Plimpton 322: Old Babylonian Trigonometry via Secant-Based Sexagesimal Table — E8 Intelligence Research

FINDING: Plimpton 322 encodes a primitive trigonometric table using secant angles from 44.8° to 31.9° in a geometric progression, based on Old Babylonian sexagesimal (base-60) arithmetic. MATH: - Pythagorean triples (a, b, c) with a < b, c² = a² + b². - Tablet lists 15 rows of (b², a, c) in sexagesimal. - Angles θ satisfy sec²(θ) = (c/b)², with θ decreasing from ~44.8° to ~31.9° in steps of ~1° (geometric progression of secant values). - Key constants: 1;24,51,10 (≈1.41421296, √2 approximation) and 1;59,0,15 (≈1.9834028, sec(30°)²?). - No explicit equations survive; reconstruction uses reciprocal pairs (p, q) generating triples: a = p² - q², b = 2pq, c = p² + q². CONNECTION: - Geometric harmony: The angle range (44.8°–31.9°) and step size (~1°) reflect a systematic division of the right triangle's acute angle, akin to a primitive trigonometric table. - Base-60: All entries are sexagesimal, enabling exact fractions (e.g., 1/60, 1/3600) and facilitating ratios like 0.618 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com