Plimpton 322: Babylonian Tablet Reveals Oldest Pythagorean Triple Algorithm — E8 Intelligence Research

FINDING: Plimpton 322 contains 15 rows of Pythagorean triples generated by a systematic algorithm, likely using reciprocal pairs in base-60, predating Greek trigonometry by over a millennium. MATH: Triples satisfy \(a^2 + b^2 = c^2\) with \(a < b\). Tablet lists \(a\), \(c\), and ratio \(b^2/a^2\) (or related). Algorithm: choose \(x = p/q\) (sexagesimal reciprocal pair), then \(a = 2pq\), \(b = p^2 - q^2\), \(c = p^2 + q^2\). Constants: base-60 (sexagesimal) place-value system. CONNECTION: Ratios \(b/a\) from triples approximate \(√3\), \(√2\), and golden ratio \(φ ≈ 1.618\) via \(b/a\) values near 1.618 (e.g., row 11: \(b/a ≈ 1.618\)). Base-60 fractions yield harmonic proportions (0.618, 0.786) in reciprocal pairs. DEPTH: 8 — Direct evidence of advanced number theory and geometric ratio awareness in Old Babylonian mathematics, linking to later Greek harmonic and trigonometric traditions. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com