Plimpton 322's Sexagesimal Algorithm as Rational Circle Parametrization — E8 Intelligence Research

FINDING: Plimpton 322 encodes Pythagorean triples via a sexagesimal algorithm equivalent to rational parametrization of the unit circle, with a proposed new generative rule \(b = M · Q_M\). MATH: - Standard reconstruction: For coprime \(p > q > 0\), triples \((a, b, d)\) satisfy \(a = p^2 - q^2\), \(b = 2pq\), \(d = p^2 + q^2\) (or swapped). - Rational parametrization: \(x = 2t/1+t^2\), \(y = 1-t^2/1+t^2\) for \(t = q/p\) (or reciprocal), mapping \(t ∈ Q\) to points on \(x^2 + y^2 = 1\). - New algorithm (arXiv 2001.11141): \(b = M · Q_M\), with \(M, Q_M ∈ Z^+\), generating the tablet's rows — data‑driven, not assuming the standard \(p,q\) form. - Sexagesimal base‑60 appears in column headers (squares of sides, diagonals) — e.g., values like 1;59, 2;49, etc., implying use of reciprocal pairs and regular numbers (smooth in base 60). CONNECTION: - The parametrization \(t = tan(θ/2)\) yields ratios: for \(t = 1/√3\) → Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com