FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing 15 rows of Pythagorean triples, now understood as the world's oldest trigonometric table, predating Greek trigonometry by over 1000 years. | MATH: Each row lists a pair of numbers (a, c) from a right triangle with sides (a, b, c) satisfying a² + b² = c². The triples are generated using reciprocal pairs (x, 1/x) in base-60, yielding ratios b/a = (x² - 1) / (2x) and c/a = (x² + 1) / (2x). Key constants: base-60 (sexagesimal) place-value system; exact ratios include 0. 5, 0. 6, 0. 75, 1. 333. . . , 1. 666. . . , etc. , derived from regular numbers (2ᵃ·3ᵇ·5ᶜ). | CONNECTION: The triples correspond to rational approximations of the golden ratio φ = (1+√5) /2 ≈ 1. 618, with some rows yielding b/a ratios near 0. 618 (1/φ) and 1. 618 (φ). The base-60 system aligns with 60° symmetry in hexagonal/crystallographic lattices (e. g. , 60°, 120° angles). The tablet's structure mirrors a secant table: c/b = 1/sin (θ), with angles decreasing in regu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Mon,) studied this question.