Ancient Babylonian Tablet Plimpton 322: Earliest Exact Trigonometric Table — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian table of 15 Pythagorean triples, likely generated by a sexagesimal (base-60) parameterization, and reinterpreted as an exact trigonometric table using ratios rather than angles. | MATH: The triples satisfy \(a^2 + b^2 = c^2\). Standard reconstruction: for parameters \(p > q\) (coprime, opposite parity), \(a = p^2 - q^2\), \(b = 2pq\), \(c = p^2 + q^2\). The tablet lists \(b^2/c^2\) (or \(a^2/c^2\)) as a column of sexagesimal fractions, e.g., row 1 gives \(119/169^2\) etc. The key ratio is \(c/a\) (secant-like) and \(b/a\) (tangent-like) in base-60, with values like 1.9834027… (sexagesimal 1;59,0,15). | CONNECTION: The ratios \(b/c\) and \(a/c\) are precisely the sine/cosine values in base-60. The tablet's column structure encodes \(tan^2θ = b^2/a^2\) — and the reciprocal pairs yield the golden-ratio-adjacent values: e.g., \(1/1.9834 ≈ 0.504\), but more Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com