Plimpton 322 as Base-60 Encoding of Circle Parametrization — E8 Intelligence Research

FINDING: The rational parametrization of the unit circle — via the slope through (−1,0) — generates all primitive Pythagorean triples, and Plimpton 322 encodes this via reciprocal pairs in base-60. MATH: - Unit circle: \(x^2 + y^2 = 1\). - Rational parametrization: \(x = 1-t^2/1+t^2,\; y = 2t/1+t^2\), with \(t ∈ Q\). - Pythagorean triple: \(a = m^2 - n^2,\; b = 2mn,\; c = m^2 + n^2\) (Euclid's formula), where \(t = n/m\). - Plimpton 322: columns give \(c/a\) and \(b/a\) (or \(c/b\)) for 15 triples; generated by reciprocal pairs \(p/q\) and \(q/p\) in base-60, with \(p,q\) regular sexagesimal integers. - Key ratios on the tablet: e.g., line 1 gives \(c/a = 1.9834027...\) (base-60: 1;59,0,15) and \(b/a = 0.783333...\) (0;47,0) — these are rational values of \( (1+t^2)/(1-t^2) \) and \(2t/(1-t^2)\) for \(t = 1/60\)? No — exact: \(t = 1/60\) gives \(b/a = 2t/(1-t^2) = 120/3599 ≈ 0.03334\), not 0.7833. The tablet's \(t\) values are specific regular sex Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com