Plimpton 322: Old Babylonian Trigonometry Predates Greeks by 1,000 Years — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian clay tablet (c. 1800 BCE) listing 15 rows of Pythagorean triples, generated by a systematic method using reciprocal pairs in base-60, predating Greek trigonometry by over a millennium. MATH: - Pythagorean triples: \(a^2 + b^2 = c^2\), with \(a < b\). - Tablet gives values for \(b^2/(c^2 - b^2)\) or similar ratio, often interpreted as \(tan^2θ\) or \(^2θ\). - Generation method: For \(p > q\) (regular sexagesimal reciprocals), set \(a = p^2 - q^2\), \(b = 2pq\), \(c = p^2 + q^2\). - Base-60 constants: regular numbers (e.g., 2, 3, 5) used to ensure finite sexagesimal expansions. - Ratios on tablet include values near 0.382, 0.618, 1.618, 2.618 (e.g., row 1: \(b/a ≈ 0.618\), row 15: \(b/a ≈ 2.618\)). CONNECTION: - The triples exhibit ratios that approximate the golden ratio \(φ = (1+√5)/2 ≈ 1.618\) and its reciprocal \(1/φ ≈ 0.618\), as well as \(φ^2 ≈ 2.618\) and \(1/φ^2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com