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 \(\frac{b^2}{c^2}\) (or \(\frac{a^2}{c^2}\)) as a column of sexagesimal fractions, e.g., row 1 gives \(\frac{119}{169}^2\) etc. The key ratio is \(\frac{c}{a}\) (secant-like) and \(\frac{b}{a}\) (tangent-like) in base-60, with values like 1.9834027… (sexagesimal 1;59,0,15). | CONNECTION: The ratios \(\frac{b}{c}\) and \(\frac{a}{c}\) are precisely the sine/cosine values in base-60. The tablet's column structure encodes \(\tan^2\theta = \frac{b^2}{a^2}\) — and the reciprocal pairs yield the golden-ratio-adjacent values: e.g., \(\frac{1}{1.9834} \approx 0.504\), but more Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com