Plimpton 322: The World's Oldest Trigonometric Table — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian table of Pythagorean triples organized by squared secant (or tangent) ratios for angles 30° to 45°, representing the world's earliest known trigonometric table. MATH: - Each row corresponds to a right triangle with sides (a, b, c) in sexagesimal, where b² = c² – a². - The tablet lists values of (c/a)² = sec²(θ) for decreasing angles θ from ~45° to ~30°. - Key ratios derived: for angle θ, sec²(θ) = (c/a)², and tan²(θ) = (b/a)². - Sexagesimal base-60 system used: e.g., row 1 gives sec²(θ) ≈ 1.9834 (sexagesimal 1;59,0,15) corresponding to θ ≈ 44.76°. - The triples are generated by the parametric form: a = p² – q², b = 2pq, c = p² + q², with p, q regular sexagesimal numbers. CONNECTION: - The angle range 30°–45° yields sec² values from 1.3333 to 2.0000, which map to ratios near 1.618 (golden ratio) and 0.618 (its reciprocal) when inverted or scaled. For example, sec(36°) ≈ 1.236, and sec²(36°) ≈ 1.527, close to 1.618/√2. - Base-60 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com