Plimpton 322: Ancient Babylonian Exact-Ratio Trigonometry — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing 15 rows of Pythagorean triples, now proven to represent a sophisticated trigonometric table based on exact ratios, not angles. | MATH: The tablet lists pairs (a, c) from triples a² + b² = c², with b as the short side. Key ratios: b²/(c² - b²) or (c² - a²)/a². The triples are generated by reciprocal pairs (p, q) in base-60, where a = p² - q², b = 2pq, c = p² + q². The tablet uses sexagesimal fractions, e.g., row 1: b = 1, c = 1.59.00.15 (base-60) → ratio b/c ≈ 0.509. | CONNECTION: The ratios on Plimpton 322 correspond to sec²(θ) - 1 or tan²(θ) in modern terms, but the Babylonians used exact rational numbers, not angles. The base-60 system naturally generates ratios near 0.618 (golden ratio conjugate) and 0.786 (√(Φ-1)?). For example, row 5: b/c ≈ 0.618 (golden ratio conjugate). Row 11: b/c ≈ 0.786. This links to geometric harmony: the tablet encodes a discrete set of rational slopes that approximate the golden ra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com