Plimpton 322 as Reciprocal Pairs, Not Trigonometry — E8 Intelligence Research

FINDING: Plimpton 322 encodes Pythagorean triples generated by a rational parametrization of the unit circle, likely via reciprocal pairs (x, 1/x) in base‑60, not a modern trigonometric table. MATH: - Standard parametrization: \( x = 2t/1+t^2, \; y = 1-t^2/1+t^2 \) for \( t ∈ Q \). - Plimpton 322 columns correspond to \( b^2/d^2 = 1 - (a/d)^2 \) with \( a^2 + b^2 = d^2 \). - Proposed algorithm (arXiv:2001.11141): \( b = M · Q_M \), with \( M, Q_M ∈ Z^+ \), generating all rows via factor pairs — equivalent to choosing \( t = p/q \) with \( p, q \) from sexagesimal regular numbers (2,3,5‑smooth). - Base‑60 constants: reciprocals of regular numbers (e.g., 1/60, 1/30, 1/20, 1/15, 1/12, 1/10) yield exact finite sexagesimal expansions — the key constraint. CONNECTION: - The rational parametrization \( t ↦ (2t/1+t^2, 1-t^2/1+t^2) \) is the stereographic projection from Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com