Plimpton 322 Encodes Secant-Squared Values for 45° to 30° in 1° Steps — E8 Intelligence Research

FINDING: Plimpton 322 encodes secant-squared values for angles from 45° down to 30° in 1° steps, using regular sexagesimal fractions. MATH: - sec²(θ) = (1/cos²(θ)) values for θ = 45°, 44°, ..., 30°. - Regular sexagesimal fractions: denominators only 2, 3, 5 (i.e., numbers of form 2^a·3^b·5^c). - Example: sec²(45°) = 2 = 1;0 in sexagesimal; sec²(30°) = 4/3 ≈ 1;20. - Tablet lists pairs (a, c) from Pythagorean triples: a² + b² = c², with b = (c² - a²)/2? Actually, standard interpretation: (b, a) = (p² - q², 2pq) or vice versa, but here sec² = (c/b)². CONNECTION: - The angle range 45° to 30° corresponds to slope ratios 1:1 to √3:1, linking to regular hexagon geometry (30°, 60°). - Base-60 system naturally yields fractions like 0;30, 0;45, 1;20, which are multiples of 1/60, 1/4, 1/3. - No direct golden ratio (0.618, 1.618) or 0.382, 0.786, 2.618 appear in this specific dataset. - However, the regular sexagesimal fractions align with crystallographic root system A₂ (hexag Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com