Plimpton 322: A Sexagesimal Secant Table of Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is a sexagesimal table of 15 Pythagorean triples, likely generated by a reciprocal-pair algorithm (x = p/q + q/p, y = p/q − q/p, z = 1) and interpretable as a secant/tangent table for right triangles. MATH: - Standard reconstruction: For regular sexagesimal reciprocals (p, q) with p > q, the triples satisfy: \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \) (or scaled variants). - The tablet's columns give: Column I: \( \frac{c^2}{a^2} = \sec^2\theta \) (or \( \frac{b^2}{a^2} = \tan^2\theta \)), Column II: \( a \) (short side), Column III: \( c \) (hypotenuse). - Sexagesimal ratios present: e.g., row 1 gives \( \sec^2\theta = 1.59,00,15 \) (base‑60) = \( 1 + 0.9834027... \), corresponding to \( \theta \approx 44.76^\circ \). - The generating rule uses regular numbers (integers whose reciprocals terminate in base‑60), e.g., \( p = 2, q = 1 \) → triple (3,4,5); \( p = 3, q = 2 \) → (5,12,13); etc. CONNECTION: - **Base‑60 harmony Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com