Plimpton 322: A Sexagesimal Algorithm for Pythagorean Triples with √2 Approximation — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic sexagesimal algorithm for generating Pythagorean triples, with an embedded approximation of √2 as 1;24,51,10 (1.41421296...). | MATH: √2 ≈ 1;24,51,10 = 1 + 24/60 + 51/3600 + 10/216000 = 30547/21600 ≈ 1.41421296; error < 2×10⁻⁶. Pythagorean triple generator: (p² - q², 2pq, p² + q²) in sexagesimal regular numbers (p, q with only 2,3,5 prime factors). | CONNECTION: 1;24,51,10 is geometrically linked to the diagonal of a unit square (√2). The ratio 1;24,51,10 / 1 = 1.41421296 approximates the golden ratio conjugate φ⁻¹ = 0.618? No — but note 1.414² = 2.000006, a near-perfect square doubling. Base-60 regular numbers enable exact division in geometric constructions (e.g., 1/2, 1/3, 1/5, 1/6, 1/10). | DEPTH: 8 — Directly reveals ancient understanding of irrationality via rational approximation, systematic triple generation, and the power of base-60 for computational geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com