FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing 15 rows of Pythagorean triples, now proven to be the world's first trigonometric table, predating Greek trigonometry by over 1000 years. | MATH: The tablet lists pairs (a, c) from triples (a, b, c) satisfying a² + b² = c², with a/b ratios forming a decreasing sequence of squared secant values (c/b)². Key constants: base-60 (sexagesimal) system used; ratios range from approximately 1.983 to 1.387 in sexagesimal fractions. The triples are generated by a method equivalent to modern parameterization: a = p² - q², b = 2pq, c = p² + q², with p, q regular sexagesimal numbers. | CONNECTION: The ratios a/b (or b/a) correspond to slopes or angles, linking to geometric harmony via the golden ratio family: the tablet's angle range (roughly 30° to 45°) includes the angle whose secant squared is 1.618 (golden ratio φ) — specifically, row 11 yields a ratio near φ² = 2.618? Check: row 11 (a=3, b=4, c=5) gives b/a = 4/3 = 1.333, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Andrew Stewart Caldin (Sat,) studied this question.