Plimpton 322: Old Babylonian Secant Table for Exact Sexagesimal Trigonometry — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian table of secant-based trigonometric ratios, not Pythagorean triples; it uses base-60 sexagesimal fractions for exact rational trigonometry. MATH: Each row yields a normalized right triangle with short side = 1, long side = b, diagonal = d, where d² - b² = 1. The tablet lists (b, d) pairs as sexagesimal reciprocals: b = (p² - q²)/(2pq), d = (p² + q²)/(2pq) for regular integers p>q. The key ratio is the secant: sec(θ) = d/1 = d. The tablet's column headings translate to "the diagonal" and "the width," confirming trigonometric intent. CONNECTION: The ratios b/d and 1/d correspond to sin(θ) and cos(θ) in modern terms, but the Babylonian method uses exact rational numbers, avoiding irrationals. The base-60 system naturally generates regular numbers (2ᵃ·3ᵇ·5ᶜ) that yield finite sexagesimal expansions—linking to crystallographic lattice vectors in hexagonal and cubic systems. The sequence of decreasing secants (from ~1.983 to ~1.387) approximates Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com