Babylonian Tablet Plimpton 322: Oldest Trigonometric Table Predating Greek Math — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing 15 rows of Pythagorean triples, likely constructed via reciprocal pairs in base-60, representing the oldest known trigonometric table — predating Greek trigonometry by over a millennium. | MATH: The tablet lists triples (a, b, c) satisfying a² + b² = c². Reconstruction (Neugebauer & Sachs, 1945) shows the scribe used parameters p, q (with p > q, both regular sexagesimal numbers) to generate triples via: a = p² − q², b = 2pq, c = p² + q². The tablet's columns correspond to ratios: - Column I: (c/a)² or (c/b)² — specifically, the values are (c/a)² = 1 + (b/a)², yielding sexagesimal values like 1.9834027… (for row 1) and 1.3871604… (for row 15). - The diagonal-to-short-side ratio (c/b) ranges from ~1.4142 (√2) to ~1.787. - Base-60 notation: e.g., row 1 gives a = 119, b = 120, c = 169; row 15 gives a = 56, b = 90, c = 106. Key constants: The tablet's ratios include values close to 1.4142 (√2), 1.732 (√3) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com