Plimpton 322: Babylonian Sexagesimal Parametrization of the Unit Circle — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic generation of Pythagorean triples via a sexagesimal (base-60) rational parametrization of the unit circle, likely using reciprocal pairs (x, 1/x) to produce integer sides. | MATH: For a unit circle, rational parametrization: \( t \mapsto \left( \frac{2t}{1+t^2}, \frac{1-t^2}{1+t^2} \right) \). In base-60, choose \( t = p/q \) with p,q regular sexagesimal integers. Then triple: \( a = 2pq \), \( b = q^2 - p^2 \), \( d = q^2 + p^2 \). Plimpton 322 columns correspond to \( (d/a)^2 \) or \( (b/a) \) ratios; e.g., row 1 gives \( b/a = 1.9834027... \) (sexagesimal 1;59,0,15) and \( d/a = 2.414... \) (approx √(1+ (b/a)^2)). The arXiv paper (2001.11141) proposes \( b = M \cdot Q_M \) where \( Q_M \) is a divisor function of M, yielding a data-driven generator. | CONNECTION: The ratios on Plimpton 322 include values near 0.786 (e.g., row 11: \( b/d \approx 0.7857 \), close to \( \pi/4 \approx 0.7854 \)) and near 0.618 (row 5: \( b/d \approx 0.6180 \),

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com