Plimpton 322: Old Babylonian Trigonometry Predates Greek Methods by 1000 Years — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian trigonometric table based on exact ratios (sexagesimal) of sides of right triangles, using a novel cotangent-squared (or squared ratio) approach, predating Greek trigonometry by over 1000 years. | MATH: The tablet lists 15 rows of Pythagorean triples (a, b, c) with a < b. Column I contains (b/a)² or equivalently cot²(θ) = (adjacent/opposite)² in base-60. For example, row 1: b/a = 1.9834... → cot² = 3.933... (sexagesimal: 3 56 00). The triples satisfy a² + b² = c², but the table is organized by decreasing cot²(θ) from ~3.93 to ~0.23, corresponding to angles from ~45° to ~30°. No explicit π or trigonometric functions; uses exact sexagesimal fractions. | CONNECTION: The ratios b/a (cotangent) range from ~1.98 to ~0.48, which includes the golden ratio conjugate 0.618 (cot ≈ 0.618 → angle ≈ 58.3°, not in tablet) and 1.618 (cot ≈ 1.618 → angle ≈ 31.7°, near row 15). The base-60 system naturally yields fractions with denominators 2,3,5 — key to cryst Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com