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

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing 15 rows of Pythagorean triples, likely the oldest known trigonometric table, predating Greek mathematics. MATH: The tablet lists pairs (a, c) from triples (a, b, c) satisfying a² + b² = c². The triples are generated using the Old Babylonian method: let p, q be regular sexagesimal numbers (p > q), then a = p² - q², b = 2pq, c = p² + q². The ratios b²/(c² - b²) or equivalently (b/a)² appear as column headings, forming a secant-squared or tangent-squared table. Key constants: base-60 (sexagesimal) place-value system; no explicit constants like π or φ appear, but the triples imply rational approximations of √2 and √3 (e.g., 1;24,51,10 = 1.41421296 for √2). CONNECTION: The triples encode rational approximations of geometric ratios. The ratio b/a (opposite/adjacent) yields values near 0.382, 0.618, 0.786, 1.618, 2.618 when normalized. For example, triple (119, 120, 169) gives b/a = 120/119 ≈ 1.0084 (near 1), while ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com