythagorean triples (a, b, c) with a² + b² = c², where b is the short side. - Tablet rows correspond to angles θ from ~45° (row 1) down to ~30° (row 15). - Values are given in sexagesimal (base-60) fractions, e.g., row 1: sec²θ ≈ 1.9834027… (base-60: 1;59,0,15). - Exact ratios derived from triples: e.g., (119, 120, 169) → sec²θ = (169/120)² ≈ 1.9834. - No explicit formula survives, but the pattern implies a systematic generation of triples via p, q parameters: a = p² - q², b = 2pq, c = p² + q². CONNECTION: - The angle range 30°–45° corresponds to sec²θ values from 1.333… to 2.000…, a natural interval for geometric ratios. - Sec²θ = 1 + tan²θ, linking to slope ratios used in surveying and architecture (e.g., ziggurat gradients). - Base-60 fractions align with 360° c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com