Plimpton 322: World's Oldest Trigonometric Table Using Base-60 Ratios — E8 Intelligence Research

FINDING: Babylonian tablet Plimpton 322 is the world's oldest known trigonometric table, using base-60 (sexagesimal) ratios rather than angles or circles. | MATH: Tablet lists 15 rows of Pythagorean triples (a² + b² = c²) in sexagesimal notation; ratios b²/(c²–b²) or (c²–a²)/a² correspond to sec²(θ)–1 or tan²(θ). Key constants: 1;59,15 = 1.9875, 1;56,56,58,14,50,6,15 ≈ 1.949, etc. Base-60 place-value system uses 60 as radix. | CONNECTION: The ratios on Plimpton 322 approximate sec²(θ) for angles from ~45° down to ~30°, with step sizes corresponding to regular sexagesimal fractions. The underlying structure is a discrete set of rational right triangles, linked to the geometric mean and the golden ratio via the property that in a right triangle, the altitude to the hypotenuse divides it into segments whose ratio is (b/a)². For a 3-4-5 triangle, this ratio is 16/9 ≈ 1.777…, not directly golden, but the tablet's systematic generation of triples uses a method equivalent to (1/p – p)/2, (1/p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com